An elastic safety control method for uncertain nonlinear systems

Abstract

The application discloses an elastic safety adaptive fault-tolerant control method and system for an uncertain nonlinear system, aiming at the composite problem of state jump and actuator failure caused by pulse FDI attack, proposes a pulse hybrid dynamic model, and constructs a hybrid regulator function accordingly. Through nonlinear coordinate transformation and the regulator function, the original constrained system can be converted into an unconstrained system, and the safety problem can be converted into a stability analysis problem. The actuator failure factor and deviation are estimated to offset the fault influence, an event-triggered fault-tolerant control law containing adaptive fault compensation is designed, and the communication load is reduced through an event-triggered mechanism. Lyapunov analysis proves that the system meets the safety constraint and is asymptotically stable under the double threats, effectively solves the problem of simultaneously coping with state jump, fault and hard constraint, and significantly enhances the system elasticity and fault tolerance.

Description

Technical Field

[0001] This invention belongs to the field of control science and engineering technology, and particularly relates to an elastic safety adaptive fault-tolerant control method and system for uncertain nonlinear systems. Background Technology

[0002] In modern engineering systems, such as autonomous vehicles, industrial robots, and aerospace vehicles, two crucial performance indicators are typically considered simultaneously: stability and safety. Stability requires the system state to converge to a predetermined equilibrium point or trajectory; while safety requires the system state to remain strictly within a predefined set of safety constraints throughout its operation. For example, a vehicle must strictly avoid collisions with obstacles while driving, and a robotic arm must always be confined to a specific workspace. Designing a controller that simultaneously satisfies asymptotic stability requirements and full-state safety constraints is an extremely complex and challenging task.

[0003] With the rapid development of digital technology, more and more control systems are connecting various components through wired or wireless communication networks, forming cyber-physical systems. While the introduction of communication networks has improved system flexibility, it has also brought the risk of network attacks. Among them, FDI attacks are a typical deception attack, in which attackers tamper with control signals to disrupt system performance. In particular, pulsed FDI attacks typically occur at discrete points in time, causing transient changes in the system state, thus transforming the originally continuous nonlinear system into a complex nonlinear pulse system.

[0004] Existing technologies have significant shortcomings in addressing the aforementioned complex problems. First, at the theoretical level, most mainstream safety control methods (such as control barrier functions or barrier Lyapunov functions) are designed based on the assumption of continuous and smooth evolution of the system state, lacking "prediction" or "buffering" mechanisms for discrete state transitions. When a pulse FDI attack causes an instantaneous state transition, these methods are prone to failure, causing the system to directly cross the safety boundary. Simultaneously, existing adaptive or robust control methods (such as sliding mode control and control systems) primarily focus on the asymptotic convergence or anti-interference capability of the system, but are weak in handling full-state hard constraints, making it difficult to guarantee that the system strictly meets safety limits at every moment during transient processes subjected to large-amplitude pulse disturbances.

[0005] At the engineering implementation and resource level, to simultaneously handle hard constraints and uncertainties, some existing technologies (such as Model Predictive Control, MPC) often require complex online optimization calculations, placing extremely high demands on the computing power of the controller hardware, making it difficult to run in real time on resource-constrained embedded devices. Moreover, to maintain high-performance control, these methods typically rely on high-frequency control signal updates, which not only consumes significant communication bandwidth but also increases the risk of eavesdropping or interference by attackers, leading to an irreconcilable contradiction between computational and communication resource consumption and system security. Therefore, there is an urgent need for a resilient safety control method that can uniformly handle state impulse transitions, parameter uncertainties, and full-state safety constraints, while consuming low computational and communication resources. Furthermore, in practical engineering, actuators, as core components of physical systems, are prone to aging, wear, and even partial failure after long-term operation. Such failures typically manifest as a decrease in control performance and zero-point drift (additive bias). Existing technologies (such as passive robust control) often assume that the lower bound of the fault parameters is known and design high-gain controllers based on worst-case scenarios. However, this conservative design leads to wasted control energy and even unmodeled dynamics when the fault is minor or non-faulty. More advanced adaptive fault-tolerant control can estimate unknown fault parameters online and perform accurate compensation, but how to organically combine it with hybrid regulator technology for handling hard state constraints and impulse control theory for handling network attacks remains an unsolved problem. Summary of the Invention

[0006] To address the aforementioned problems, the present invention aims to provide an elastic, safe, adaptive, fault-tolerant control method for uncertain nonlinear systems. This method can solve the problems of existing technologies in effectively handling state transitions and balancing full-state safety constraints and stability when facing FDI attacks and actuator failures.

[0007] The technical solution provided by this invention is: an elastic, safe, adaptive, fault-tolerant control method for uncertain nonlinear systems, comprising the following steps: Step S1: Establish a nonlinear system model of the controlled object and a set of preset safety constraints. The model includes a nonlinear affine dynamics equation with parameter uncertainty and input gain uncertainty, and a composite fault model characterizing partial failure of the actuator and additive deviation. Step S2: Construct a hybrid regulator function, which is used to detect whether the system state is operating within the set of safety constraints; Step S3: Construct a nonlinear state transformation based on the hybrid regulator function, and introduce unconstrained intermediate state variables; Step S4: Estimate the real-time failure factor and deviation fault amplitude of the actuator; Step S5: Design an adaptive compensation-based elastic safety fault-tolerant controller. The controller constructs an inverse compensation term based on the real-time failure factor of the actuator and the online estimate of the deviation fault amplitude, and calculates the control signal by combining the intermediate state variables generated by the hybrid regulator function, and performs Lyapunov function analysis based on this. Step S6: Based on the event triggering mechanism, monitor the measurement error between the controller's calculated signal and the actual actuator's received signal in real time. When the measurement error exceeds a preset threshold, update and send a new control signal to the actuator.

[0008] Preferably, the nonlinear system model of the controlled object is: , where x∈R n Let u ∈ R be the system state vector. n For control input, θ is an uncertain parameter vector. and For system functions, ∈ (0, 1] is the time-varying failure factor of the actuator. This is an actuator additive deviation fault; The control input under a pulse FDI attack is: ,in For the attack moment, This is a false signal injection.

[0009] Preferably, the hybrid regulator function is: ,in A function to describe the set of security constraints. For safety boundary constants, For pre-designed parameters, It is a smoothing function.

[0010] Preferably, the nonlinear state transformation is as follows: when hour when hour in, It is a non-decreasing function. and These are parameters to be set. It is a vector consisting entirely of 1s.

[0011] Preferably, the parameter constraints constructed based on Lyapunov stability theory further include: To construct the Lyapunov function and ensure the convergence of V(t), the system parameters must satisfy the following inequality conditions: in Here, b represents the upper bound of the system gain, and b is the attack signal strength coefficient. To adjust the parameters, For controller gain, This is the lower bound of the attack interval; Select based on the inequality conditions and The value of .

[0012] Preferably, the resilient safety fault-tolerant controller includes a parameter adaptive update law and a control law, wherein the parameter adaptive update law is: The control law of the elastic safety controller for: in, and These are the online estimates of the failure factor and the deviation failure, respectively. For adaptive gain; The coefficients of the intermediate state variable m are determined by step S4. For robustness term gain, This represents the boundary of a nonlinear function.

[0013] Preferably, the triggering condition of the event triggering mechanism is: in, β is the previous trigger time, β is the trigger threshold parameter, and m is the current intermediate state variable.

[0014] Preferably, the spurious injection signal under the pulsed FDI attack Satisfies the Lipschitz continuity condition: And the system function Satisfying boundedness conditions Where b is the attack strength constant, and These are the lower and upper bounds of the control gain, respectively.

[0015] Based on the same concept, the present invention also provides a resilient safety control system for uncertain nonlinear systems, comprising: The model building module is used to build a nonlinear system model of the controlled object and a set of preset safety constraints. The model includes a nonlinear affine dynamics equation with parameter uncertainty and input gain uncertainty, and a composite fault model characterizing partial failure of actuators and additive deviation. A function construction module is used to construct a hybrid regulator function, which is used to detect whether the system state is operating within the set of safety constraints; A state transformation construction module is used to construct nonlinear state transformations based on the hybrid regulator function, introducing unconstrained intermediate state variables; The constraint construction module is used to estimate the real-time failure factor and deviation fault amplitude of the actuator; The controller design module is used to design an adaptive compensation-based elastic safety fault-tolerant controller. The controller constructs an inverse compensation term based on the real-time failure factor of the actuator and the online estimate of the deviation fault amplitude, and calculates the control signal by combining the intermediate state variables generated by the hybrid regulator function. Based on this, a Lyapunov function is constructed for stability analysis. The monitoring module is used to monitor the measurement error between the controller's calculated signal and the actual actuator's received signal in real time based on an event-triggered mechanism. When the measurement error exceeds a preset threshold, it updates and sends a new control signal to the actuator.

[0016] Based on the same concept, the present invention also provides a controller, including at least one processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, it implements the elastic safety adaptive fault-tolerant control method for uncertain nonlinear systems described above.

[0017] Based on the same concept, the present invention also provides a readable storage medium storing a processing program, which, when executed by a processor, implements the elastic safety adaptive fault-tolerant control method for uncertain nonlinear systems described above.

[0018] Because the present invention adopts the above technical solution, it has the following advantages and positive effects compared with the prior art: 1. Existing technologies largely focus on DoS attacks that cause communication blockages, neglecting more covert and destructive data tampering behaviors. This invention addresses this weakness by establishing a pulsed FDI attack model and transforming it into a pulsed hybrid system that causes instantaneous state jumps. Compared to traditional methods that treat attacks merely as external bounded interference, this invention accurately characterizes the severe instantaneous impact of malicious attacks on the system's physical state. This allows the control system to maintain stable operation even under extreme attack scenarios that lead to abrupt state changes, significantly enhancing the survivability and robustness of nonlinear cyber-physical systems. Furthermore, with an adaptive parameter estimation mechanism, the control gain can be adjusted online to maintain system performance when an actuator experiences an unknown fault.

[0019] 2. To address the problem that traditional obstacle functions are prone to failure or controller singularity when handling abrupt state changes, this invention innovatively constructs a hybrid regulator function. This function combines a smoothing segmentation mechanism with an increasing constraint coefficient, inheriting not only the advantage of obstacle functions in strictly limiting state boundaries but also possessing "elastic tolerance" for state jumps. When an attack causes an instantaneous state change, the hybrid regulator can absorb the impact through its own increasing characteristics, preventing the system from collapsing due to instantaneous boundary overflow, thereby improving the system's dynamic adaptability while ensuring absolute safety. 3. This invention proposes a robust control law based on intermediate state transformation and an event-triggered communication mechanism. By transforming the full-state constraint problem into a boundedness problem of an intermediate dynamic system, complex online optimization calculations are avoided. Simultaneously, the designed event-triggered mechanism can adaptively adjust the control signal update frequency according to the ratio of measurement error to the current safety margin (intermediate state norm): reducing communication load when the safety margin is sufficient and automatically encrypting control when attacked or approaching the boundary, thus achieving dual protection of system security and asymptotic stability within limited communication bandwidth. Attached Figure Description

[0020] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a trajectory of the system state under safety constraints in one embodiment; Figure 3 This is a curve showing the change of the system state norm trajectory under safety constraints in one embodiment. Detailed Implementation

[0021] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The advantages and features of the present invention will become clearer from the following description and claims. It should be noted that the drawings are all in a very simplified form and use non-precise ratios, and are only used to facilitate and clarify the illustration of the embodiments of the present invention.

[0022] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0023] First Embodiment This embodiment provides a resilient, safe, adaptive, fault-tolerant control method for uncertain nonlinear systems, including the following steps: Step S1: Establish a nonlinear system model of the controlled object and a set of preset safety constraints. The model includes a nonlinear affine dynamics equation with parameter uncertainty and input gain uncertainty, and a composite fault model characterizing partial failure of the actuator and additive deviation. Establish a nonlinear system model of the controlled object, and establish a timing model of a pulse-type FDI attack that causes instantaneous changes in the system state.

[0024] Step S2: Construct a hybrid regulator function, which is used to detect whether the system state is operating within the set of safety constraints; Step S3: Construct a nonlinear state transformation based on the hybrid regulator function, introduce unconstrained intermediate state variables, and transform the original controlled nonlinear system with hard state constraints into an unconstrained intermediate dynamic system. Step S4: Estimate the real-time failure factor and deviation fault amplitude of the actuator; Step S5: Design an adaptive compensation-based elastic safety fault-tolerant controller. The controller constructs an inverse compensation term based on the real-time failure factor of the actuator and the online estimate of the amplitude of the deviation fault to offset the effects of the actuator efficiency decline and deviation fault. It also calculates the control signal by combining the intermediate state variables generated by the hybrid regulator function and constructs a Lyapunov function based on this for stability analysis. Step S6: Based on the event triggering mechanism, monitor the measurement error between the controller's calculated signal and the actual actuator's received signal in real time. When the measurement error exceeds a preset threshold, update and send a new control signal to the actuator.

[0025] This invention establishes a pulsed FDI attack model and transforms it into a pulsed hybrid system that causes instantaneous state jumps. Compared to traditional methods that treat attacks merely as external bounded disturbances, this invention can accurately characterize the severe instantaneous impact of malicious attacks on the system's physical state. This allows the control system to maintain stable operation even under extreme attack scenarios that lead to abrupt state changes, significantly enhancing the survivability and robustness of nonlinear cyber-physical systems. Furthermore, with the addition of an adaptive parameter estimation mechanism, the control gain can be adjusted online to maintain system performance when an actuator experiences an unknown failure.

[0026] Preferably, the nonlinear system model of the controlled object is: , where x∈R n Let u ∈ R be the system state vector. n For control input, θ∈U R nw Let U be an uncertain parameter vector, and U be a compact set containing the origin. and For a fully smooth nonlinear function, ∈ (0, 1] is the time-varying failure factor (efficiency coefficient) of the actuator. This is an actuator additive deviation fault; Among them, the control input that actually acts on the system Commands issued by the controller The relationship between them is: This invention assumes and Since these are unknown parameters, they need to be estimated online through subsequent steps. Substituting the fault model into the system equations, we obtain the above closed-loop system model that includes both fault and parameter uncertainties.

[0027] To account for the uncertainty of system parameters, the following assumption is made: there exists a known positive scalar. and This makes it possible for all The input gain function satisfies: .

[0028] Meanwhile, considering that the sensor-actuator network is subjected to a pulsed FDI attack, the control input under a pulsed FDI attack is: ,in For the attack moment, This is a false signal injection.

[0029] Preferably, the spurious injection signal under the pulsed FDI attack Satisfies the Lipschitz continuity condition: And the system function Satisfying boundedness conditions Where b is the attack strength constant, and These are the lower and upper bounds of the control gain, respectively.

[0030] To account for the uncertainty of system parameters, the following assumptions are made: There exists a known positive scalar. and Such that for all θ∈U, the input gain function satisfy: .

[0031] Meanwhile, considering that the sensor-actuator network is subjected to a pulsed FDI attack, the control input after the attack is described as follows: This causes the closed-loop system state to be affected at the moment of the attack. A sudden change occurs: .

[0032] To handle state constraints and tolerate jumps caused by attacks, the hybrid regulator function is preferably: ,in A function to describe the set of security constraints. For safety boundary constants, These are pre-designed parameters (constants). It is a class of smooth functions that satisfy the condition 0 when the independent variable approaches infinity and 1 when the independent variable is less than or equal to 0.

[0033] Furthermore, a non-decreasing smooth piecewise function is introduced. To handle singularities near the origin: in and These are parameters related to the geometric characteristics of the safety zone.

[0034] The hybrid regulator function satisfies the growth constraint property: at the attack time... There is a growth coefficient , so that: .

[0035] A nonlinear coordinate transformation mechanism based on a hybrid regulator function is used to introduce an intermediate state variable m and perform coordinate transformation.

[0036] Preferably, the nonlinear state transformation is as follows: when hour in, It is a vector of all 1s. To adjust the gain. At the moment of the FDI attack, the transition relationship of the intermediate state m is determined by the transition relationship of the original state x: when hour in, It is a non-decreasing function. and These are parameters to be set. It is a vector consisting entirely of 1s.

[0037] By using this transformation, as long as the intermediate variable m is bounded, it can be deduced that the original state x always lies within the safe set.

[0038] Preferably, the parameter constraints constructed based on Lyapunov stability theory further include: To construct the Lyapunov function and ensure the convergence of V(t), the system parameters must satisfy the following inequality conditions: in Here, b represents the upper bound of the system gain, and b is the attack signal strength coefficient. To adjust the parameters, For controller gain, This is the lower bound of the attack interval; Select based on the inequality conditions and The value of .

[0039] To ensure the stability of the closed-loop system and obtain fault parameter estimates, a Lyapunov function incorporating parameter estimation errors is constructed: in, , The preset adaptive gain constant is used; the parameter estimation error is defined as... and Assuming the unknown physical fault parameters change slowly, then we have .

[0040] Taking the time derivative of the above Lyapunov function, we get: Will include actuator failure models Substitute the intermediate state dynamic equation into the above equation. Assume the known nonlinear terms and robust compensation terms of the system are combined as follows: The input coefficient term is Then we have: Using the relationship between true parameters and estimated values and By replacing the unknown parameters, expanding and reorganizing the formula, we can separate out the terms related to the estimation error: Factoring out common factors and Rewrite the above derivative equation: To eliminate the impact of unknown parameter estimation errors on system stability, it is mandatory to include and The bracketed terms are always equal to zero, from which the adaptive update law of actuator failure factor and additive bias can be directly derived: Substituting the above adaptive law back In the expression, the error terms are completely canceled out, and the derivative of the Lyapunov function simplifies to: By combining a pre-designed fault-tolerant control law based on estimates, it is possible to ensure... (Among them, design parameters) ), thereby ensuring Based on Lyapunov's stability theorem and Barbalat's lemma, all signals of the closed-loop system are bounded, and the intermediate state $m$ asymptotically converges to zero. This proves the asymptotic stability of the proposed fault-tolerant control strategy under the premise of ensuring that the system state satisfies the safety constraints.

[0041] In addition, in order to ensure Negative definite convergence leads to the following two conclusions: 1. Stability Parameter Constraints: To offset the energy impact of a pulse attack, the system parameters must satisfy the following inequalities: in For controller convergence gain, This represents the minimum attack interval. Regarding the constraint on attack frequency: where... This is the minimum interval between pulse attacks. This condition indicates the convergence rate of the controller. It must be sufficient to offset the divergence trend caused by the attack. Regarding the constraint on attack strength: the upper limit of the energy gain brought by the attack should not exceed the growth tolerance of the hybrid regulator function. Based on the above inequality, select a control gain that satisfies the conditions. and trigger coefficient β, to ensure Monotonically decreasing or bounded. This mechanism ensures that the control signal is updated only when the measurement error exceeds a certain proportion of the intermediate state norm, thus maintaining control performance under conditions of limited communication resources.

[0042] Based on satisfying the constraints in step 4, further eliminate unknown faults. and To address the impact of [the pandemic], an adaptive fault-tolerant control strategy is designed.

[0043] Preferably, the resilient safety fault-tolerant controller includes a parameter adaptive update law and a control law, wherein the parameter adaptive update law is: in, and These are the real-time estimates of the failure factor and the deviation, respectively. For adaptive learning rate, For the intermediate variable coefficients related to coordinate transformation, For auxiliary control signals.

[0044] Parameter estimates obtained through real-time calculation Design the control law for a flexible safety controller.

[0045] The control law of the elastic safety controller for: in, and These are the online estimates of the failure factor and the deviation failure, respectively. For adaptive gain; The coefficients of the intermediate state variable m are determined by step S4. For trigger coefficient, This represents the boundary of a nonlinear function.

[0046] Through real-time adjustments , This controller ensures that the control torque actually applied to the system is maintained at the desired level.

[0047] To conserve communication resources, an event-triggered mechanism based on measurement error is designed. The measurement error is defined. Design event triggering rules.

[0048] Preferably, the triggering condition of the event triggering mechanism is: in, β is the trigger threshold parameter, m is the current intermediate state variable, and β is the previous trigger time. The control signal is only triggered to update when the measurement error exceeds a certain proportion of the intermediate state norm.

[0049] Under the premise of satisfying the parameter conditions described in step 4, run the closed-loop system and prove the safety and stability of the system based on Lyapunov stability theory: 1. For any initial state ∈R, the corresponding intermediate state Bounded.

[0050] 2. During non-attack periods ( Since the adaptive fault-tolerant controller (step 5) can effectively offset actuator failures and uncertainties, and the event triggering mechanism (step 6) ensures that the measurement error is bounded, the derivative of the Lyapunov function along the system trajectory satisfies This indicates that the energy of the intermediate system exhibits an exponential decay trend over a continuous interval.

[0051] 3. When a pulsed FDI attack occurs ( The system state undergoes a transient change. Based on the growth constraint characteristics of the hybrid regulator function in step 2, the Lyapunov function satisfies: That is, the energy jump caused by the attack is limited to a certain coefficient. Inside.

[0052] 4. Based on the above analysis, as long as the system parameters meet the attack frequency constraint in step 4, it can be guaranteed that... It gradually approaches zero over time. Therefore, we can conclude... Security: Boundedness means Bounded, thus guaranteeing the system state Always stay away from the safety boundary ,Right now No boundary crossing occurred.

[0053] Asymptotic stability: This means the intermediate state The state of the original system can be deduced by inversely based on the coordinate transformation relationship. This achieves asymptotic stability of the closed-loop system.

[0054] Compared with the prior art, the present invention has the following beneficial effects: 1. Significantly Enhanced Realism and Resilience of Attack Modeling: Existing technologies largely focus on DoS attacks that cause communication blockages, neglecting more covert and destructive data tampering behaviors. This invention addresses this weakness by establishing a pulsed FDI attack model and transforming it into a pulsed hybrid system that causes instantaneous state jumps. Compared to traditional methods that treat attacks merely as external bounded disturbances, this invention accurately characterizes the severe instantaneous impact of malicious attacks on the system's physical state. This allows the control system to maintain stable operation even under extreme attack scenarios that lead to abrupt state changes, significantly enhancing the survivability and robustness of nonlinear cyber-physical systems. Furthermore, with the addition of an adaptive parameter estimation mechanism, the control gain can be adjusted online to maintain system performance when an actuator experiences an unknown failure.

[0055] 2. Enhanced Flexibility and Reliability of the State Constraint Mechanism: Addressing the issue of traditional barrier functions easily failing or causing controller singularities when handling abrupt state changes, this invention innovatively constructs a hybrid regulator function. This function combines a smoothing segmentation mechanism with an increasing constraint coefficient, inheriting not only the advantage of barrier functions in strictly limiting state boundaries but also possessing "elastic tolerance" for state jumps. When an attack causes a sudden change in state, the hybrid regulator can absorb the impact through its own growth characteristics, preventing the system from collapsing due to instantaneous boundary overflows, thereby improving the system's dynamic adaptability while ensuring absolute safety.

[0056] 3. Dynamic Co-optimization of Communication Resources and Control Performance: This invention proposes a robust control law based on intermediate state transformation and an event-triggered communication mechanism. By transforming the full-state constraint problem into a boundedness problem of an intermediate dynamic system, complex online optimization calculations are avoided. Simultaneously, the designed event-triggered mechanism can adaptively adjust the control signal update frequency according to the ratio of measurement error to the current safety margin (intermediate state norm): reducing communication load when the safety margin is sufficient, and automatically encrypting control when attacked or approaching the boundary, thus achieving dual protection of system security and asymptotic stability within limited communication bandwidth.

[0057] To verify the effectiveness of the proposed adaptive fault tolerance with state constraints under pulsed FDI attacks, this embodiment constructs a specific second-order nonlinear system for numerical simulation experiments.

[0058] Simulation results are as follows Figures 2-3 As shown, the specific steps include: Step 1: Establish the nonlinear dynamic model and state constraints of the simulation system.

[0059] Choosing a classic nonlinear oscillating system as the controlled object, its system dynamics equations are as follows: in, For system status, To control the input. Uncertain parameters are set as follows: Input gain Its nominal value is 1.

[0060] Fault model setting: efficiency factor This represents an actuator failure of 20%. The additive bias is... This invention assumes that both of these are unknown and need to be estimated online.

[0061] Define the system's full-state safety constraints as a circular region: That is, the safety threshold The initial state is chosen as follows: ,satisfy This means that the system is initially within the safe zone.

[0062] Step 2: Configure the hybrid regulator function, controller parameters, and fault-tolerant adaptive parameters.

[0063] According to the method described in this invention, a hybrid regulator function is constructed. Select parameters Adjusting the gain Set geometric parameters And construct the corresponding smooth piecewise function. The controller gain is set to... The trigger parameter β is calculated based on stability conditions. An adaptive gain is set. .

[0064] Step 3: Set the pulse-type FDI attack model and timing parameters.

[0065] The model of the false data signal injected by the attacker into the communication channel is defined as follows: Based on the assumption, the attack signal satisfies the Lipschitz condition, and the intensity coefficient... Set the minimum interval between pulse attacks. During the simulation time interval The system is designed to launch attacks at random times (e.g., seven pulse attacks in total), with each attack causing a momentary change in the system state.

[0066] Step 4: Perform numerical simulation and analyze the system's security (corresponding to...) Figure 2 ).

[0067] With the above parameter configuration, run the closed-loop system for simulation. Figure 1The phase plane trajectories of system states x1 and x2 are shown. Simulation results show that although the system suffered multiple pulse-type FDI attacks during operation, causing momentary discontinuities and "jumps" in the state trajectory, thanks to the growth constraint characteristics of the hybrid regulator function, the system state trajectory was always strictly limited to a radius of [missing information]. Within the circular safe zone, no boundary violations occurred. This verifies the invention's ability to protect state constraints under extreme attacks.

[0068] Step 5) Analyze the convergence and stability of the system (corresponding to...) Figure 3 ).

[0069] Figure 2 The evolution of the system's state norm over time is illustrated. It can be seen that, in arrive During the process, whenever an FDI attack occurs (corresponding moment in the figure), the state norm experiences a momentary surge. However, the robust controller responds quickly, pulling the state back to the convergence trajectory. Over time, both system states x1 and x2 exhibit a trend of oscillatory decay, eventually converging to near the origin around t=10s. This demonstrates that the control law designed in this invention can effectively counteract the energy injection caused by the attack, achieving asymptotic stability of the closed-loop system.

[0070] Step 6: Verify the overall conclusions.

[0071] Based on the above Figure 2 and Figure 3 Based on the simulation data, the following comprehensive conclusions are drawn: 1. Strict Guarantee of Hard Constraints on State: Simulation results clearly show that under extreme conditions where a pulsed FDI attack causes a significant instantaneous change in the system state, the hybrid regulator function proposed in this invention, with its unique growth constraint characteristics, can effectively "absorb" the impact energy brought by the attack. The system state trajectory is always confined within the preset safety set, and there is no violation of physical constraints at any time. This verified the reliability of the method in safety-critical systems.

[0072] 2. Robustness to Attacks and Uncertainty: Although attacks cause sudden increases in the state norm at random moments, the closed-loop system does not diverge. The robust control law responds quickly and suppresses the accumulation of errors, forcing the system state to return to its convergent trajectory after a brief fluctuation, and eventually asymptotically approaching the equilibrium point (origin). This confirms the effectiveness of the designed controller gain. and parameters Satisfying the stability constraints can effectively offset the uncertain parameter θ and spurious data signals. The impact.

[0073] 3. Verification of fault tolerance under actuator failure: Compared with traditional methods without adaptive compensation, this invention introduces an adaptive law, which enables online automatic adjustment of control gain and bias even when the actuator performance is unknown to have decreased. Simulation results show that the system state did not become unstable due to the sudden failure, verifying that this method has significant active fault tolerance capability for actuator physical failures.

[0074] 4. Compared to traditional nonlinear control strategies that do not employ this method (which typically cannot handle constraint violations caused by state transitions).

[0075] 5. This invention successfully solves the problem of security stabilization of nonlinear systems under network attack environments through a collaborative mechanism of "hybrid regulator + event triggering + robust fault-tolerant control". While ensuring that the system does not crash or go out of bounds, it achieves the expected control performance.

[0076] The present invention also provides a resilient safety control system for uncertain nonlinear systems, comprising: The model building module is used to build a nonlinear system model of the controlled object and a set of preset safety constraints. The model includes a nonlinear affine dynamics equation with parameter uncertainty and input gain uncertainty, and a composite fault model characterizing partial failure of actuators and additive deviation. A function construction module is used to construct a hybrid regulator function, which is used to detect whether the system state is operating within the set of safety constraints; A state transformation construction module is used to construct nonlinear state transformations based on the hybrid regulator function, introducing unconstrained intermediate state variables; The constraint construction module is used to estimate the real-time failure factor and deviation fault amplitude of the actuator; The controller design module is used to design an adaptive compensation-based elastic safety fault-tolerant controller. The controller constructs an inverse compensation term based on the real-time failure factor of the actuator and the online estimate of the deviation fault amplitude, and calculates the control signal by combining the intermediate state variables generated by the hybrid regulator function. Based on this, a Lyapunov function is constructed for stability analysis. The monitoring module is used to monitor the measurement error between the controller's calculated signal and the actual actuator's received signal in real time based on an event-triggered mechanism. When the measurement error exceeds a preset threshold, it updates and sends a new control signal to the actuator.

[0077] The present invention also provides a controller, including at least one processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, it implements the elastic safety adaptive fault-tolerant control method for uncertain nonlinear systems as described above.

[0078] Based on the same concept, the present invention provides an electronic device, comprising: The memory is used to store the processing program; A processor, which, when executing the processing program, implements the elastic security control method for a state-constrained nonlinear system under pulsed FDI attack as described above.

[0079] Based on the same concept, the present invention provides a readable storage medium storing a processing program, which, when executed by a processor, implements the elastic security control method for a state-constrained nonlinear system under pulsed FDI attack as described above.

[0080] If the elastic security control method for a state-constrained nonlinear system under a pulsed FDI attack is implemented in the form of program instructions and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this embodiment, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in software. This computer software is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this disclosure. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0081] Those skilled in the art will readily understand that, for the sake of convenience and brevity, the specific identification content executed by the systems and devices described above can be referred to the corresponding processes in the foregoing method embodiments. The embodiments of the present invention have been described in detail above with reference to the accompanying drawings; however, the present invention is not limited to the above embodiments. Even if various modifications are made to the present invention, if these modifications fall within the scope of the claims of the present invention and their equivalents, they shall still fall within the protection scope of the present invention.

Claims

1. A method for elastic, safe, adaptive, fault-tolerant control of uncertain nonlinear systems, characterized in that, Includes the following steps: Step S1: Establish a nonlinear system model of the controlled object and a set of preset safety constraints. The model includes a nonlinear affine dynamics equation with parameter uncertainty and input gain uncertainty, and a composite fault model characterizing partial failure of the actuator and additive deviation. Step S2: Construct a hybrid regulator function, which is used to detect whether the system state is operating within the set of safety constraints; Step S3: Construct a nonlinear state transformation based on the hybrid regulator function, and introduce unconstrained intermediate state variables; Step S4: Estimate the real-time failure factor and deviation fault amplitude of the actuator; Step S5: Design an adaptive compensation-based elastic safety fault-tolerant controller. The controller constructs an inverse compensation term based on the real-time failure factor of the actuator and the online estimate of the deviation fault amplitude, and calculates the control signal by combining the intermediate state variables generated by the hybrid regulator function. Based on this, a Lyapunov function is constructed and stability analysis is performed. Step S6: Based on the event triggering mechanism, monitor the measurement error between the controller's calculated signal and the actual actuator's received signal in real time. When the measurement error exceeds a preset threshold, update and send a new control signal to the actuator.

2. The elastic safety adaptive fault-tolerant control method for uncertain nonlinear systems according to claim 1, characterized in that, The nonlinear system model of the controlled object is as follows: , where x∈R n Let u ∈ R be the system state vector. n For control input, θ is an uncertain parameter vector. and For system functions, ∈ (0, 1] is the time-varying failure factor of the actuator. This is an actuator additive deviation fault; The control input under a pulse FDI attack is: ,in For the attack moment, This is a false signal injection.

3. The elastic safety adaptive fault-tolerant control method for uncertain nonlinear systems according to claim 1. Its characteristic is that... The constructed hybrid regulator function is as follows: ,in A function to describe the set of security constraints. For safety boundary constants, For pre-designed parameters, It is a smoothing function.

4. The elastic safety adaptive fault-tolerant control method for uncertain nonlinear systems according to claim 1, characterized in that, The nonlinear state transformation is: when hour when hour in, It is a non-decreasing function. and These are parameters to be set. It is a vector consisting entirely of 1s.

5. The elastic safety adaptive fault-tolerant control method for uncertain nonlinear systems according to claim 1, characterized in that, The parameter constraints based on Lyapunov stability theory further include: To construct the Lyapunov function and ensure the convergence of V(t), the system parameters must satisfy the following inequality conditions: in Here, b represents the upper bound of the system gain, and b is the attack signal strength coefficient. To adjust the parameters, For controller gain, This is the lower bound of the attack interval; Select based on the inequality conditions and The value of .

6. The elastic safety adaptive fault-tolerant control method for uncertain nonlinear systems according to claim 1, characterized in that, The resilient safety fault-tolerant controller includes a parameter adaptive update law and a control law. The parameter adaptive update law is as follows: The control law of the elastic safety controller for: in, and These are the online estimates of the failure factor and the deviation failure, respectively. For adaptive gain; For the coefficients of the intermediate state variable m, Determined by step S4, For robustness term gain, This represents the boundary of a nonlinear function.

7. The elastic safety adaptive fault-tolerant control method for uncertain nonlinear systems according to claim 1, characterized in that, The triggering conditions for the event triggering mechanism are as follows: in, β is the previous trigger time, β is the trigger threshold parameter, and m is the current intermediate state variable.

8. The elastic safety adaptive fault-tolerant control method for uncertain nonlinear systems according to claim 2, characterized in that, The spurious injection signal under the pulse FDI attack Satisfies the Lipschitz continuity condition: And the system function Satisfying boundedness conditions Where b is the attack strength constant, and These are the lower and upper bounds of the control gain, respectively.

9. A resilient safety control system for uncertain nonlinear systems, characterized in that, include: The model building module is used to build a nonlinear system model of the controlled object and a set of preset safety constraints. The model includes a nonlinear affine dynamics equation with parameter uncertainty and input gain uncertainty, and a composite fault model characterizing partial failure of actuators and additive deviation. A function construction module is used to construct a hybrid regulator function, which is used to detect whether the system state is operating within the set of safety constraints; A state transformation construction module is used to construct nonlinear state transformations based on the hybrid regulator function, introducing unconstrained intermediate state variables; The constraint construction module is used to estimate the real-time failure factor and deviation fault amplitude of the actuator; The controller design module is used to design an adaptive compensation-based elastic safety fault-tolerant controller. The controller constructs an inverse compensation term based on the real-time failure factor of the actuator and the online estimate of the deviation fault amplitude, and calculates the control signal by combining the intermediate state variables generated by the hybrid regulator function. Based on this, a Lyapunov function is constructed for stability analysis. The monitoring module is used to monitor the measurement error between the controller's calculated signal and the actual actuator's received signal in real time based on an event-triggered mechanism. When the measurement error exceeds a preset threshold, it updates and sends a new control signal to the actuator.

10. A controller, characterized in that, It includes at least one processor and a memory, the memory storing a computer program that, when executed by the processor, implements the elastic safety adaptive fault-tolerant control method for uncertain nonlinear systems as described in any one of claims 1 to 8.

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