A Tracking Control Method for a Three-Degree-of-Freedom Unmanned Surface Vehicle

Abstract

The present invention discloses a tracking control method for a three-degree-of-freedom unmanned surface vehicle. The method comprises: using a radial basis function neural network to estimate the nonlinear terms of the unknown dynamics and external time-varying disturbances contained in the three-degree-of-freedom unmanned surface vehicle; constructing a finite-time preset performance function to improve the transient and steady-state performance of the system output during the convergence process; designing two adaptive controllers, event-based and self-triggered, and combining the trigger conditions of the event-based and self-triggered mechanisms to construct a one-bit encoding and decoding communication mechanism, thereby reducing the occupancy of communication channels, alleviating communication pressure, and significantly reducing communication costs. This control method not only ensures that all signals in the closed-loop system are fixed-time semi-globally eventually uniformly bounded, but also that the system output is constrained within a preset range within a finite time.

Description

Technical Field

[0001] The present invention belongs to the field of tracking and control of unmanned surface boats, and in particular relates to a tracking and control method for a three-degree-of-freedom unmanned surface boat. Background Art

[0002] With the advancement of science and technology and the continuous depletion of natural resources on land, the exploration and development of the ocean has become a social imperative, driving the rapid development of tracking and control for unmanned surface vehicles (USVs). With advantages such as small size, high maneuverability, intelligence, and modularity, USVs are finding an increasingly wide range of applications, including water quality monitoring, aquatic waste removal, bank and dam protection, aquatic resource and product observation, maritime communications relay, and other military applications. As a crucial tool for ocean exploration, they have garnered widespread attention from scholars across various fields.

[0003] The ocean environment is characterized by significant uncertainty. When operating on the surface, unmanned surface vehicles (USVs) are inevitably affected by external time-varying disturbances such as ocean currents, wind and waves, and eddies. Furthermore, the system models of USVs often contain unknown dynamic components, and their inherent structural complexity complicates the development of accurate equivalent models for them, making tracking and control of USVs a challenging task. The influence of unknown dynamics and external time-varying disturbances significantly degrades the tracking performance of USVs. To ensure their ability to track desired trajectories, research is necessary on their anti-interference capabilities and ability to handle unknown dynamics.

[0004] With the development of computer and network technologies, networked control systems have gained popularity in many fields due to their strong scalability and high flexibility. However, most existing control methods are based on periodic sampling or time triggering. Traditional time-triggered control methods periodically transmit and update control signals at discrete, equally spaced time points, resulting in an increasing amount of network data transmission. This results in a large amount of unnecessary redundant information being transmitted, which in turn wastes limited network resources. For networked control systems, periodic sampling not only incurs excessive computational costs but also increases the communication burden. How to effectively reduce the amount of data transmitted in the network, reduce the occupancy of communication channels, and thus conserve network bandwidth resources has become a significant research topic. Summary of the Invention

[0005] In view of this, in order to address the deficiencies of the above-mentioned prior art, the purpose of the present invention is to provide a tracking control method for a three-degree-of-freedom surface unmanned boat, which not only improves the tracking accuracy of the system and improves the transient performance of the system, but also limits the system output to a preset range within a limited time, so that the tracking error converges to a small neighborhood of zero within a fixed time; and significantly reduces the communication cost and the occupancy of the communication channel, saving network bandwidth resources.

[0006] To achieve the above object, the technical solution adopted by the present invention is: a tracking control method for a three-degree-of-freedom unmanned surface vehicle, comprising the following steps:

[0007] S1. Based on the dynamic model of the three-degree-of-freedom unmanned surface vehicle, the state equation of the unmanned surface vehicle is constructed taking into account the unknown dynamics and external time-varying disturbances;

[0008] S2. Based on the state equation constructed in step S1, design a finite time preset performance function v i (t), and define the error conversion function T i (ε i ), the signal constrained by the performance function is converted into an unconstrained variable, and then the error equation of the secondary system is obtained through coordinate transformation;

[0009] S3, for the unconstrained variables and the first-level system obtained in S2, construct the first Lyapunov function V1, differentiate V1 with respect to time to obtain its first-order derivative, and then design the first virtual control signal α1 and the first adaptive law based on the backstepping method to make the first-level system tend to be stable

[0010] S4, using the event-triggered communication strategy, for the second-level system of the three-degree-of-freedom surface unmanned boat, construct the second Lyapunov function V2, take the derivative of V2 with respect to time to obtain its first-order derivative, and then design the second virtual control signal α2 and the second adaptive law based on the backstepping method. and compound perturbation adaptive law The first Lyapunov function V1 and the second Lyapunov function V2 are combined to obtain the total Lyapunov function that makes the system closed-loop stable. Combined with the lemma, the controller guarantees that all signals in the closed-loop system are fixed-time semi-globally eventually uniformly bounded;

[0011] S5. Using the self-triggering communication strategy, for the second-level system of the three-degree-of-freedom surface unmanned boat, the third Lyapunov function V3 is constructed, and the first-order derivative of V3 is obtained by taking the derivative with respect to time. Then, the second virtual control signal α3 and the second adaptive law are designed based on the backstepping method. and compound perturbation adaptive law The first Lyapunov function V1 and the third Lyapunov function V3 are combined to obtain the total Lyapunov function that makes the closed loop of the system stable. Combined with the lemma, the controller guarantees that all signals in the closed-loop system are fixed-time semi-globally eventually uniformly bounded;

[0012] S6. Combining the triggering conditions of the event / self-triggered communication mechanism, a one-bit encoding and decoding signal transmission mechanism is constructed to prove the robustness of the one-bit encoding and decoding signal transmission mechanism.

[0013] Furthermore, the specific process of step S3 is as follows:

[0014] S3.1. Derivative the state equation obtained in step S1 and the error equation obtained in step S2 to obtain the error dynamic equation of the first-level system;

[0015] S3.2. For the first-stage system of the three-degree-of-freedom unmanned surface vehicle, construct the first Lyapunov function V1 based on the error dynamic equation of the first-stage system, and differentiate it to obtain the derivative of the first Lyapunov function;

[0016] S3.3. Approximate the partial derivatives contained in the unconstrained variables obtained in step S2 using a radial basis function neural network, and then perform scaling using Young's inequality to solve the unknown function in the derivative of the first Lyapunov function.

[0017] S3.4, based on the backstepping method, the first virtual control signal α1 and the first adaptive law are designed to make the first-level system stable. And the first virtual control signal α1 and the first adaptive law Substituting the derivative of the first Lyapunov function into the equation, we obtain the inequality equation that the first-order system tends to be stable.

[0018] Furthermore, the specific process of step S4 is as follows:

[0019] S4.1. Combining the state equation obtained in step S1 and the error equation obtained in step S2, taking the derivative of the error equation to obtain a second-order error dynamic equation;

[0020] S4.2. To address the nonlinear factors of unknown dynamics and external time-varying disturbances contained in the three-degree-of-freedom unmanned surface vehicle system, a radial basis function neural network is used for approximation. The approximation error and external time-varying disturbance are combined into a composite disturbance term Θ1. Young's inequality is then used for scaling to solve the unknown function contained in the derivative of the second Lyapunov function.

[0021] S4.3. For the second-stage system of the three-degree-of-freedom unmanned surface vehicle, construct a second Lyapunov function V2 based on the error dynamic equation of the second-stage system;

[0022] S4.4, introduce event-triggered communication mechanism;

[0023] S4.5. Derivate the second Lyapunov function V2 to obtain the derivative of the second Lyapunov function;

[0024] S4.6, design the second virtual control signal α2 and the second adaptive law based on the backstepping method and adaptive law of compound disturbances The second virtual control signal α2 and the second adaptive law and adaptive law of compound disturbances Substitute into the derivative of the second Lyapunov function;

[0025] S4.7. Combine the first Lyapunov function V1 and the second Lyapunov function V2 to obtain the total Lyapunov function that makes the system closed-loop stable. For the total Lyapunov function Derivatives satisfy the derivative This shows that all closed-loop signals of the three-degree-of-freedom surface unmanned vehicle system are fixed-time bounded.

[0026] Furthermore, the specific process of step S5 is:

[0027] S5.1. Combining the state equation obtained in step S1 and the error equation obtained in step S2, taking the derivative of the error equation to obtain a second-order error dynamic equation;

[0028] S5.2. To address the nonlinear factors of unknown dynamics and external time-varying disturbances contained in the three-degree-of-freedom unmanned surface vehicle system, a radial basis function neural network is used for approximation. The approximation error and external time-varying disturbance are combined into a composite disturbance term Θ2. Young's inequality is then used for scaling to solve the unknown function contained in the derivative of the third Lyapunov function.

[0029] S5.3. For the second-stage system of the three-degree-of-freedom unmanned surface vehicle, construct the third Lyapunov function V3 based on the error dynamic equation of the second-stage system;

[0030] S5.4, introduce a self-triggered communication mechanism;

[0031] S5.5. Derivate the third Lyapunov function V3 to obtain the derivative of the third Lyapunov function;

[0032] S5.6, design the second virtual control signal α3 based on the backstepping method, the second adaptive law and adaptive law of compound disturbances The second virtual control signal α3 and the second adaptive law and adaptive law of compound disturbances Substitute into the derivative of the third Lyapunov function;

[0033] S5.7. Combine the first Lyapunov function V1 and the third Lyapunov function V3 to obtain the total Lyapunov function that makes the system closed-loop stable. For the total Lyapunov function Derivatives satisfy the derivative This shows that all closed-loop signals of the three-degree-of-freedom surface unmanned vehicle system are fixed-time bounded.

[0034] Furthermore, the specific process of step S6 is as follows:

[0035] S6.1. Design a 1-bit encoding and decoding signal transmission mechanism based on the triggering conditions of the event triggering mechanism;

[0036] S6.2. Design a 1-bit encoding and decoding signal transmission mechanism based on the triggering conditions of the self-triggering mechanism;

[0037] S6.3. Perform robustness analysis on the designed 1-bit encoding and decoding signal transmission mechanism.

[0038] Furthermore, in step S3, the first virtual control signal α1 and the first adaptive law that make the first-level system tend to be stable are set. for:

[0039]

[0040]

[0041]

[0042] in, χ1,σ 1i ,σ 2i is the design parameter, i=1,2,3;

[0043] φ1 is the basis function of the first radial basis neural network, is the estimated value of the unknown parameter θ1, z1 is the unrestricted error variable, is the rotation matrix of the system,

[0044] Furthermore, in step S4, the second virtual control signal α2 and the second adaptive law and compound perturbation adaptive law for:

[0045]

[0046]

[0047]

[0048]

[0049] in, b i ,χ 2i ,c 1i ,c 2i ,c 3i ,c 4i ,g 1i ,g 2i is the design parameter, i=1,2,3; Δ i (t) is the time-varying design parameter, φ 2i is the basis function of the second radial basis neural network, z 2i is the velocity tracking error, is the unknown parameter θ 2i The estimated value of is the unknown parameter Θ 1i estimated value.

[0050] Furthermore, in step S5, the designed third virtual control signal α3 and the third adaptive law and compound perturbation adaptive law for:

[0051]

[0052]

[0053]

[0054] in, m i , d 1i ,d 2i ,d 3i ,d 4i ,g 1i ,g 2i is the design parameter, i=1,2,3; is a time-varying design parameter, φ 3i is the basis function of the third radial basis neural network, is the unknown parameter θ 3i The estimated value of is the unknown parameter Θ 2i estimated value.

[0055] The beneficial effects of the present invention are:

[0056] First, the present invention uses the Lyapunov-Krasovskii Function (LKF) to make the unknown dynamics and external time-varying disturbances become bounded functions approximated by the Radial Basis Function Neural Networks (RBFNNs). Through error conversion, the Finite-Time Prescribed Performance Function (FTPPF) is applied to the tracking control strategy of the three-degree-of-freedom surface unmanned vehicle. Ultimately, it is proved that all states of the closed-loop system are bounded, and the system output is limited to a preset range within a finite time, so that the tracking error converges to a small neighborhood of zero within a fixed time, so that the tracking error converges quickly and the steady-state effect is better.

[0057] Second, two adaptive controllers, event-triggered and self-triggered, were designed to reduce network data transmission and communication channel occupancy. Furthermore, a 1-bit decoding and encoding mechanism was designed for both event-triggered and self-triggered triggering mechanisms, further conserving network bandwidth resources. This invention significantly reduces communication costs and has high engineering practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0059] Figure 1 It is a schematic diagram of the structure of a three-degree-of-freedom surface unmanned boat.

[0060] Figure 2 This is a design flow chart of a three-degree-of-freedom unmanned surface boat.

[0061] Figure 3 This is the tracking control simulation result of the three-degree-of-freedom surface unmanned vehicle under the event trigger mechanism.

[0062] Figure 4 It is the simulation result of the triggering interval of the three-degree-of-freedom surface unmanned vehicle tracking control under the event triggering mechanism.

[0063] Figure 5 It is the tracking control simulation result of three-degree-of-freedom surface unmanned vehicle tracking control under the self-triggering mechanism.

[0064] Figure 6 It is the simulation result of the triggering interval of the three-degree-of-freedom surface unmanned vehicle tracking control under the self-triggering mechanism.

[0065] Figure 7 Is the sampling error included * Tracking control simulation results of three-degree-of-freedom unmanned surface vehicle tracking control under event triggering mechanism.

[0066] Figure 8 Is the sampling error included * Tracking control simulation results of three-degree-of-freedom unmanned surface vehicle tracking control under self-triggering mechanism. DETAILED DESCRIPTION

[0067] The following specific examples are given to further clearly, completely and in detail illustrate the technical solution of the present invention. This embodiment is the best embodiment based on the technical solution of the present invention, but the protection scope of the present invention is not limited to the following examples.

[0068] A tracking control method for a three-degree-of-freedom unmanned surface vehicle, which is used in Figure 1 The unmanned surface vehicle system shown in the figure has the influence of unknown dynamics and external time-varying disturbance nonlinear factors, and includes a first-level system and a second-level system;

[0069] The tracking control method comprises the following steps:

[0070] S1. Based on the mathematical model of the three-degree-of-freedom unmanned surface vehicle, the state equation of the unmanned surface vehicle is constructed taking into account the unknown dynamics and external time-varying disturbances. The specific process includes the following:

[0071] S11. First, a mathematical model of the three-degree-of-freedom unmanned surface vehicle system is established;

[0072] Consider a dynamic model of a three-degree-of-freedom unmanned surface vehicle with unknown dynamics and external time-varying disturbances. The system model expression is:

[0073]

[0074] In the formula They represent the position of the unmanned surface vehicle in (x, y) coordinates and the heading angle of the unmanned surface vehicle in the fixed ground coordinate system. Where u represents the forward speed of the surface unmanned boat, v represents the swing speed of the surface unmanned boat, and r represents the turning angular velocity of the surface unmanned boat; M is the inertia matrix and is the matrix of Coriolis and centripetal terms; is the damping matrix; The rotation matrix of the surface unmanned vehicle, and satisfies Provides control input for unmanned surface vehicles; is the external time-varying disturbance;

[0075] Its matrix M, They are:

[0076]

[0077]

[0078] in d 11 (u) = -X u -X u|u| |u|,d 22 (v,r)=-Y v -Y v|v| |v|-Y v|r| |r|,d 23 (v,r)=-Y r -Y r|v| |v|-Y r|r| |r|,d 32 (v,r)=-N v -N v|v| |v|-N v|r| |r|,d 33 (v,r)=-N r -N r|v| |v|-N r|r| |r|.

[0079] Among them, m and I z are defined as the mass of the surface unmanned vehicle model and the moment of inertia about yaw rotation; X u ,X |u|u ,Y v ,Y v|v| ,Y v|r| ,Y r ,Y r|v| ,Y r|r| ,N v ,N v|v| ,N v|r| ,N r|r| Quadratic linear drag coefficient of surface unmanned vehicle; represents the additional mass, and the detailed parameters are shown in Table 1.

[0080] Table 1 Detailed parameters of unmanned surface vehicles

[0081]

[0082]

[0083] S12. The state equation can be expressed as follows:

[0084]

[0085] S2. According to the state equation of the three-degree-of-freedom unmanned surface vehicle, a finite-time preset performance function υ is constructed. i (t), and define the error conversion function T i (ε i ), so that the performance function Convert to unconstrained variable ε=[ε1,ε2,ε3] T , specifically including:

[0086] The following finite time preset performance function expression is constructed:

[0087]

[0088] in The initial condition of the finite-time preset performance function is The tracking error of the surface unmanned vehicle will not exceed the upper and lower bounds set by the finite time preset performance function, that is, -υ i (t)<e 1i (t)<υ i (t), where e 1i (t) represents the tracking error of the surface unmanned vehicle;

[0089] Furthermore, the design error conversion function is:

[0090]

[0091] where ε i Expressed as the transition error, the error transition function is a strictly monotonically increasing function and satisfies and T i (ε i )∈(-1,1), then define as follows:

[0092] e 1i =υ i (t)T i (ε i )i=1,2,3 (5)

[0093] in x d represents the expected trajectory of the surface unmanned vehicle on the x-axis, y d represents the expected trajectory of the surface unmanned vehicle on the y-axis, represents the expected trajectory of the heading angle of the surface unmanned vehicle in the fixed ground coordinate system;

[0094] Furthermore, according to formula (5), 1i After taking the derivative, we can get:

[0095]

[0096] Furthermore, through formula (6), we can get:

[0097]

[0098] in and So we can further get Here F i F i The unknown lower bound of is not used for controller design but only for stability analysis.

[0099] Furthermore, the error equation is obtained after the coordinate change:

[0100]

[0101] in, and They are defined as position tracking error and velocity tracking error respectively.

[0102] S3, for the unconstrained variables and the first-level system obtained in S2, construct the first Lyapunov function V1, differentiate V1 with respect to time t to obtain its first-order derivative, and then design the first virtual control signal α1 and the first adaptive law based on the backstepping method to make the first-level system tend to be stable

[0103] The specific process includes the following:

[0104] S3.1. Combining the state equation in step S1 with the error equation obtained in step S2, the error dynamic equation of the first-level system can be obtained:

[0105]

[0106] where Υ=[Υ1, Υ2, Υ3] T , F=diag{F1,F2,F3};

[0107] S3.2. Further construction of the first Lyapunov function in, is the parameter θ 1i Estimated value, where θ 1i =||W 1i|| 2 ;

[0108] S3.3. Taking the derivative of V1, we can get the derivative of the first Lyapunov function:

[0109]

[0110] in f1=[f1 1 ,f1 2 ,f1 3 ] T , using radial basis neural networks to approximate unknown nonlinear functions And using Young's inequality to process it, we can get:

[0111]

[0112] where a 1i >0 (i=1,2,3) is the design parameter; is the approximation error,

[0113] S3.4. Design the following virtual control signal:

[0114]

[0115]

[0116]

[0117] in χ1,σ 1i and σ 2i is the design parameter, i=1,2,3; φ1 is the basis function of the first radial basis neural network, is the estimated value of the unknown parameter θ1, z1 is the unrestricted error variable, is the rotation matrix of the system,

[0118] Using Lemma 2, the formula (10) Can be simplified to:

[0119]

[0120] Substituting formulas (11)-(15) into formula (10), we can obtain:

[0121]

[0122] in and

[0123] according to and Using Young's inequality we can get:

[0124]

[0125]

[0126]

[0127] By using Lemma 4, we can get:

[0128]

[0129] in and

[0130] Substituting (17)-(20) into (16), we can obtain:

[0131]

[0132] in

[0133] Take it here and We can get:

[0134]

[0135] definition and By using Lemma 3 and Lemma 5, we can obtain the following inequality equation for the stability of the first-order system:

[0136]

[0137] in

[0138] S4, using the event-triggered communication strategy, for the second-level system of the three-degree-of-freedom surface unmanned boat, construct the second Lyapunov function V2, take the derivative of V2 with respect to time t to obtain its first-order derivative, and then design the second virtual control signal α2 and the second adaptive law based on the backstepping method. and compound perturbation adaptive law The first Lyapunov function and the second Lyapunov function are combined to obtain the total Lyapunov function that makes the system closed-loop stable. Combined with the lemma, it is proved that the designed controller can achieve fixed-time stability of the system closed-loop. The specific process includes the following:

[0139] S4.1. Transform the second equation in formula (1);

[0140]

[0141] in

[0142] Combining the state equation in step S1 and the error equation obtained in step S2, the error equation is derived to obtain the following error dynamic equation of the second-level system:

[0143]

[0144] in,

[0145] S4.2, using radial basis neural network By approximation, formula (25) can be changed to:

[0146]

[0147] in Defined as an unknown composite perturbation that satisfies in is the approximation error of the radial basis neural network, and satisfies is an unknown constant; is the unknown upper bound of the external time-varying disturbance;

[0148] S4.3. Construct the second Lyapunov function for the second-level system of the three-degree-of-freedom unmanned surface vehicle:

[0149]

[0150] where g 1i ,g 2i are design parameters, where is the parameter θ 2i Estimated value, is the parameter Θ 1i estimated value;

[0151] S4.4. At the same time, the following event trigger control mechanism is introduced to reduce communication resource waste and other problems: The event trigger controller is represented as follows:

[0152]

[0153]

[0154] where t k ,t k+1 ∈Z+ ; 0<δ i <1,

[0155]

[0156] Among them, μ 1i >0,κ 1i ,κ 2i is a time-varying parameter, and |κ 1i (t)|≤1,|κ 2i (t)|≤1;

[0157] S4.5. Taking the derivative of the second Lyapunov function, we can obtain the following derivative of the second Lyapunov function:

[0158]

[0159] S4.6, then design the second virtual control signal α2 and the second adaptive law based on the backstepping method and compound perturbation adaptive law

[0160]

[0161]

[0162]

[0163]

[0164] in, b i ,χ2,c 1i ,c 2i ,c 3i ,c 4i ,g 1i ,g 2i is the design parameter, i=1,2,3; Δ i (t) is the time-varying design parameter, φ 2i is the basis function of the second radial basis neural network, z 2i is the velocity tracking error, is the unknown parameter θ 2i The estimated value of is the unknown parameter Θ 1i estimated value of;

[0165] Substituting formulas (32)-(35) into (31), we can obtain:

[0166]

[0167] in Similar to formulas (17)-(19), define

[0168] We can get:

[0169]

[0170] in

[0171] S4.7, the first Lyapunov function V1 and the second Lyapunov function V2 are combined to obtain the total Lyapunov function that makes the system closed-loop stable

[0172]

[0173] Total Lyapunov function Taking the derivative, we get the derivative of the total Lyapunov function:

[0174]

[0175] in

[0176] Through the above analysis, it can be proved that the three-degree-of-freedom surface unmanned boat system has achieved fixed-time stability.

[0177] The above is a specific implementation plan of an embodiment of the present invention. The present invention simulates the control system through Matlab and analyzes its stability and real-time performance, and obtains the closed-loop stability of the three-degree-of-freedom surface unmanned vehicle system.

[0178] S5. Using the self-triggering communication strategy, for the second-level system of the three-degree-of-freedom surface unmanned boat, the third Lyapunov function V3 is constructed. The first-order derivative of V3 is obtained by taking the derivative of time t, and then the second virtual control signal α3 and the second adaptive law are designed based on the backstepping method. and compound perturbation adaptive law The first Lyapunov function and the third Lyapunov function are combined to obtain the total Lyapunov function that makes the system closed-loop stable. Combined with the lemma, the system achieves closed-loop fixed-time stability.

[0179] The specific process includes the following:

[0180] S5.1. Similar to step 4, the following error dynamic equation of the second-level system is obtained:

[0181]

[0182] in f3=[f3 1 ,f32 ,f3 3 ] T ;

[0183] S5.2. Using radial basis neural network By approximation, formula (24) can be transformed into:

[0184]

[0185] in Defined as an unknown composite perturbation that satisfies in is the approximation error of the radial basis neural network, and satisfies is an unknown constant; is the unknown upper bound of the external time-varying disturbance;

[0186] S5.3. For the second-level system of the three-degree-of-freedom unmanned surface vehicle, construct the third Lyapunov function V3:

[0187]

[0188] where r 1i ,r 2i are design parameters, where is the parameter θ 3i Estimated value, is the parameter Θ 2i estimated value;

[0189] S5.4. At the same time, the following self-triggering control mechanism is introduced:

[0190]

[0191] where t k ,t k+1 ∈Z + ; 0<δ i <1,0<Λ i <1, and η i is a positive constant, Indicates the control signal interval between two consecutive trigger moments, and η i is the rate of change of the control signal interval; when the above conditions are met, Will be used to control the object, the next trigger point t s+1 Will be obtained, control signal In [t s ,ts+1 ) is maintained within the period of

[0192] The self-triggering controller is expressed as follows:

[0193]

[0194]

[0195] Where χ3>0,σ 1i ,σ 2i is a time-varying parameter, and |σ 1i (t)|≤1,|σ 2i (t)|≤1.

[0196] S5.5. Taking the derivative of the third Lyapunov function V3, we obtain the following derivative of the third Lyapunov function:

[0197]

[0198] S5.6, then design the third virtual control signal α3 and the third adaptive law based on the backstepping method and compound perturbation adaptive law

[0199]

[0200]

[0201]

[0202] in, m i , d 1i ,d 2i ,d 3i ,d 4i ,r 1i ,r 2i (i=1,2,3) are design parameters, is a time-varying design parameter, φ 3i is the basis function of the third radial basis neural network,

[0203] The virtual control signal α3, the adaptive law and compound perturbation adaptive law Substitute into formula (47) and take

[0204] We can get:

[0205]

[0206] in

[0207] S5.7, the first Lyapunov function V1 and the third Lyapunov function V3 are combined to obtain the total Lyapunov function that makes the system closed-loop stable

[0208]

[0209] For the total Lyapunov function Taking the derivative, we get the derivative of the total Lyapunov function:

[0210]

[0211] in

[0212] Through the above analysis, it can be proved that the three-degree-of-freedom surface unmanned boat system has achieved fixed-time stability.

[0213] The above is a specific implementation plan of an embodiment of the present invention. The present invention simulates the control system through Matlab and analyzes its stability and real-time performance, and obtains the closed-loop stability of the three-degree-of-freedom surface unmanned vehicle system.

[0214] S6. Combine the trigger conditions of the event-triggered communication mechanism to construct a one-bit encoding and decoding signal transmission mechanism to prove the robustness of the encoding mechanism. The specific process includes the following:

[0215] S6.1. Design a 1-bit encoding and decoding signal transmission mechanism based on the trigger conditions of the event trigger mechanism. First, use the measurement error Encoding is performed when the measurement error satisfies The encoder encodes the trigger signal; assuming that at t∈[t k ,t k+1 ),k=0,1,2,…, the encoder is designed as follows:

[0216]

[0217] The encoder's output p1 is then transmitted to the decoder for decoding. At this time, the value of the trigger condition and the latest control signal Will be stored, the decoder is designed as follows:

[0218]

[0219] S6.2. Design a 1-bit encoding and decoding signal transmission mechanism based on the triggering conditions of the self-triggering mechanism;

[0220] First, use the measurement error Encoding is performed when the measurement error satisfies The encoder encodes the trigger signal; assuming that at t∈[t s ,t s+1 ),s=0,1,2,…, the encoder is designed as follows:

[0221]

[0222] The output p of the encoder is then transmitted to the decoder for decoding. At this time, the value of the trigger condition and the latest control signal Will be stored, the decoder is designed as follows:

[0223]

[0224] S6.3. The following is a robustness analysis of the 1-bit decoding and 1-bit encoding signal transmission mechanism:

[0225] The robustness analysis of a single-bit encoding and decoding signal transmission mechanism specifically includes three cases:

[0226] Case 1: In an ideal situation, the system signal can be measured continuously and accurately, and the trigger conditions of the event / self-trigger mechanism are and At this time, the system's decoder and controller get the same value, that is,

[0227] Case 2: In actual operation, when the system status is sampled at a certain time, the trigger condition will likely become and This will produce a bounded error between the system controller and the decoder. * , where o * It can be positive or negative, so that the control signal after triggering becomes as well as In the simulation experiment, take * Bounded error value ∈[-0.2,0.2];

[0228] In order to solve the error caused by the sensor o * , you can select the design parameters and And take:

[0229]

[0230]

[0231] This can solve the error caused by the sensor. * , further ensuring the stability of the system.

[0232] Case 3: In this case, the sampling error of the system is o * It will continue to increase and increase to a certain large value, which will eventually affect the stability of the system. The solution to this problem is to reduce the sampling error after multiple transmissions. * When the error increases to the point where it affects the stability of the system, the decoder is corrected to make the sampling error o * Cleared.

[0233] The goal of this application is to design a fixed-time preset performance adaptive control strategy so that all closed-loop signals of the system are bounded within a fixed time and the output of the three-degree-of-freedom unmanned surface vehicle is guaranteed to converge to a preset range within a finite time interval; Figure 3 This is the tracking control simulation result of the three-degree-of-freedom unmanned surface vehicle under the event trigger mechanism; Figure 4 This is the simulation result of the trigger interval of the three-degree-of-freedom surface unmanned vehicle tracking control under the event trigger mechanism; Figure 5 This is the tracking control simulation result of the three-degree-of-freedom unmanned surface vehicle under the self-triggering mechanism; Figure 6 This is the simulation result of the trigger interval of the three-degree-of-freedom surface unmanned vehicle tracking control under the self-trigger mechanism; Figure 7 Is the sampling error included * The simulation results of tracking control of three-degree-of-freedom unmanned surface vehicle under event-triggered communication mechanism; Figure 8 Is the sampling error included * Tracking control simulation results of three-degree-of-freedom unmanned surface vehicle under self-triggering communication mechanism.

[0234] In practical control engineering applications, constraints are imposed on system tracking performance (such as overshoot, convergence speed, and maximum steady-state error) to ensure that the system's tracking error converges within a preset error range. To meet these requirements, a preset performance control method is proposed. This method uses a prescribed performance function (PPC) to constrain the system's tracking error. The finite-time prescribed performance function (FTPPC) optimizes traditional PPC to ensure that the system's tracking error converges to a small neighborhood of zero within a preset finite time. This method improves both the transient and steady-state performance of the system and offers fast convergence time.

[0235] Asymptotically stable control theory states that all closed-loop signals in a system reach stability within infinite time, but this rarely meets control requirements in practical systems. Finite-time control theory was subsequently proposed, aiming to achieve system stability within a finite time. However, finite-time control theory suffers from the influence of the system's initial state. When the system's initial state is far from equilibrium, the system's convergence time can be excessive or difficult to predict. Fixed-time control theory ensures that system errors are not affected by the initial state during convergence, ensuring that all closed-loop signals in the system stabilize within a fixed time.

[0236] In summary, this application limits the system's tracking error to a pre-set range by designing a finite-time prescribed performance function (FTPPF), thereby improving the system control progress and convergence speed; combining the trigger conditions of the event / self-trigger mechanism to construct a 1-bit encoding and decoding communication mechanism, further reducing the occupancy of the communication channel and alleviating communication pressure; ultimately, it can be proved that the proposed control method not only ensures that all states of the closed-loop system are bounded, but also that the system output is limited to a pre-set range within a limited time, significantly reducing the communication cost.

[0237] The above shows and describes the main features, basic principles, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and improvements may be made to the present invention based on actual circumstances without departing from the spirit and scope of the present invention. Such changes and improvements are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A tracking control method for a three-degree-of-freedom unmanned surface vehicle, characterized in that: The following steps are involved: S1. Based on the dynamic model of the three-degree-of-freedom unmanned surface vehicle, the state equation of the unmanned surface vehicle is constructed taking into account the unknown dynamics and external time-varying disturbances; S2. Based on the state equation constructed in step S1, design a finite time preset performance function v i (t), and define the error conversion function T i (ε i ), the signal constrained by the performance function is converted into an unconstrained variable, and then the error equation of the secondary system is obtained through coordinate transformation; S3, for the unconstrained variables and the first-level system obtained in S2, construct the first Lyapunov function V1, differentiate V1 with respect to time to obtain its first-order derivative, and then design the first virtual control signal α1 and the first adaptive law based on the backstepping method to make the first-level system tend to be stable S4, using the event-triggered communication strategy, for the second-level system of the three-degree-of-freedom surface unmanned boat, construct the second Lyapunov function V2, take the derivative of V2 with respect to time to obtain its first-order derivative, and then design the second virtual control signal α2 and the second adaptive law based on the backstepping method. and compound perturbation adaptive law The first Lyapunov function V1 and the second Lyapunov function V2 are combined to obtain the total Lyapunov function that makes the closed loop of the system stable. Combined with the lemma, the controller guarantees that all signals in the closed-loop system are fixed-time semi-globally eventually uniformly bounded; S5. Using the self-triggering communication strategy, for the second-level system of the three-degree-of-freedom surface unmanned boat, the third Lyapunov function V3 is constructed, and the first-order derivative of V3 is obtained by taking the derivative with respect to time. Then, the second virtual control signal α3 and the second adaptive law are designed based on the backstepping method. and compound perturbation adaptive law The first Lyapunov function V1 and the third Lyapunov function V3 are combined to obtain the total Lyapunov function that makes the closed loop of the system stable. Combined with the lemma, the controller guarantees that all signals in the closed-loop system are fixed-time semi-globally eventually uniformly bounded; S6. Combining the triggering conditions of the event / self-triggered communication mechanism, a one-bit encoding and decoding signal transmission mechanism is constructed to prove the robustness of the one-bit encoding and decoding signal transmission mechanism.

2. The tracking control method for a three-degree-of-freedom unmanned surface vehicle according to claim 1, characterized in that: The specific process of step S3 is: S3.

1. Derivative the state equation obtained in step S1 and the error equation obtained in step S2 to obtain the error dynamic equation of the first-level system; S3.

2. For the first-stage system of the three-degree-of-freedom unmanned surface vehicle, construct the first Lyapunov function V1 based on the error dynamic equation of the first-stage system, and differentiate it to obtain the derivative of the first Lyapunov function; S3.

3. Approximate the partial derivatives contained in the unconstrained variables obtained in step S2 using a radial basis function neural network, and then perform scaling using Young's inequality to solve the unknown function in the derivative of the first Lyapunov function. S3.4, based on the backstepping method, the first virtual control signal α1 and the first adaptive law are designed to make the first-level system stable. And the first virtual control signal α1 and the first adaptive law Substituting the derivative of the first Lyapunov function into the equation, we obtain the inequality equation that the first-order system tends to be stable.

3. The tracking control method for a three-degree-of-freedom unmanned surface vehicle according to claim 2, characterized in that: The specific process of step S4 is as follows: S4.

1. Combining the state equation obtained in step S1 and the error equation obtained in step S2, taking the derivative of the error equation to obtain a second-order error dynamic equation; S4.

2. To address the nonlinear factors of unknown dynamics and external time-varying disturbances contained in the three-degree-of-freedom unmanned surface vehicle system, a radial basis function neural network is used for approximation. The approximation error and external time-varying disturbance are combined into a composite disturbance term Θ1. Young's inequality is then used for scaling to solve the unknown function contained in the derivative of the second Lyapunov function. S4.

3. For the second-stage system of the three-degree-of-freedom unmanned surface vehicle, construct a second Lyapunov function V2 based on the error dynamic equation of the second-stage system; S4.4, introduce event-triggered communication mechanism; S4.

5. Derivate the second Lyapunov function V2 to obtain the derivative of the second Lyapunov function; S4.6, design the second virtual control signal α2 and the second adaptive law based on the backstepping method and adaptive law of compound disturbances The second virtual control signal α2 and the second adaptive law and adaptive law of compound disturbances Substitute into the derivative of the second Lyapunov function; S4.

7. Combine the first Lyapunov function V1 and the second Lyapunov function V2 to obtain the total Lyapunov function that makes the closed-loop system stable. For the total Lyapunov function Derivatives are derived so that the derivatives satisfy This shows that all closed-loop signals of the three-degree-of-freedom surface unmanned vehicle system are fixed-time bounded.

4. The tracking control method for a three-degree-of-freedom unmanned surface vehicle according to claim 3, characterized in that: The specific process of step S5 is: S5.

1. Combining the state equation obtained in step S1 and the error equation obtained in step S2, taking the derivative of the error equation to obtain a second-order error dynamic equation; S5.

2. To address the nonlinear factors of unknown dynamics and external time-varying disturbances contained in the three-degree-of-freedom unmanned surface vehicle system, a radial basis function neural network is used for approximation. The approximation error and external time-varying disturbance are combined into a composite disturbance term Θ2. Young's inequality is then used for scaling to solve the unknown function contained in the derivative of the third Lyapunov function. S5.

3. For the second-stage system of the three-degree-of-freedom unmanned surface vehicle, construct the third Lyapunov function V3 based on the error dynamic equation of the second-stage system; S5.4, introduce a self-triggered communication mechanism; S5.

5. Derivate the third Lyapunov function V3 to obtain the derivative of the third Lyapunov function; S5.6, design the second virtual control signal α3 based on the backstepping method, the second adaptive law and adaptive law of compound disturbances The second virtual control signal α3 and the second adaptive law and adaptive law of compound disturbances Substitute into the derivative of the third Lyapunov function; S5.

7. Combine the first Lyapunov function V1 and the third Lyapunov function V3 to obtain the total Lyapunov function that makes the closed-loop system stable. For the total Lyapunov function Derivatives are derived so that the derivatives satisfy This shows that all closed-loop signals of the three-degree-of-freedom surface unmanned vehicle system are fixed-time bounded.

5. The tracking control method for a three-degree-of-freedom unmanned surface vehicle according to claim 4, characterized in that: The specific process of step S6 is as follows: S6.

1. Design a 1-bit encoding and decoding signal transmission mechanism based on the triggering conditions of the event triggering mechanism; S6.

2. Design a 1-bit encoding and decoding signal transmission mechanism based on the triggering conditions of the self-triggering mechanism; S6.

3. Perform robustness analysis on the designed 1-bit encoding and decoding signal transmission mechanism.

6. The tracking control method for a three-degree-of-freedom unmanned surface vehicle according to claim 2, characterized in that: In step S3, the first virtual control signal α1 and the first adaptive law that make the first-level system tend to be stable are set. for: in, χ1,σ 1i ,σ 2i is the design parameter, i=1,2,3; φ1 is the basis function of the first radial basis neural network, is the estimated value of the unknown parameter θ1, z1 is the unrestricted error variable, is the rotation matrix of the system, 7. The tracking control method for a three-degree-of-freedom unmanned surface vehicle according to claim 3, characterized in that: In step S4, the second virtual control signal α2 and the second adaptive law and compound perturbation adaptive law for: in, b i ,χ 2i ,c 1i ,c 2i ,c 3i ,c 4i ,g 1i ,g 2i is the design parameter, i=1,2,3; Δ i (t) is the time-varying design parameter, φ 2i is the basis function of the second radial basis neural network, z 2i is the velocity tracking error, is the unknown parameter θ 2i The estimated value of is the unknown parameter Θ 1i estimated value.

8. The tracking control method for a three-degree-of-freedom unmanned surface vehicle according to claim 4, characterized in that: In step S5, the designed third virtual control signal α3 and the third adaptive law and compound perturbation adaptive law for: in, m i , d 1i ,d 2i ,d 3i ,d 4i ,g 1i ,g 2i is the design parameter, i=1,2,3; is a time-varying design parameter, φ 3i is the basis function of the third radial basis neural network, is the unknown parameter θ 3i The estimated value of is the unknown parameter Θ 2i estimated value.

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