A predefined time nonsingular terminal sliding mode surface-water underwater heterogeneous collaborative control method and control system for active and passive defense against denial of service attacks

Abstract

The application provides a predefined time nonsingular terminal sliding mode water surface and underwater heterogeneous collaborative control method and control system for active and passive defense of denial of service attack, and belongs to the technical field of trajectory tracking safety control of unmanned system; the method comprises the following steps: constructing a dynamic model of a water surface unmanned ship and an underwater unmanned vehicle, and establishing a distributed leader-follower collaborative control framework; constructing a non-periodic DoS attack model, a DoS attack state label and an adaptive clock reset mechanism; when a DoS attack occurs, the predefined time distributed observer is switched to a constant speed open loop prediction mode according to the attack state label, so that passive defense is realized; when the attack duration exceeds a tolerance threshold, active topology switching is adaptively triggered based on the continuous residence time; and according to the predefined time and Lyapunov stability theory, a predefined time nonsingular terminal sliding mode controller based on a hyperbolic tangent function is obtained. The application realizes efficient and reliable collaborative operation of the water surface and underwater collaborative control system in a complex marine environment.

Description

Technical Field

[0001] This invention belongs to the field of unmanned system trajectory tracking safety control technology, specifically involving a predefined time non-singular terminal sliding mode surface and underwater heterogeneous cooperative control method for active and passive defense against denial-of-service attacks. Background Technology

[0002] In recent years, heterogeneous collaborative systems composed of unmanned surface vehicles (USVs) and autonomous underwater vehicles (AUVs) have been widely applied in marine exploration, environmental monitoring, and search and rescue operations due to their significant advantages such as high flexibility, high operational efficiency, and wide coverage. However, in the complex and ever-changing marine environment, these systems not only face the challenge of unknown external disturbances, but their cross-domain communication networks are also vulnerable to malicious cyberattacks. In particular, denial-of-service (DoS) attacks targeting communication links can disrupt data interaction between heterogeneous platforms, severely weakening the system's trajectory tracking accuracy and response speed, and easily triggering instability and divergence in the entire heterogeneous collaborative system.

[0003] Current passive defense methods against denial-of-service attacks can maintain control signal updates during communication interruptions using state observers. However, they are highly dependent on the upper limits of attack frequency and duration. Once faced with extreme attack conditions exceeding these limits, defenses are prone to failure or even system state divergence. Among active defense methods, the commonly used control laws based on active detection and mode switching are difficult to design, and parameter optimization often heavily relies on global topological information such as the eigenvalues ​​of the Laplace matrix, limiting their application in practical multi-agent system engineering. Furthermore, considering the convergence time of system state errors after communication topology restoration, traditional finite-time control and fixed-time control methods often rely on initial system conditions or complex parameter adjustments, making them difficult to meet the needs of practical engineering applications. Simultaneously, these methods often employ static time bases and cumulative timing, making them ill-suited for dynamic topology switching under denial-of-service attacks and hindering rapid convergence of system state errors after communication topology restoration.

[0004] In summary, under complex operating conditions where external disturbances and denial-of-service attacks coexist, developing a predefined time non-singular terminal sliding mode surface and underwater heterogeneous cooperative control method for active and passive defense against denial-of-service attacks is of great practical significance for ensuring efficient and reliable cooperative operation of surface and underwater cooperative control systems in complex marine environments. Summary of the Invention

[0005] The purpose of this invention is to propose a predefined-time non-singular terminal sliding mode cooperative control method and control system for surface and underwater heterogeneous systems to defend against denial-of-service attacks. This method constructs an active-passive defense strategy against denial-of-service attacks, integrating a passive defense method based on open-loop prediction using a predefined-time distributed observer with an active defense method based on continuous dwell time-adaptive topology switching. This enables surface and underwater heterogeneous systems to safely and stably perform cooperative tracking tasks even under denial-of-service attacks of varying intensities. Simultaneously, this invention constructs a predefined-time non-singular terminal sliding mode control strategy based on the hyperbolic tangent function, achieving predefined-time convergence of the system state and effectively avoiding singularity problems in the control process. This provides a solid guarantee for high-precision operation of surface and underwater heterogeneous systems in complex environments intertwined with disturbances and network attacks.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A predefined-time non-singular terminal sliding mode surface and underwater heterogeneous cooperative control method for active and passive defense against denial-of-service attacks includes the following steps:

[0008] Step S1: Considering the cross-domain heterogeneous characteristics of surface and underwater platforms, dynamic models of surface unmanned vessels and underwater unmanned vehicles are constructed respectively, and a distributed control-leader-follower communication framework is established. Among them, the surface unmanned vessel, as the leader, relies on its own state to track the global expected trajectory, and the underwater unmanned vehicle formation, as the follower, only the control node can obtain the horizontal state information of the surface unmanned vessel. The nodes within the formation conduct bidirectional information exchange between neighbors through an undirected circular topology.

[0009] Step S2: Construct an aperiodic DoS attack model to provide basic operating conditions. Based on the aperiodic DoS attack model, perform multi-dimensional DoS attack state label detection and adaptive clock reset. The multi-dimensional DoS attack state label includes three dimensions: a self-attack state label representing the connectivity between the follower and the leader; a neighbor attack state label representing whether the follower can obtain effective leader state estimation information from the topological neighbor; and a restraint attack state label representing the connectivity between the leader and the current restraining node. The time-varying Boolean state represents the communication connectivity between nodes in real time. The adaptive clock is set to be reset to zero and restarted the clock the instant the communication topology is restored, so that the error convergence time boundary is completely independent of the initial state of the system and the attack duration.

[0010] Step S3: Perform passive defense based on a predefined time-distributed observer using multidimensional DoS attack state labels; embed the multidimensional DoS attack state labels into the local location coordination error and the local velocity coordination error to adjust the observer's error correction term; when a DoS attack causes communication disruption, the corresponding state label is reset to zero, making the error correction term ineffective, the position estimation is transformed into an open-loop integral update, and the velocity estimation remains constant, achieving constant velocity open-loop prediction and realizing passive defense during the attack.

[0011] Step S4: Adaptive topology switching based on continuous dwell time; construct a duration timer for single-stage secure communication and DoS attack, use the duration of single-stage secure communication as a dynamic variable to evaluate the system stability margin, and adaptively generate a time tolerance threshold; when the attack duration exceeds the dynamic threshold that the current topology can tolerate, trigger topology switching to suppress the continued accumulation of open-loop prediction errors and quickly restore convergence, thereby achieving proactive defense.

[0012] Step S5: Closed-loop control is performed using a predefined time non-singular terminal sliding mode control law; based on the adaptive clock in step S2 and the state estimation output by the predefined time distributed observer in step S3, the equivalent and switching control law is calculated using a nonlinear disturbance observer (to estimate and compensate for complex marine environmental disturbances in real time) and a predefined time non-singular terminal sliding mode control based on the hyperbolic tangent function (to completely eliminate the singularity divergence risk caused by the traditional fractional error term), combined with the predefined time stability theory, and the actual thrust and torque commands are output to drive the underlying actuator;

[0013] Step S6: After completing the active and passive defense decision-making and sliding mode control calculations of steps S2 to S5 within the control cycle, return to step S2 in a loop. Through the synergistic effect of passive prediction by the observer, active topology switching and predefined time non-singular terminal sliding mode bottom-level control, the system can flexibly resist network attacks and ocean disturbances, ensure that the tracking error converges within a predetermined time, and complete the collaborative operation task.

[0014] Preferably, in step S1, dynamic models of the surface unmanned vessel and the underwater unmanned vehicle are constructed respectively, establishing that cross-domain collaborative tracking focuses on pose consistency within the horizontal plane. A distributed strait leader-follower communication topology is constructed, where the surface unmanned vessel, as the leader, relies on its own state to track the globally desired trajectory. Only the strait leader node of the underwater unmanned vehicle formation can obtain the horizontal plane state information of the surface unmanned vessel. Within the formation, bidirectional information exchange between neighbors is conducted through an undirected circular topology.

[0015] Introducing undirected graphs Modeling of follower communication networks; where It is a set of nodes, with each node corresponding to one underwater unmanned vehicle. The number of underwater unmanned vehicles in the formation. It is a bidirectional communication edge set;

[0016] The adjacency matrix of an undirected ring topology formed by followers is represented as , Represents a node With nodes The status of the bidirectional communication link between them This indicates the existence of a two-way communication link. This indicates that there is no bidirectional communication link. Represents the set of real numbers. and For underwater unmanned vehicles or node indexes; the effective links of the adjacency matrix are defined as follows: and , ,otherwise Furthermore, the nodes do not have self-loops;

[0017] Laplace matrix corresponding to the adjacency matrix Defined as: diagonal element Off-diagonal elements , ;

[0018] The unmanned surface vessel is defined as virtual leader node 0. The direct connection between the virtual leader node and the follower formation is via a control matrix. Depicting and restraining matrix elements Indicates underwater unmanned vehicle It can directly receive information from unmanned surface vessels; otherwise, the value is 0.

[0019] Preferably, step S2, based on the cross-domain heterogeneous topology network constructed in step S1, introduces an aperiodic DoS attack model, multi-dimensional DoS attack status labels, and an adaptive clock reset mechanism to transform external uncertain network damage into dynamic driving signals and independent time bases within the system, as detailed below:

[0020] A non-periodic DoS attack model is constructed to provide the basic operating conditions for subsequent attack status label detection and segmented timer operation in proactive defense; non-periodic DoS attacks occur on the control link, defining the first... The consecutive time interval between the occurrences of this DoS attack is: ,in , For the set of natural numbers, and They represent the first The start and end times of a DoS attack, and the secure communication interval between the two attacks, are defined as follows: ;

[0021] Construct a multi-dimensional DoS attack status label model; define its own attack status label. , A value of 1 indicates an underwater unmanned vehicle. Currently, it is possible to effectively obtain leader status information; define neighbor attack status labels. , A value of 1 indicates an underwater unmanned vehicle. Currently, it is possible to obtain information from topological neighbors. Obtain effective leader state estimation information; define restraint attack state labels. Used as a dynamic trigger switch for the active defense mechanism in step S4. A value of 1 indicates that the leader and the current restraining node are... The two are in normal communication status.

[0022] An adaptive clock reset mechanism is constructed, which instantly resets the clock to zero upon the end of an attack or when a proactive topology switch restores the communication topology. By calculating the duration of a single phase, the cumulative impact of historical states is eliminated, thus providing an effective time reference for the predefined time convergence of the underlying non-singular sliding mode control in step S5; adaptive clock. The update rules are as follows:

[0023] (1)

[0024] in, Indicates the current time; Indicates the time when the communication topology is restored; Indicates the instant immediately preceding the moment when the communication topology is restored; and These represent the communication topology being in an interrupted state before restoration and the communication topology being in a normal state after restoration, respectively. Used to select the most recent communication topology recovery time up to the current moment.

[0025] Preferably, step S3 introduces a local cooperative error based on DoS attack status labels to enable the distributed observer to switch between error correction mode and open-loop prediction mode, and performs constant-rate open-loop prediction to achieve passive defense when subjected to a DoS attack, as detailed below:

[0026] Step S3-1: Construct local collaborative error based on multidimensional DoS attack state labels; Local cooperative error in the position of the Taiwanese underwater unmanned vehicle Local Co-operational Error with Velocity The design is as follows:

[0027] (2)

[0028] (3)

[0029] in, To cooperate with underwater unmanned vehicles corresponding nodes The set of neighboring nodes, , underwater unmanned vehicles and underwater unmanned vehicles augmented reference position state The estimated vector, including Direction and position Orientation, desired depth, and heading angle; Used to characterize underwater unmanned vehicles Is it a checkpoint node? Let be the augmented reference position state vector composed of the horizontal position state of the surface unmanned vessel and the desired depth of the underwater unmanned vehicle. These represent unmanned surface vessels. Direction and position Orientation and position, desired depth of underwater unmanned vehicles and heading angle of surface unmanned vessels; for The first time derivative, , underwater unmanned vehicles and underwater unmanned vehicles For augmented reference speed state The estimated vectors include longitudinal velocity, lateral drift velocity, heave velocity, and yaw rate; and underwater unmanned vehicles Self-attack status tags and underwater unmanned vehicles For topological neighbor nodes The neighbor attack status label.

[0030] Step S3-2: Perform observer mode switching and open-loop passive prediction; The design of the predefined time-distributed observer for the underwater unmanned vehicle is as follows:

[0031] (4)

[0032]

[0033] in, , The gain is positive definite. , They are respectively , The first time derivative; For nodes The current effective in-degree; for The first time derivative; for The second time derivative; For adaptive clock The constructed time-varying gain function, where the index , and They are used for position state estimation and velocity state estimation of a predefined time-distributed observer, respectively. Sliding mode approach process for a predefined time nonsingular terminal sliding mode controller for unmanned surface vessels. Sliding mode approach process for a predefined time nonsingular terminal sliding mode controller for underwater unmanned vehicles; This is the adjustment gain constant corresponding to the time-varying gain function; It is a predefined upper limit of convergence time set manually during the corresponding control phase. or hour, Predefined convergence time for predefined time-distributed observers , and They are respectively and The gain adjustment constant; or hour, Predefined convergence time for sliding mode reaching law , and They are respectively and The gain adjustment constant.

[0034] When a system suffers a DoS attack that disrupts the communication link between surface unmanned vessels and underwater unmanned vehicles, the attack status label is displayed. Instantaneous zeroing, local cooperative error and Subsequently, the value is reset to zero, at which point the predefined time-distributed observer switches from error correction mode to open-loop prediction mode. Location estimation dynamics. Transformation into a state based on internal velocity estimation The open-loop integral is updated, while the velocity estimation is dynamic. This then transforms into maintaining the last effective speed before communication is blocked, thus forming a constant-speed open-loop prediction. When facing a DoS attack, this design relies on the internal state of the observer to continuously predict and evolve, thereby achieving passive defense during the attack.

[0035] Preferably, step S4 introduces a single-stage duration timer based on continuous dwell time and an adaptive topology switching mechanism to quantify network condition evolution in real time and dynamically calculate the system's tolerance threshold. When the duration of passive defense exceeds the dynamic threshold that the current topology can tolerate, active topology switching is triggered to suppress the continued accumulation of open-loop prediction errors; specifically as follows:

[0036] Step S4-1: Based on the restraint attack status label As a driving signal, a single-stage secure communication duration timer is constructed. With a single-phase DoS attack duration timer The system quantifies the duration of a single-phase secure communication and the duration of an attack in real time, and resets this value each time the communication topology is restored.

[0037]

[0038]

[0039] in, This represents the cumulative upper limit of the effective communication duration within a single secure communication phase, i.e., the predefined upper limit of convergence time for the observer; Represents the cumulative duration of secure communication at the moment of the attack;

[0040] Step S4-2: Construct an adaptive topology switching mechanism for the restraining node based on the persistent residence time criterion, and define the switching trigger condition as follows:

[0041] (5)

[0042] Based on the theory of dolyapunov functions and the stability of persistent residence time, the dynamic time threshold function The design is as follows:

[0043] (6)

[0044] in, This represents the convergence rate of Lyapunov energy exponential decay during secure communication; This represents the number of times the switching mechanism occurs. Standard symbolic functions; This represents the maximum jump factor of the Lyapunov function caused by the state jump at the instant of topology switching; This represents the worst-case rate limit of error energy growth when the system loses effective leader information and enters an open-loop prediction state due to the loss of negative feedback correction.

[0045] In this adaptive topology switching mechanism, the duration of single-phase secure communication accumulated by the system before encountering the current DoS attack. This is introduced as a core dynamic variable. When the frequency of external attacks is low, the duration of secure communication... A larger tolerance time threshold indicates that the system has accumulated sufficient health in the early stages, playing a dominant role in global convergence. The mechanism will automatically allocate a higher tolerance time threshold, allowing the system to maintain a passive defense strategy for a longer period under open-loop prediction, avoiding system oscillations caused by frequent topology switching. Conversely, when attacks exhibit a high-frequency and dense trend, the secure communication duration... A shorter time threshold indicates a weak system stability margin. The mechanism automatically assigns a smaller threshold to limit the continued accumulation of open-loop prediction errors and trigger timely topology switching. Simultaneously, based on the physical constraint that the time threshold must satisfy non-negativity, the outer layer of the formula... The operator establishes a hard lower bound constraint: if the stability margin accumulated in the early stages of the system is insufficient to offset the state transition penalty caused by topology switching, the tolerance threshold will be forcibly set to zero. In this case, once an attack disrupts the communication link, the system will proactively switch topology. This dynamic adjustment strategy based on historical secure communication duration not only ensures the control accuracy of the restraining node under severe DoS attacks but also effectively suppresses redundant topology switching under unnecessary operating conditions.

[0046] Step S4-3: Perform active topology switching. The switching rules for the restraining node are designed as follows:

[0047] (7)

[0048] (8)

[0049] in, This represents the transient moment when the switching trigger condition is met; This represents the number of the underwater unmanned vehicle control node before the switchover was triggered. This represents the newly selected underwater unmanned vehicle control node number after the switchover is triggered. Represents the modulo operator, ensuring that the node index is within the range of the modulo operator. arrive Loop between; This represents the restraint matrix after the switch is triggered; Represents the binding status of the new binding node; The effective value of the restraint state, and This indicates that the current underwater unmanned vehicle can directly receive status information from surface unmanned vessels. When a topology switch is triggered, the leader's communication connection object changes to the next underwater unmanned vehicle node in the ring topology, and the non-zero elements of the restraint matrix are also instantly shifted.

[0050] Preferably, in step S5, a predefined time-nonsingular terminal sliding mode control law is designed for closed-loop control. The system state estimate output from the observer in step S3 is received and combined with the adaptive clock from step S2. By employing a nonlinear disturbance observer and predefined time-nonsingular terminal sliding mode control based on the hyperbolic tangent function, the actual thrust and torque control commands for driving the underlying actuators are output; specifically as follows:

[0051] Step S5-1: Use a nonlinear disturbance observer to perform feedforward compensation for complex ocean disturbances to obtain disturbance estimates;

[0052] The nonlinear disturbance observer for unmanned surface vessels is designed as follows:

[0053] (9)

[0054] in, This represents the disturbance estimate of the unmanned surface vessel obtained from the nonlinear disturbance observer. These represent the estimated values ​​of the longitudinal, lateral, and yaw disturbance moments, respectively, with superscripts indicating their relative magnitudes. Indicates transpose; This represents the auxiliary state vector of the nonlinear disturbance observer; for The first time derivative; This represents the design gain matrix of the nonlinear disturbance observer; The inertial matrix representing the unmanned surface vessel; The velocity vector of the unmanned surface vessel includes longitudinal velocity, lateral drift velocity, and bow roll velocity. It refers to the Coriolis and centripetal force matrix of unmanned surface vessels; It is the damping matrix of the unmanned surface vessel; The control vector represents the control input of the unmanned surface vessel, including forward force, lateral force, and yaw moment.

[0055] The nonlinear interference observer for the underwater unmanned vehicle is designed as follows:

[0056] (10)

[0057] in, The first value obtained from the nonlinear disturbance observer is... Disturbance estimates for the Taiwanese underwater unmanned vehicle These represent the estimated values ​​of the disturbance moment in the forward direction, the lateral direction, the heave direction, and the yaw direction, respectively. For the first Auxiliary state vector of the nonlinear disturbance observer of the underwater unmanned vehicle. for The first time derivative; This represents the design gain matrix of the nonlinear disturbance observer; The inertial matrix represents the inertial matrix of an underwater unmanned vehicle; Indicates the first The velocity vector of the underwater unmanned vehicle includes longitudinal velocity, lateral drift velocity, heave velocity, and bow roll velocity; It refers to the Coriolis and centripetal force matrix of underwater unmanned vehicles; It is the damping matrix of an underwater unmanned vehicle; This represents the position vector of the underwater unmanned vehicle in the inertial coordinate system; This represents the restoring force and torque generated by gravity and buoyancy; The control vector represents the control input of an underwater unmanned vehicle, including forward force, lateral force, heave force, and yaw moment.

[0058] Step S5-2: Construct a predefined time nonsingular terminal sliding mode controller based on the hyperbolic tangent function to calculate the underlying actual thrust and torque;

[0059] Define the position error of unmanned surface vessels as follows:

[0060] (11)

[0061] in, This represents the position and state vector of the unmanned surface vessel in the inertial coordinate system. These represent unmanned surface vessels. Direction and position Orientation and heading angle; This represents the desired position and state vector of the unmanned surface vessel. Representing the expected values ​​of unmanned surface vessels. Direction, position, expectation Orientation and desired heading angle.

[0062] Predefined time terminal sliding surface of unmanned surface vessels The specific design is as follows:

[0063] (12)

[0064] in, for First-order time derivative; correlation coefficient The calculation formula is:

[0065] (13)

[0066] (14)

[0067] (15)

[0068] in, and Let be the nonlinear power-law parameters of the sliding mode surface of the unmanned surface vessel, and satisfy the condition. and ; These are the positive definite gain coefficients calculated based on the predefined upper limit of convergence time. For the reason and Determined auxiliary parameters; This indicates the predefined upper limit of convergence time for the sliding surface, which is set manually.

[0069] The equivalent control law for the unmanned surface vessel is as follows:

[0070] (16)

[0071] in, Let be the equivalent control input vector for the unmanned surface vessel. Desired position state of unmanned surface vessel The second time derivative; This represents the coordinate transformation matrix of the unmanned surface vessel. These are parameters related to the model; other correlation coefficients The calculation formula is:

[0072] (17)

[0073] (18)

[0074] The switching control law for the unmanned surface vessel is designed as follows:

[0075] (19)

[0076] in, This represents the switching control input vector for the unmanned surface vessel. , This represents the positive definite adjustment gain of the switching control law; The gain parameter representing the robust switching term; For adaptive clock The constructed time-varying gain function.

[0077] The predefined time-nonsingular terminal sliding mode control law for the synthetic unmanned surface vessel is as follows:

[0078] (20)

[0079] Combined with a predefined time-distributed observer, define the first Position error of Taiwan underwater unmanned vehicle and speed error as follows:

[0080] (twenty one)

[0081] in, Indicates the first The position and state vector of the underwater unmanned vehicle. They represent Direction and position Orientation, depth, and heading angle; Indicates underwater unmanned vehicle An estimated vector for the augmented reference position state; Indicates the first The velocity vector of the underwater unmanned vehicle in Taiwan Indicates underwater unmanned vehicle The estimated vector of the augmented reference velocity state, Indicates the first Coordinate transformation matrix of the underwater unmanned vehicle.

[0082] Regarding the first Predefined time nonsingular terminal sliding surface of the underwater unmanned vehicle The specific design is as follows:

[0083] (twenty two)

[0084] Among them, the correlation coefficient The calculation formula is:

[0085] (twenty three)

[0086] (twenty four)

[0087] (25)

[0088] in, and Let be the nonlinear power-law parameters of the sliding mode surface of the underwater unmanned vehicle, and satisfy the condition... and ; These are the positive definite gain coefficients calculated based on the predefined upper limit of convergence time. For the reason and Determined auxiliary parameters; It is a predefined upper limit time for convergence of the sliding surface, which is set manually.

[0089] Design No. The equivalent control law for the Taiwanese underwater unmanned vehicle is as follows:

[0090] (26)

[0091] in, For the first The equivalent control input vector of the underwater unmanned vehicle. for The second time derivative; For the first Coordinate transformation matrix of the underwater unmanned vehicle. These are parameters related to the model; other correlation coefficients The calculation formula is:

[0092] (27)

[0093] (28)

[0094] Design No. The switching control law for the Taiwanese underwater unmanned vehicle is as follows:

[0095] (29)

[0096] in, Indicates the first Switching control input vectors for the underwater unmanned vehicle. , This represents the positive definite adjustment gain of the switching control law; The gain parameter representing the robust switching term. For adaptive clock The constructed time-varying gain function.

[0097] Synthesis of the first The predefined time-terminal sliding mode control law for the underwater unmanned vehicle is as follows:

[0098] (30)

[0099] Merging sliding mode convergence law predefined convergence time and the predefined convergence time of the sliding surface The predefined convergence time of the tracking error of the surface-underwater heterogeneous cooperative system is obtained as follows:

[0100] (31)

[0101] A predefined time non-singular terminal sliding mode surface and underwater heterogeneous cooperative control system for active and passive defense against denial-of-service attacks includes a processor, a memory, and a computer program stored in the memory. When the processor executes the computer program, it specifically performs any of the steps in the above-mentioned cooperative control method.

[0102] Compared with the prior art, the present invention has the following beneficial effects:

[0103] This invention provides a collaborative control strategy for active and passive defense against denial-of-service attacks. This strategy resets the system clock upon detecting effective communication recovery, improving the system's ability to smoothly recover from network attacks. The strategy deeply integrates a predefined time-distributed observer with an adaptive topology switching mechanism. When encountering a network attack, the system enters an open-loop prediction tolerance period, relying on the observer's internal state to perform open-loop prediction, maintaining continuous evolution of state estimation and achieving passive defense. When the duration of a single-stage attack exceeds the tolerance threshold, an active topology switching mechanism based on the duration of the attack initiates active topology switching, avoiding system loss of control and formation paralysis caused by prolonged network outages. This significantly improves the security defense capabilities of heterogeneous surface and underwater systems under network attacks, ensuring the continuity and stability of collaborative operations.

[0104] This invention provides a sliding mode cooperative control method based on predefined-time nonsingular terminals. This method constructs a predefined-time nonsingular terminal sliding surface based on a hyperbolic tangent function, avoiding the control input divergence caused by the fractional error term being in the denominator position in traditional methods. This fundamentally eliminates the singularity problem of the control system and effectively suppresses high-frequency chattering of the underlying actuators. Simultaneously, by combining a time-varying gain predefined-time reaching law dependent on a reset clock with nonlinear disturbance compensation, it ensures that the cooperative tracking error of the surface and underwater unmanned systems converges to zero within a predefined time, completely independent of the system's initial state. Facing complex and ever-changing marine environments, this method can significantly improve the rapid response capability, steady-state tracking accuracy, and global robust stability of surface and underwater heterogeneous systems. Attached Figure Description

[0105] Figure 1 This is a flowchart of the predefined time non-singular terminal sliding mode surface and underwater heterogeneous cooperative control method for active and passive defense against denial-of-service attacks according to the present invention.

[0106] Figure 2 This is a block diagram of the predefined time non-singular terminal sliding mode surface and underwater heterogeneous collaborative control for active and passive defense against denial-of-service attacks in this invention.

[0107] Figure 3 This is a switching topology diagram of the heterogeneous cooperative system for surface and underwater environments according to the present invention.

[0108] Figure 4This is a three-dimensional spatial image showing the heterogeneous cooperative trajectory tracking of the water surface and underwater structures according to the present invention.

[0109] Figure 5 This is a two-dimensional planar underwater heterogeneous cooperative trajectory tracking diagram of the present invention.

[0110] Figure 6 This is a trajectory tracking error diagram of the unmanned surface vessel of the present invention;

[0111] Figure 7 This is a trajectory tracking error diagram of the underwater unmanned vehicle of the present invention;

[0112] Figure 8 This is a diagram showing the evolution of the strait link weights in the underwater unmanned vehicle formation of this invention.

[0113] Figure 9 This is a diagram showing the observation error of the predefined time-distributed observer for the underwater unmanned vehicle of this invention. Detailed Implementation

[0114] The following is in conjunction with the appendix Figure 1-9 The technical solution of the present invention will be described in detail below.

[0115] This invention proposes a predefined time-based non-singular terminal sliding mode heterogeneous cooperative control method for active and passive defense against denial-of-service attacks, specifically including the following steps:

[0116] Step S1: Construct dynamic models of surface unmanned vessels and underwater unmanned vehicles, and establish a distributed restraint-leader-follower cooperative control framework.

[0117] Step S1-1: The dynamic model of the unmanned surface vessel is as follows:

[0118]

[0119]

[0120] in: This represents the position vector of the unmanned surface vessel in the inertial coordinate system. They represent Direction and position Direction and heading angle, superscript Indicates transpose. Represents the set of real numbers. Velocity vector. Represented in a fixed body coordinate system, including longitudinal velocity. Horizontal drift speed and bow roll rate . The control vector represents the control input of the unmanned surface vessel, where and These represent forward force and lateral force, respectively. This indicates the yaw moment. This represents the external environmental disturbances acting on the unmanned surface vessel in the attached coordinate system. These represent the longitudinal disturbance force, the lateral disturbance force, and the yaw disturbance moment, respectively. Meanwhile, Represents the coordinate transformation matrix. Represents the inertia matrix. It is the Coriolis and centripetal force matrix. It is the damping matrix.

[0121] The dynamic model of the underwater unmanned vehicle is as follows:

[0122]

[0123]

[0124] in: Indicates the first Taiwan underwater unmanned vehicle, The number of underwater unmanned vehicles. This represents the position vector of the underwater unmanned vehicle in the inertial coordinate system. They represent Direction and position Orientation, position, depth, and heading angle; velocity vector In a fixed coordinate system, represented by the longitudinal velocity Horizontal drift speed heave speed and bow roll rate composition. The control vector represents the control input of an underwater unmanned vehicle, derived from the forward force. lateral force Heave force and yaw moment composition. This represents the external environmental disturbances acting on the underwater unmanned vehicle in the attached coordinate system. These represent the disturbance forces in the forward direction, the lateral direction, the heave direction, and the yaw disturbance moment, respectively. Meanwhile, Represents the coordinate transformation matrix. Represents the inertia matrix. It is the Coriolis and centripetal force matrix. It is the damping matrix. This represents the restoring force and torque generated by gravity and buoyancy.

[0125] Step S1-2: For the trajectory tracking and control problem of heterogeneous cooperative surface and underwater systems, a distributed leader-follower model is constructed. In this model, the surface unmanned vessel tracks the target trajectory solely based on its own state, while simultaneously acting as the leader to guide the underwater unmanned vehicle formation for precise trajectory tracking. Considering the heterogeneity of cross-domain platforms, the cooperative control of the surface unmanned vessel and the underwater unmanned vehicles mainly involves… The experiment is conducted in the horizontal plane. Due to the three-degree-of-freedom physical characteristics of surface unmanned vessels, their depth information is set to zero by default; meanwhile, for a four-degree-of-freedom follower underwater unmanned vehicle formation, its expected depth reference trajectory is determined. As a reference quantity independent of the motion of the horizontal plane, it is allowed to change and be controlled independently.

[0126] At the network communication level, the unmanned surface vessel (USV) serves as an underwater reference source, providing information on the water level state. The formation of underwater unmanned vehicles uses an undirected ring topology for bidirectional information exchange between neighbors. The information flow of the entire formation is asymmetric, meaning that the leader's state information is injected into a single restraining node in the formation at a specific time via a one-way direct connection. Non-restraining nodes must indirectly obtain the leader's state through the internal undirected cooperative network.

[0127] Introducing undirected graphs Modeling of follower communication networks, in which For a set of nodes, This is a bidirectional communication edge set. Followers form an undirected ring topology, whose adjacency matrix is ​​represented as follows. , Represents a node With nodes The status of the bidirectional communication link between them, and the specific definition of an effective link. ( )and ,otherwise Furthermore, the nodes have no self-loops. The corresponding Laplace matrix... Defined as diagonal element Off-diagonal elements ( This structure enables It is a symmetric positive semi-definite matrix. Furthermore, the unmanned surface vessel is defined as the virtual leader node 0, and its direct connection to the follower formation is mediated by the control matrix. Depiction, among which Indicates underwater unmanned vehicle It can directly receive information from unmanned surface vessels; otherwise, it will receive 0.

[0128] Step S2: Construct an aperiodic DoS attack model and a DoS attack status label model, and design an adaptive clock reset mechanism.

[0129] Step S2-1: Construct an aperiodic DoS attack model. This provides the basic operating conditions for subsequent attack status label detection and segmented timer operation in proactive defense. Considering the cross-domain characteristics of heterogeneous surface and underwater systems, it is assumed that a series of aperiodic DoS attacks occur on the restraining link. Define the... The consecutive time interval between the occurrences of this DoS attack is: ,in , For the set of natural numbers, and These represent the start and end times of the attack, respectively. Within this interval, the control link is blocked, and the system is in a connectivity-damaged mode. Conversely, the secure communication interval between the two attacks is defined as... .

[0130] Step S2-2: Construct a DoS attack status label model with three dimensions: self, neighbors, and restraining nodes, to determine whether the link is under a DoS attack. First, define the self-attack status label. , A value of 1 indicates an underwater unmanned vehicle. Currently, it is possible to effectively obtain leader status information; define neighbor attack status labels. , A value of 1 indicates an underwater unmanned vehicle. Currently, it is possible to obtain information from topological neighbors. Obtain effective leader state estimation information; define restraint attack state labels. Representing the leader and current restraining nodes The connection state between them is used as a dynamic trigger switch for the active defense mechanism in step S4.

[0131] Step S2-3: Construct an adaptive clock reset mechanism. To ensure that observation and tracking errors converge within a predefined time boundary, and that this time boundary is completely independent of the initial state and the duration of the DoS attack, an adaptive clock is designed. The update rules are as follows:

[0132]

[0133] in, Indicates the current time; Indicates the time when the communication topology is restored; Indicates the instant immediately preceding the moment when the communication topology is restored; and These represent the communication topology being in an interrupted state before restoration and the communication topology being in a normal state after restoration, respectively. Used to select the most recent communication topology recovery time up to the current moment.

[0134] Step S3: When subjected to a DoS attack, construct a predefined time-distributed observer based on the attack status label to perform open-loop prediction and achieve passive defense.

[0135] Step S3-1: Construct local cooperative error based on attack state labels. For each underwater unmanned vehicle node, its local cooperative error is calculated. Local Co-operational Error with Velocity The design is as follows:

[0136]

[0137]

[0138] in, To cooperate with underwater unmanned vehicles corresponding nodes The set of neighboring nodes, , underwater unmanned vehicles and underwater unmanned vehicles augmented reference position state The estimated vector, including Direction and position Orientation, desired depth, and heading angle; Used to characterize underwater unmanned vehicles Is it a checkpoint node? Let be the augmented reference position state vector composed of the horizontal position state of the surface unmanned vessel and the desired depth of the underwater unmanned vehicle. These represent unmanned surface vessels. Direction and position Orientation and position, desired depth of underwater unmanned vehicles and heading angle of surface unmanned vessels; for The first time derivative, , underwater unmanned vehicles and underwater unmanned vehicles For augmented reference speed state The estimated vectors include longitudinal velocity, lateral drift velocity, heave velocity, and yaw rate; and underwater unmanned vehicles Self-attack status tags and underwater unmanned vehicles For topological neighbor nodes The neighbor attack status label.

[0139] To ensure that the observer and subsequent controller converge within a specified time, an adaptive clock-based approach is introduced. Constructed predefined time-varying gain function :

[0140]

[0141] in This is the adjustment gain constant corresponding to the time-varying gain function; It is a predefined upper limit of convergence time set manually in the corresponding control phase, index. , and They are used for position state estimation and velocity state estimation of a predefined time-distributed observer, respectively. Sliding mode approach process for a predefined time nonsingular terminal sliding mode controller for unmanned surface vessels. Sliding mode approaching process for a predefined-time nonsingular terminal sliding mode controller for underwater unmanned vehicles. When or hour, Predefined convergence time for predefined time-distributed observers , and They are respectively and The gain adjustment constant; or hour, Predefined convergence time for sliding mode reaching law , and They are respectively and The gain adjustment constant.

[0142] Step S3-2: Perform observer mode switching and open-loop passive prediction. The design of the predefined time-distributed observer for the underwater unmanned vehicle is as follows:

[0143]

[0144] in, , The gain is positive definite. , They are respectively , The first time derivative; For nodes The current effective in-degree; for The first time derivative; for The second time derivative.

[0145] When a system suffers a DoS attack that disrupts the communication link between surface unmanned vessels and underwater unmanned vehicles, the attack status label is displayed. Instantaneous zeroing, local cooperative error and Subsequently, the value is reset to zero, at which point the predefined time-distributed observer switches from error correction mode to open-loop prediction mode. Location estimation dynamics. Transformation into a state based on internal velocity estimation The open-loop integral is updated, while the velocity estimation is dynamic. This then transforms into maintaining the last effective speed before communication is blocked, thus forming a constant-speed open-loop prediction. When facing a DoS attack, this design relies on the internal state of the observer to continuously predict and evolve, thereby achieving passive defense during the attack.

[0146] Step S4: When the duration of a DoS attack exceeds the tolerance threshold, an adaptive topology switching mechanism is designed based on the duration of the attack to perform an active topology switch.

[0147] Step S4-1: Based on the restraint attack status label As a driving signal, a single-stage secure communication duration timer is constructed. With a single-phase DoS attack duration timer The system quantifies the duration of a single-phase secure communication versus the duration of an attack in real time, and resets this value each time the communication topology is restored.

[0148] Single-phase secure communication duration timer :

[0149]

[0150] in, Indicates the current timing phase corresponding to the first... This is a DoS attack. This represents the cumulative upper limit of the effective communication duration within a single secure communication phase, i.e., the predefined upper limit of convergence time for the observer. This represents the cumulative duration of secure communication at the moment of the attack.

[0151] Single-phase DoS attack duration timer :

[0152]

[0153] Step S4-2: Construct an adaptive topology switching mechanism based on persistent dwell time criterion for the control node. To overcome the problem that traditional average dwell time or fixed threshold triggering schemes are prone to frequent switching under high-frequency aperiodic attacks, the duration of single-stage secure communication in the system is introduced to dynamically evaluate the triggering conditions. For the control link under DoS attack, the switching triggering condition is defined as follows:

[0154]

[0155] Based on the theory of dolyapunov functions and the stability of persistent residence time, a dynamic time threshold function is designed. as follows:

[0156]

[0157] in, This represents the convergence rate of the Lyapunov energy index decay during secure communication. This represents the number of times the trigger mechanism occurs. These are standard symbolic functions. This represents the maximum jump factor of the Lyapunov function caused by the state jump at the instant of topology switching. This represents the worst-case rate limit of error energy growth due to the loss of negative feedback correction when the system loses effective leader information and enters an open-loop prediction state. In this adaptive topology switching mechanism, this represents the duration of single-stage secure communication accumulated before encountering the current DoS attack. This is introduced as a core dynamic variable. When the frequency of external attacks is low, the duration of secure communication... A larger tolerance time threshold indicates that the system has accumulated sufficient health in the early stages, playing a dominant role in global convergence. The mechanism will automatically allocate a higher tolerance time threshold, allowing the system to maintain a passive defense strategy for a longer period under open-loop prediction, avoiding system oscillations caused by frequent topology switching. Conversely, when attacks exhibit a high-frequency and dense trend, the secure communication duration... A shorter time threshold indicates a weak system stability margin. The mechanism automatically assigns a smaller threshold to limit the continued accumulation of open-loop prediction errors and trigger timely topology switching. Simultaneously, based on the physical constraint that the time threshold must satisfy non-negativity, the outer layer of the formula... The operator establishes a hard lower bound constraint: if the stability margin accumulated in the early stages of the system is insufficient to offset the state transition penalty caused by topology switching, the tolerance threshold will be forcibly set to zero. In this case, once an attack disrupts the communication link, the system will proactively switch topology. This dynamic adjustment strategy based on historical secure communication duration not only ensures the control accuracy of the restraining node under severe DoS attacks but also effectively suppresses redundant topology switching under unnecessary operating conditions.

[0158] Step S4-3: Perform active topology switching. The rules for controlling topology node switching are designed as follows:

[0159]

[0160]

[0161] in, This represents the transient moment when the switching trigger condition is met. This represents the control node number of the underwater unmanned vehicle before the switchover was triggered. This represents the newly selected underwater unmanned vehicle control node number after the switchover is triggered. Represents the modulo operator, ensuring that the node index is within the range of the modulo operator. arrive It cycles between them. This represents the restraint matrix after the switch is triggered; Represents the binding status of the new binding node; The effective value of the restraint state, and This indicates that the current underwater unmanned vehicle can directly receive status information from surface unmanned vessels. When a topology switch is triggered, the leader's communication connection object changes to the next underwater unmanned vehicle node in the ring topology, and the non-zero elements of the restraint matrix also change instantaneously.

[0162] Step S5: Design the control law based on the predefined time stability theory and Lyapunov stability theory to obtain a predefined time non-singular terminal sliding mode controller based on the hyperbolic tangent function.

[0163] Step S5-1: Use a nonlinear disturbance observer to perform feedforward compensation for complex ocean disturbances to obtain disturbance estimates. The nonlinear disturbance observer for the unmanned surface vessel is designed as follows:

[0164]

[0165] in, This represents the disturbance estimate of the unmanned surface vessel obtained from the nonlinear disturbance observer. These represent the estimated values ​​of the longitudinal, lateral, and yaw disturbance moments, respectively, with superscripts indicating their relative magnitudes. Indicates transpose; This represents the auxiliary state vector of the nonlinear disturbance observer; for The first time derivative; This represents the design gain matrix of the nonlinear disturbance observer; The inertial matrix representing the unmanned surface vessel; The velocity vector of the unmanned surface vessel includes longitudinal velocity, lateral drift velocity, and bow roll velocity. It refers to the Coriolis and centripetal force matrix of unmanned surface vessels; It is the damping matrix of the unmanned surface vessel; The control vector represents the control input of the unmanned surface vessel, including forward force, lateral force, and yaw moment.

[0166] The nonlinear interference observer for the underwater unmanned vehicle is designed as follows:

[0167]

[0168] in, The first value obtained from the nonlinear disturbance observer is... Disturbance estimates for the Taiwanese underwater unmanned vehicle These represent the estimated values ​​of the disturbance moments in the forward direction, lateral direction, heave direction, and yaw direction, respectively, with superscripts indicating their relative magnitudes. Indicates transpose; For the first Auxiliary state vector of the nonlinear disturbance observer of the underwater unmanned vehicle. for The first time derivative; This represents the design gain matrix of the nonlinear disturbance observer; The inertial matrix represents the inertial matrix of an underwater unmanned vehicle; Indicates the first The velocity vector of the underwater unmanned vehicle includes longitudinal velocity, lateral drift velocity, heave velocity, and bow roll velocity; It refers to the Coriolis and centripetal force matrix of underwater unmanned vehicles; It is the damping matrix of an underwater unmanned vehicle; This represents the position vector of the underwater unmanned vehicle in the inertial coordinate system; This represents the restoring force and torque generated by gravity and buoyancy; The control vector represents the control input of an underwater unmanned vehicle, including forward force, lateral force, heave force, and yaw moment.

[0169] Step S5-2: Construct a predefined time-nonsingular terminal sliding mode controller based on the hyperbolic tangent function to calculate the underlying actual thrust and torque. First, define the position error of the unmanned surface vessel. as follows:

[0170]

[0171] in, This represents the position and state vector of the unmanned surface vessel in the inertial coordinate system. These represent unmanned surface vessels. Direction and position Orientation and heading angle; This represents the desired position and state vector of the unmanned surface vessel. Representing the expected values ​​of unmanned surface vessels. Direction, position, expectation Orientation and desired heading angle.

[0172] Secondly, the design of the predefined time terminal sliding surface is as follows:

[0173]

[0174] in, for First-order time derivative; correlation coefficient The calculation formula is:

[0175]

[0176]

[0177]

[0178] in, and Let be the nonlinear power-law parameters of the sliding mode surface of the unmanned surface vessel, and satisfy the condition. and ; These are the positive definite gain coefficients calculated based on the predefined upper limit of convergence time. For the reason and Determined auxiliary parameters; This indicates the predefined upper limit of convergence time for the sliding surface, which is set manually.

[0179] The equivalent control law for the unmanned surface vessel is as follows:

[0180]

[0181] in, Let be the equivalent control input vector for the unmanned surface vessel. Desired position state of unmanned surface vessel The second time derivative; This represents the coordinate transformation matrix of the unmanned surface vessel. These are parameters related to the model; other correlation coefficients The calculation formula is:

[0182]

[0183]

[0184] Model-related parameters Defined as:

[0185]

[0186] The switching control law for the unmanned surface vessel is designed as follows:

[0187]

[0188] in, This represents the switching control input vector for the unmanned surface vessel. , This represents the positive definite adjustment gain of the switching control law; The gain parameter representing the robust switching term; For adaptive clock The constructed time-varying gain function.

[0189] Finally, the predefined time-nonsingular terminal sliding mode control law for the unmanned surface vessel is as follows:

[0190]

[0191] Combined with a predefined time-distributed observer, define the first Position error of Taiwan underwater unmanned vehicle and speed error as follows:

[0192]

[0193] in, Indicates the first The position and state vector of the underwater unmanned vehicle. They represent Direction and position Orientation, depth, and heading angle; Indicates underwater unmanned vehicle An estimated vector for the augmented reference position state; Indicates the first The velocity vector of the underwater unmanned vehicle in Taiwan Indicates underwater unmanned vehicle The estimated vector of the augmented reference velocity state, Indicates the first Coordinate transformation matrix of the underwater unmanned vehicle.

[0194] Regarding the first Predefined time nonsingular terminal sliding surface of the underwater unmanned vehicle The specific design is as follows:

[0195]

[0196] Among them, the correlation coefficient The calculation formula is:

[0197]

[0198]

[0199]

[0200] in, and Let be the nonlinear power-law parameters of the sliding mode surface of the underwater unmanned vehicle, and satisfy the condition... and ; These are the positive definite gain coefficients calculated based on the predefined upper limit of convergence time. For the reason and Determined auxiliary parameters; It is a predefined upper limit time for convergence of the sliding surface, which is set manually.

[0201] Design No. The equivalent control law for the Taiwanese underwater unmanned vehicle is as follows:

[0202]

[0203] in, For the first The equivalent control input vector of the underwater unmanned vehicle. for The second time derivative; For the first Coordinate transformation matrix of the underwater unmanned vehicle. These are parameters related to the model; other correlation coefficients The calculation formula is:

[0204]

[0205]

[0206] Model-related parameters Defined as:

[0207]

[0208] Design No. The switching control law for the Taiwanese underwater unmanned vehicle is as follows:

[0209]

[0210] in, Indicates the first Switching control input vectors for the underwater unmanned vehicle. , This represents the positive definite adjustment gain of the switching control law; The gain parameter representing the robust switching term. For adaptive clock The constructed time-varying gain function.

[0211] Finally, the first The predefined time-terminal sliding mode control law for the underwater unmanned vehicle is as follows:

[0212]

[0213] Merging sliding mode convergence law predefined convergence time and the predefined convergence time of the sliding surface The predefined convergence time of the tracking error of the surface-underwater heterogeneous cooperative system is obtained as follows:

[0214]

[0215] Step S6: Closed-loop iteration of defense control cycle and completion of collaborative tasks. After completing the active and passive defense decisions and sliding mode control calculations from S2 to S5 within a single cycle, the system returns to S2. Through the synergistic effect of passive prediction by the observer, active topology switching, and predefined time non-singular terminal sliding mode underlying control, the system resiliently resists network attacks and ocean disturbances, ensuring that tracking errors converge within a predetermined time and completing the collaborative operation task.

[0216] Example: To verify the effectiveness of the safety tracking and control method of the present invention, based on the system models of surface unmanned vessels and underwater unmanned vehicles, Figure 2 The proposed active and passive defense method for denial-of-service attacks with predefined time non-singular terminals is verified by simulation.

[0217] based on Figure 3 The simulation shown considers a heterogeneous cooperative system consisting of a surface unmanned vessel leader and three underwater unmanned vehicles followers. The model parameters of the surface unmanned vessel and the underwater unmanned vehicles are given in Tables 1 and 2.

[0218] Table 1 Parameters of the unmanned surface vessel model

[0219]

[0220] Table 2 Parameters of Underwater Unmanned Vehicle Model

[0221]

[0222]

[0223] in, The inertial matrix represents the inertial matrix of the unmanned surface vessel. These represent the inertia coefficients corresponding to the longitudinal, lateral, and yaw motions of the unmanned surface vessel, respectively. It is the damping matrix of the unmanned surface vessel. These represent the damping coefficients in the longitudinal, lateral, and yaw directions, respectively. This represents the coupling damping coefficient between lateral motion and yaw motion.

[0224]

[0225] in, This represents the inertial matrix of an underwater unmanned vehicle. These represent the inertia coefficients corresponding to the longitudinal, lateral, heave, and yaw motions of the underwater unmanned vehicle, respectively. It is the damping matrix of an underwater unmanned vehicle. These represent the damping coefficients in the longitudinal, lateral, heave, and yaw directions, respectively.

[0226] Reference trajectory selected as

[0227]

[0228] In particular, .

[0229] Environmental interference settings for unmanned surface vessels

[0230]

[0231] Environmental interference affecting underwater unmanned vehicles Set as

[0232]

[0233] The initial position of the unmanned surface vessel was selected as follows: The initial velocity is The initial position of underwater unmanned vehicle 1 was selected as follows: The initial velocity is The initial position of underwater unmanned vehicle 2 was selected as follows: The initial velocity is The initial position of underwater unmanned vehicle 3 was selected as follows: The initial velocity is The DoS attack range is selected as: .

[0234] The observer parameters are designed as follows: , , , , , , , The controller parameters are designed as follows: , , , , , , , , , , , , , , , .

[0235] The simulation results for this example can be obtained using Matlab software. Figure 3 This is a switching topology diagram of a heterogeneous cooperative system for surface and underwater environments. Figure 4 This is a three-dimensional spatial image showing the heterogeneous cooperative trajectory tracking between the water surface and underwater. Figure 5 This is a two-dimensional planar underwater heterogeneous cooperative trajectory tracking diagram. Figure 6 This is a map showing the tracking error of unmanned surface vessels. Figure 7 This is a graph showing the trajectory tracking error of an underwater unmanned vehicle. Figure 8 Evolution diagram of the strait link weights for underwater unmanned vehicle formations. Figure 9 Predefined time-distributed observer error map for underwater unmanned vehicles.

[0236] in, Figure 4 middle Representing the inertial coordinate system respectively Direction and position Orientation and depth; Figure 5 The x-coordinate represents the coordinates in the inertial coordinate system. Direction and position, with the vertical axis representing the inertial coordinate system. Direction and position; Figure 6 The horizontal axis represents the system runtime, and the three vertical axes represent the unmanned surface vessel's [time / duration]. Orientation and position tracking error Orientation and position tracking error and heading angle tracking error; Figure 7 The horizontal axis represents the system's operating time, and the four vertical axes represent the operating times of the three underwater unmanned vehicles. Orientation and position tracking error Orientation and position tracking error, depth tracking error, and heading angle tracking error; Figure 8The horizontal axis represents the system running time, and the vertical axis represents the traction link weights of the three underwater unmanned vehicles. Figure 9 The horizontal axis represents the system runtime, and the four vertical axes represent the predefined time distributed observations of the three underwater unmanned vehicles at different times. Direction and position Observational errors in orientation, position, depth, and heading angle channels.

[0237] from Figure 4 and Figure 5 Simulation results show that even under the influence of unknown external disturbances and denial-of-service attacks, the method of this invention can still successfully control heterogeneous surface and underwater systems to complete cooperative trajectory tracking tasks. From Figure 6 and Figure 7 The simulation results show that the tracking error converges to near 0 in about 10 seconds, and the convergence time is within the predefined time range, exhibiting good tracking performance and verifying the effectiveness of the proposed tracking control method.

[0238] from Figure 7 , Figure 8 and Figure 9 The simulation results show that during the gray period, the restraint link is disconnected due to a DoS attack, and the restraint weight... It is zero. The duration of the interval attack did not exceed the tolerance threshold, and passive defense was carried out solely based on the open-loop prediction of the observer. The system communication topology remained unchanged. Figure 3 As shown in (a); in and When the interval exceeds the tolerance threshold, the topology switching mechanism is actively triggered, and the system communication topology diagram changes from... Figure 3 (a) Switch to Figure 3 Switching to (b) again Figure 3 (c) It can be seen that the tolerance threshold for the second trigger is smaller than that for the first trigger. Furthermore, after the restrained link communication topology is restored, the observation error and tracking error can converge to near zero in about 8 seconds under the clock reset mechanism. The convergence time is within the predefined time range, and the surface-underwater heterogeneous cooperative system can still complete the cooperative trajectory tracking task, verifying the effectiveness of the proposed clock reset mechanism and the active-passive defense DoS attack strategy.

[0239] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A predefined-time non-singular terminal sliding mode heterogeneous cooperative control method for active and passive defense against denial-of-service attacks, characterized in that, Includes the following steps: Step S1: Construct dynamic models of surface unmanned vessels and underwater unmanned vehicles, and establish a distributed control-leader-follower communication framework; in which, the surface unmanned vessel, as the leader, relies on its own state to track the global desired trajectory, and the underwater unmanned vehicle formation, as the follower, only the control node can obtain the horizontal state information of the surface unmanned vessel, and the nodes within the formation conduct bidirectional information exchange between neighbors through an undirected circular topology. Step S2: Construct an aperiodic DoS attack model to provide basic operating conditions. Based on the aperiodic DoS attack model, perform multi-dimensional DoS attack state label detection and adaptive clock reset. The multi-dimensional DoS attack state label includes three dimensions: a self-attack state label representing the connectivity between the follower and the leader; a neighbor attack state label representing whether the follower can obtain effective leader state estimation information from topological neighbor followers; and a restraint attack state label representing the connectivity between the leader and the current restraining node. The communication connectivity between nodes is represented in real time using a time-varying Boolean state. The adaptive clock is set to be reset to zero and restarted the timer the moment the communication topology is restored. Step S3: Perform passive defense based on a predefined time-distributed observer using multidimensional DoS attack state labels; embed the multidimensional DoS attack state labels into the local location coordination error and the local velocity coordination error to adjust the observer's error correction term; when a DoS attack causes communication disruption, the corresponding state label is reset to zero, making the error correction term ineffective, the position estimation is transformed into an open-loop integral update, and the velocity estimation remains constant, achieving constant velocity open-loop prediction and realizing passive defense during the attack. Step S4: Adaptive topology switching is performed based on the duration of the attack. When the duration of the attack exceeds the dynamic threshold that the current topology can tolerate, a topology switch is triggered to achieve proactive defense. Step S5: Closed-loop control is performed using a predefined time non-singular terminal sliding mode control law; based on the adaptive clock in step S2 and the state estimation output by the predefined time distributed observer in step S3, the actual thrust and torque commands are output to drive the underlying actuator through a nonlinear disturbance observer and a predefined time non-singular terminal sliding mode control based on the hyperbolic tangent function. Step S6: After completing the active and passive defense decision-making and sliding mode control calculations of steps S2 to S5 within the control cycle, return to step S2 in a loop to complete the collaborative operation task.

2. The method for predefined-time non-singular terminal sliding mode heterogeneous cooperative control of surface and underwater surfaces against active and passive defense against denial-of-service attacks as described in claim 1, characterized in that... In step S1, an undirected graph is introduced. Modeling of follower communication networks; where It is a set of nodes, with each node corresponding to one underwater unmanned vehicle. The number of underwater unmanned vehicles in the formation. It is a bidirectional communication edge set; The adjacency matrix of an undirected ring topology formed by followers is represented as , Represents a node With nodes The status of the bidirectional communication link between them This indicates the existence of a two-way communication link. This indicates that there is no bidirectional communication link. Represents the set of real numbers. and For underwater unmanned vehicles or node indexes; the effective links of the adjacency matrix are defined as follows: and , ,otherwise Furthermore, the nodes do not have self-loops; Laplace matrix corresponding to the adjacency matrix Defined as: diagonal element Off-diagonal elements , ; The unmanned surface vessel is defined as virtual leader node 0. The direct connection between the virtual leader node and the follower formation is via a control matrix. Depicting and restraining matrix elements Indicates underwater unmanned vehicle It can directly receive information from surface unmanned vessels, if underwater unmanned vehicles If information cannot be directly received from unmanned surface vessels, then... .

3. The method for predefined-time non-singular terminal sliding mode heterogeneous cooperative control of surface and underwater surfaces against active and passive defense against denial-of-service attacks as described in claim 2, characterized in that... Step S2 is as follows: Construct an aperiodic DoS attack model; aperiodic DoS attacks occur on the constrained link, defining the first... The consecutive time interval between the occurrences of this DoS attack is: ,in , For the set of natural numbers, and They represent the first The start and end times of a DoS attack, and the secure communication interval between the two attacks, are defined as follows: ; Construct a multi-dimensional DoS attack status label model; define its own attack status label. , A value of 1 indicates an underwater unmanned vehicle. Currently, it is possible to effectively obtain leader status information; Define Neighbor Attack Status Label , A value of 1 indicates an underwater unmanned vehicle. Currently, it is possible to obtain information from topological neighbors. Obtain effective leader state estimation information; define diversion attack state labels. , A value of 1 indicates that the leader and the current restraining node are... The two are in normal communication status. Construct an adaptive clock reset mechanism, adaptive clock The update rules are as follows: （1） in, Indicates the current moment; Indicates the time when the communication topology is restored; Indicates the instant immediately preceding the moment when the communication topology is restored; and These represent the communication topology being in an interrupted state before restoration and the communication topology being in a normal state after restoration, respectively. Used to select the most recent communication topology recovery time up to the current moment.

4. The method for predefined-time non-singular terminal sliding mode heterogeneous cooperative control of surface and underwater surfaces against active and passive defense against denial-of-service attacks as described in claim 3, characterized in that... Step S3 is as follows: Step S3-1: Construct local collaborative error based on multidimensional DoS attack state labels; Local cooperative error in the position of the Taiwanese underwater unmanned vehicle Local Co-operational Error with Velocity The design is as follows: （2） （3） in, To cooperate with underwater unmanned vehicles corresponding nodes The set of neighboring nodes, , underwater unmanned vehicles and underwater unmanned vehicles augmented reference position state The estimated vector, including Direction and position Orientation, desired depth, and heading angle; Used to characterize underwater unmanned vehicles Is it a checkpoint node? Let be the augmented reference position state vector composed of the horizontal position state of the surface unmanned vessel and the desired depth of the underwater unmanned vehicle. These represent unmanned surface vessels. Direction and position Orientation and position, desired depth of underwater unmanned vehicles and heading angle of surface unmanned vessels; for The first time derivative, , underwater unmanned vehicles and underwater unmanned vehicles For augmented reference speed state The estimated vectors include longitudinal velocity, lateral drift velocity, heave velocity, and yaw rate; and underwater unmanned vehicles Self-attack status tags and underwater unmanned vehicles For topological neighbor nodes Neighbor attack status label; Step S3-2: Perform observer mode switching and open-loop passive prediction; The design of the predefined time-distributed observer for the underwater unmanned vehicle is as follows: （4） in, , The gain is positive definite. , They are respectively , The first time derivative; For nodes The current effective in-degree; for The first time derivative; for The second time derivative; For adaptive clock The constructed time-varying gain function, where the index , and They are used for position state estimation and velocity state estimation of a predefined time-distributed observer, respectively. Sliding mode approach process for a predefined time nonsingular terminal sliding mode controller for unmanned surface vessels. Sliding mode approach process for a predefined time nonsingular terminal sliding mode controller for underwater unmanned vehicles; This is the adjustment gain constant corresponding to the time-varying gain function; It is a predefined upper limit of convergence time set manually during the corresponding control phase. or hour, Predefined convergence time for predefined time-distributed observers , and They are respectively and The gain adjustment constant; or hour, Predefined convergence time for sliding mode reaching law , and They are respectively and The gain adjustment constant.

5. The method for predefined-time non-singular terminal sliding mode heterogeneous cooperative control of surface and underwater surfaces against active and passive defense against denial-of-service attacks, as described in claim 4, is characterized in that... Step S4 is as follows: Step S4-1: Based on the restraint attack status label As a driving signal, a single-stage secure communication duration timer is constructed. With a single-phase DoS attack duration timer : in, This represents the cumulative upper limit of the effective communication duration within a single secure communication phase, i.e., the predefined upper limit of convergence time for the observer; Represents the cumulative duration of secure communication at the moment of the attack; Step S4-2: Construct an adaptive topology switching mechanism for the restraining node based on the persistent residence time criterion, and define the switching trigger condition as follows: （5） Based on the theory of dolyapunov functions and the stability of persistent residence time, the dynamic time threshold function The design is as follows: （6） in, This represents the convergence rate of Lyapunov energy exponential decay during secure communication; This represents the number of times the switching mechanism occurs. Standard symbolic functions; This represents the maximum jump factor of the Lyapunov function caused by the state jump at the instant of topology switching; This represents the worst-case rate limit of error energy growth when the system loses effective leader information and enters an open-loop prediction state due to the loss of negative feedback correction. Step S4-3: Perform active topology switching. The switching rules for the restraining node are designed as follows: （7） （8） in, This represents the transient moment when the switching trigger condition is met; This represents the number of the underwater unmanned vehicle control node before the switchover was triggered. This represents the newly selected underwater unmanned vehicle control node number after the switchover is triggered. Represents the modulo operator, ensuring that the node index is within the range of the modulo operator. arrive Loop between; This represents the restraint matrix after the switch is triggered; Represents the binding status of the new binding node; The effective value of the restraint state, and This means that the current underwater unmanned vehicle can directly receive the status information of the surface unmanned vessel.

6. The method for predefined-time non-singular terminal sliding mode heterogeneous cooperative control of surface and underwater surfaces against active and passive defense against denial-of-service attacks, as described in claim 5, is characterized in that... Step S5 is as follows: Step S5-1: Use a nonlinear disturbance observer to perform feedforward compensation for complex ocean disturbances to obtain disturbance estimates; The nonlinear disturbance observer for unmanned surface vessels is designed as follows: （9） in, This represents the disturbance estimate of the unmanned surface vessel obtained from the nonlinear disturbance observer. These represent the estimated values ​​of the longitudinal disturbance force, lateral disturbance force, and yaw disturbance force moments, respectively, with superscripts indicating their relative magnitudes. Indicates transpose; This represents the auxiliary state vector of the nonlinear disturbance observer; for The first time derivative; This represents the design gain matrix of the nonlinear disturbance observer; The inertial matrix representing the unmanned surface vessel; The velocity vector of the unmanned surface vessel includes longitudinal velocity, lateral drift velocity, and bow roll velocity. It is the Coriolis and centripetal force matrix of unmanned surface vessels; It is the damping matrix of the unmanned surface vessel; The control vector represents the control input of the unmanned surface vessel, including forward force, lateral force, and yaw moment; The nonlinear interference observer for the underwater unmanned vehicle is designed as follows: （10） in, The first value obtained from the nonlinear disturbance observer is... Disturbance estimates for the Taiwanese underwater unmanned vehicle These represent the estimated values ​​of the disturbance moment in the forward direction, the lateral direction, the heave direction, and the yaw direction, respectively. For the first Auxiliary state vector of the nonlinear disturbance observer of the underwater unmanned vehicle. for The first time derivative; This represents the design gain matrix of the nonlinear disturbance observer; The inertial matrix represents the inertial matrix of an underwater unmanned vehicle; Indicates the first The velocity vector of the underwater unmanned vehicle includes longitudinal velocity, lateral drift velocity, heave velocity, and bow roll velocity; It refers to the Coriolis and centripetal force matrix of underwater unmanned vehicles; It is the damping matrix of an underwater unmanned vehicle; This represents the position vector of the underwater unmanned vehicle in the inertial coordinate system; This represents the restoring force and torque generated by gravity and buoyancy; The control vector represents the control input of an underwater unmanned vehicle, including forward force, lateral force, heave force, and yaw moment; Step S5-2: Construct a predefined time nonsingular terminal sliding mode controller based on the hyperbolic tangent function to calculate the underlying actual thrust and torque; Define the position error of unmanned surface vessels as follows: （11） in, This represents the position and state vector of the unmanned surface vessel in the inertial coordinate system. These represent unmanned surface vessels. Direction and position Orientation and heading angle; This represents the desired position and state vector of the unmanned surface vessel. Representing the expected values ​​of unmanned surface vessels. Direction, position, expectation Orientation and desired heading angle; Predefined time terminal sliding surface of unmanned surface vessels The specific design is as follows: （12） in, for First-order time derivative; correlation coefficient The calculation formula is: （13） （14） （15） in, and Let be the nonlinear power-law parameters of the sliding mode surface of the unmanned surface vessel, and satisfy the condition. and ; These are the positive definite gain coefficients calculated based on the predefined upper limit of convergence time. For the reason and Determined auxiliary parameters; This represents the predefined upper limit of convergence time for the sliding surface, which is set manually. The equivalent control law for the unmanned surface vessel is as follows: （16） in, Let be the equivalent control input vector for the unmanned surface vessel. Desired position state of unmanned surface vessel The second time derivative; This represents the coordinate transformation matrix of the unmanned surface vessel. These are parameters related to the model; other correlation coefficients The calculation formula is: （17） （18） The switching control law for the unmanned surface vessel is designed as follows: （19） in, This represents the switching control input vector for the unmanned surface vessel. , This represents the positive definite adjustment gain of the switching control law; The gain parameter representing the robust switching term; For adaptive clock Constructed time-varying gain function; The predefined time-nonsingular terminal sliding mode control law for the synthetic unmanned surface vessel is as follows: （20） Combined with a predefined time-distributed observer, define the first Position error of Taiwan underwater unmanned vehicle and speed error as follows: （21） in, Indicates the first The position and state vector of the underwater unmanned vehicle. They represent Direction and position Orientation, depth, and heading angle; Indicates underwater unmanned vehicle An estimated vector for the augmented reference position state; Indicates the first The velocity vector of the underwater unmanned vehicle in Taiwan Indicates underwater unmanned vehicle The estimated vector of the augmented reference velocity state, Indicates the first Coordinate transformation matrix of the underwater unmanned vehicle; Regarding the first Predefined time nonsingular terminal sliding surface of the underwater unmanned vehicle The specific design is as follows: （22） Among them, the correlation coefficient The calculation formula is: （23） （24） （25） in, and Let be the nonlinear power-law parameters of the sliding mode surface of the underwater unmanned vehicle, and satisfy the condition. and ; These are the positive definite gain coefficients calculated based on the predefined upper limit of convergence time. For the reason and Determined auxiliary parameters; It is a predefined upper limit of convergence time for the sliding surface, which is set manually. Design No. The equivalent control law for the Taiwanese underwater unmanned vehicle is as follows: （26） in, For the first The equivalent control input vector of the underwater unmanned vehicle. for The second time derivative; For the first Coordinate transformation matrix of the underwater unmanned vehicle. These are parameters related to the model; other correlation coefficients The calculation formula is: （27） （28） Design No. The switching control law for the Taiwanese underwater unmanned vehicle is as follows: （29） in, Indicates the first Switching control input vectors for the underwater unmanned vehicle. , This represents the positive definite adjustment gain of the switching control law; The gain parameter representing the robust switching term. For adaptive clock Constructed time-varying gain function; Synthesis of the first The predefined time-terminal sliding mode control law for the underwater unmanned vehicle is as follows: （30）。 7. A predefined-time non-singular terminal sliding mode surface and underwater heterogeneous cooperative control system for active and passive defense against denial-of-service attacks, characterized in that... It includes a processor, a memory, and a computer program stored in the memory. When the processor executes the computer program, it specifically performs the steps in the cooperative control method as described in any one of claims 1-6.

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