State-constrained inverse robust control method, system and medium for perturbed strict-feedback system

Abstract

The present application relates to the technical field of nonlinear system control, and discloses a state-constrained inverse robust control method for a disturbed strict feedback system; the method first establishes a disturbed and full-state-constrained strict feedback system model, and uses a logarithmic barrier function to equivalently transform the model into an unconstrained system; unknown nonlinear dynamics are online approximated by a radial basis function neural network, a virtual controller and an adaptive iterative adjustment function are designed based on a backstepping method to estimate network weights and unknown parameters of the system; then, an inverse robust optimal controller is designed and a minimum cost functional is constructed in combination with a control Lyapunov function and a relaxed inverse optimal condition. The present application eliminates the constraints of a traditional barrier function, reduces design conservatism, does not require solving of an HJB equation and an accurate system model, can adaptively compensate for non-matching disturbances and unknown dynamics, controls input smoothness without singular points, and is suitable for control of equipment such as a mechanical arm and an aero-engine while meeting state constraints, robust stabilization, high-precision tracking and control optimization.

Description

Technical Field

[0001] This invention relates to the field of nonlinear system control technology, specifically to a state-constrained inverse robust control method, system, and medium for a disturbed strict feedback system. Background Technology

[0002] Strictly feedback nonlinear systems, due to their cascaded structure characteristics, are widely used in the modeling and control of engineering equipment such as robotic arms, aero-engine compressors, ship autopilots, and hypersonic vehicles. In actual operation, these systems are susceptible to parameter uncertainties, unknown nonlinearities, and unmatched external disturbances. They are also constrained by physical limits, safety regulations, and operational envelopes, exhibiting full-state dynamic constraints. Improperly designed control strategies can easily lead to system performance degradation, exceeding state limits, or even instability.

[0003] Currently, control methods for strictly feedback nonlinear systems are mainly divided into two categories: constraint handling and optimal control. In constraint handling, the Barrier Lyapunov function (BLF) is the mainstream method, but it has inherent drawbacks: First, it imposes strict feasibility conditions on the intermediate virtual controller, requiring it to always be within the time-varying constraint boundary, increasing design complexity and conservatism, and even leading to infeasibility when constraints are tight or change rapidly; second, it often assumes that the constraint function is positive or negative, making it unable to handle common asymmetric and zero-crossing time-varying constraints in practice; and third, it only focuses on stabilization and constraint satisfaction, neglecting the optimality of the control variable.

[0004] In terms of optimal control, traditional methods such as Linear Quadratic Gaussian (LQG), Adaptive Dynamic Programming (ADP), and H∞ optimal control require solving Hamiltonian-Jacobi-Belman (HJB) or Hamiltonian-Jacobi-Isaacs (HJI) equations. However, due to the curse of dimensionality and dependence on exact system models, these methods are computationally infeasible for general nonlinear systems and are difficult to combine with strict state constraint mechanisms. Inverse optimal control, as an alternative, does not require direct solution of the HJB equations. Instead, it designs a controller based on the control Lyapunov function (CLF) and then constructs the cost function that minimizes it, which can balance stability and performance optimization. However, existing inverse optimal control schemes are mostly for unconstrained scenarios or can only handle finite constraints, making them difficult to apply to strict feedback systems with full-state dynamic constraints and strong uncertainties. At the same time, when using neural networks to approximate unknown nonlinearities, parameter uncertainties and disturbances can easily make it difficult to satisfy the standard inverse optimality condition, which limits its engineering applications.

[0005] In summary, existing technologies cannot simultaneously achieve infeasibility handling of general time-varying asymmetric state constraints, efficient compensation for unknown nonlinearities and disturbances, inverse optimal stabilization without the need to solve HJB equations, and preset transient / steady-state tracking performance. A unified control strategy is urgently needed to fill this technological gap. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention proposes a state-constrained inverse robust control method for disturbed strict feedback systems. This method solves the problems of conservatism in state constraint handling, computational complexity of optimal control, and inefficiency of uncertainty compensation in existing control methods. It achieves a unified approach to strictly satisfying state constraints, robust stabilization, high-precision trajectory tracking, and inverse optimal optimization of control quantities in disturbed strict feedback systems.

[0007] A state-constrained inverse robust control method for a disturbed strict feedback system is implemented through the following steps:

[0008] S1: Establish a rigorous feedback nonlinear system model subject to unmatched external disturbances and full-state time-varying dynamic constraints;

[0009] The strictly feedback nonlinear system is:

[0010]

[0011] (1)

[0012]

[0013] in, Let i be the i-dimensional state sub-vector formed by the first i states of the system. for System No. Item state vector, This is an unmatched external disturbance. Let n be the n-dimensional full-state vector consisting of all n states of the system. For all real numbers, To control the input gain term, This is the external disturbance gain term. For the nth unmatched external disturbance, For system control input, For system output, , , For a smooth, unknown, nonlinear function, Moreover, times change. For a smooth, known nonlinear function;

[0014] The system satisfies time-varying dynamic constraints in all states. ,in , These are the upper and lower constraint functions that are continuously bounded for the i-th state.

[0015] The system satisfies the following assumptions: disturbance Continuous and uniformly bounded, that is , It is an unknown positive constant; it exists. function and uncertain constants , making ; Expected tracking signal for The function represents the target value of the system, and its first derivative. Second derivative Available.

[0016] S2: Construct a logarithmic barrier function to equivalently transform the system model into an unconstrained barrier nonlinear system model:

[0017] To eliminate the feasibility condition requirements for virtual controllers imposed by traditional BLF (Blocking Function Function), a novel logarithmic barrier function is designed:

[0018] (2)

[0019] in, Let i be the unconstrained variable after the barrier transformation of the i-th state. The transformed state function, , These are the transformed upper and lower bound constraint functions, respectively.

[0020] The barrier function satisfies the following condition: ;when hour, ;when hour, .

[0021] Differentiating the barrier function, we get: By inverse transformation of the barrier function, the original state-constrained strict feedback system is transformed into an unconstrained barrier nonlinear system, resulting in the following formula:

[0022]

[0023] (3)

[0024] in, , , Let i be the i-th order state mapping function after obstacle transformation. For Li Daoshu, Let be the gain coefficient of the barrier function with respect to the original state. The time-varying compensation term for the constraint boundary in the obstacle function, where and They are respectively and The derivative of This represents the unconstrained new state after the nth-order state is transformed by the obstacle function. The barrier function is transformed into a state gain function. Let be the inverse mapping function from the nth-order obstacle transformation state to the original state. For the unknown nonlinear lumped terms of the nth-order barrier system, Regarding the perturbation gain Li Daoshu, Let be the i-th Lyapunov function.

[0025] S3: Using a radial basis function neural network, the unknown nonlinear dynamics in the barrier nonlinear system model are approximated online:

[0026] For the aggregated unknown nonlinear term corresponding to the i-th state generated after the barrier system transformation Online approximation is performed using the universal approximation property of RBF neural networks. The approximation model of the neural network is expressed as:

[0027] (4)

[0028] in, Let i be the input vector of the RBF neural network in the i-th state. For the unknown nonlinear term to be approximated, For the ideal weight vector, These are Gaussian radial basis function vectors. For a bounded approximation error, the bounded condition must be satisfied. ,in It is an unknown bounded constant.

[0029] S4: Design of a virtual controller and adaptive iterative adjustment function based on the backstepping method, and online estimation of neural network weights and unknown system parameters:

[0030] Define the coordinate transformation of the tracking error to transform the tracking problem of the barrier system into an error stabilization problem:

[0031] , (5)

[0032] in, For the error variable in the backstep recursion process, This is the corrected reference signal. For the first The virtual controller for the step.

[0033] Backstepping recursive design:

[0034] Step 1: Construct the first-order Lyapunov function ,in The preset error dead zone constant, This represents the error variable in the backstepping recursion process of the first step. For error variables The relevant switching functions satisfy hour ,otherwise ;right By differentiating the results and combining them with the approximation results using radial basis functions (RBF), the first-stage virtual controller is designed. and adaptive iterative tuning function ,ensure time derivative Negative fixation achieves the first level of calm;

[0035] Step i ( ): Recursively construct the i-th level Lyapunov function ,in The preset error dead zone constant for the i-th level. ,right Find the derivative and design the i-th level virtual controller. and adaptive iterative tuning function Meeting the conditions for calming ,in =1,2,…, , To calm and enhance, For the first Error variables in the backstep recursion process of step 1 for Related switching function error variables, For the first Level preset error dead zone constant, For parameter estimation error, , This represents the optimal weight vector for the RBF neural network. The adaptive estimate;

[0036] Step n: Construct the global Lyapunov function ,in These are design parameters used for adjusting parameters. The convergence speed of adaptive updates These are design parameters used for adjusting parameters. The convergence speed of adaptive updates To control gain weighting error, Let n be the error variable in the backstepping recursion process at step n. The preset dead zone constant for the nth level error. for Related switching function error variables, for The lower bound;

[0037] right After differentiation, the final virtual controller is designed. That is, the actual control input of the system ;

[0038] To achieve online estimation of unknown parameters The following adaptive law is designed:

[0039] For the upper bound estimate of neural network weights Design update law ,in >0 is a set constant. It is an adaptive iterative tuning function;

[0040] For control gain related parameters The following piecewise adaptive law is designed:

[0041] (6)

[0042] in, As a preset positive constant, To control the derivative term of the Lyapunov function, For sign smoothing functions, For a composite term that includes neural network estimation, , Here are the basis function vectors of a radial basis function neural network. This is the input vector of the neural network. This is a preset constant.

[0043] S5: Based on the control Lyapunov function and the relaxation inverse optimality condition, design an inverse robust optimal controller and construct its minimized cost functional to achieve robust stabilization and trajectory tracking control of the system.

[0044] First, the error system after coordinate transformation and barrier transformation is rewritten in affine form:

[0045] (7)

[0046] in, The error state vector is composed of the error variables derived from each backstep recursion. For the system's nonlinear terms, To control the gain vector, This is the column vector of state gains after the barrier function transformation. For Li Daoshu, This is the column vector of system disturbance gain;

[0047] To address the approximation error and parameter uncertainty in neural networks, a relaxed inverse optimal stabilization condition is set: the standard inverse optimality requirement does not need to be satisfied. ( There is a lower bound for the error. Upper bound of error and perturbation threshold Three categories Class function, controlling Lyapunov functions satisfy ,Right now The value of matches the upper and lower bound functions corresponding to the magnitude of the error variable; when the magnitude of the error variable... When the minimum value of the control input is met, the system stability condition is satisfied, i.e., the system is stable. ;in, It is a positive definite function. This is the error threshold function corresponding to the disturbance level;

[0048] Under these conditions, design an inverse robust optimal controller. for:

[0049] (8)

[0050] Among them, the basic control law A Sontag-type formula is used to eliminate control singularities; the expression is:

[0051] (9);

[0052] Furthermore, this controller can also be equivalently represented as a form based on inverse optimal gain allocation:

[0053] (10)

[0054] in, For optimal gain, It is a positive definite symmetric matrix-valued function used to achieve inverse optimal gain allocation. For Li's derivative;

[0055] The control law is in Valid at the time; when hour, ;

[0056] To verify the inverse optimality of the controller, a cost functional minimized by the controller is constructed, with the following expression:

[0057] (11)

[0058] in, This is the system's comprehensive disturbance term, including all unmodeled effects such as external mismatch disturbances, neural network approximation errors, and parameter uncertainties. For the perturbation allowed set, For time variables, The preset disturbance adjustment parameters have a range of values. , The control Lyapunov function is constructed based on the system. It is a positive definite weight matrix. For integration variables, for Class functions are used to penalize disturbances in the worst-case scenario;

[0059] The specific form of the cost functional corresponding to this inverse robust optimal controller is as follows:

[0060] (12)

[0061] in, Let be the initial state vector of the system. Let the variable be the upper bound of the integral. The worst-case disturbance is the disturbance value that causes the system performance indicators to reach the worst-case scenario. For function The first derivative with respect to the independent variable e;

[0062] Expression of the positive definite penalty function constructed from the control Lyapunov function for: ,in For vector fields Li Daoshu, for Legendre-Fincher transform;

[0063] when When the cost function reaches its minimum value, To verify the inverse optimality of the controller.

[0064] The beneficial effects of this invention include:

[0065] 1. No conservatism in constraint handling: The novel obstacle function completely eliminates the strict constraints imposed on the virtual controller by traditional methods, and can handle arbitrary time-varying, asymmetric, and zero-crossing state constraints, making it highly versatile;

[0066] 2. Computationally efficient: There is no need to solve the HJB equation. The inverse optimal framework is adopted, which greatly reduces the computational complexity and is easy to implement in engineering.

[0067] 3. Strong robustness: The proposed relaxed inverse optimality condition, combined with the adaptive RBF neural network, can effectively compensate for unknown nonlinearities and disturbances;

[0068] 4. Superior control performance: Lyapunov theory ensures that the closed-loop system is semi-globally consistent and eventually bounded, all states strictly satisfy the constraints, and at the same time achieves the inverse optimal allocation of control variables. Attached Figure Description

[0069] Figure 1 This is a flowchart of the state-constrained inverse robust control method for a disturbed strict feedback system according to an embodiment of the present invention.

[0070] Figure 2 This is an overall framework diagram of the control strategy according to an embodiment of the present invention;

[0071] Figure 3 This is the state in Embodiment 1 of the present invention. , The tracking performance graph, where (a) represents the state. The tracking performance graph, (b) shows the state. Tracking performance graph;

[0072] Figure 4The control performance comparison charts of Embodiment 1 of the present invention are shown in the following figures: (a) is an error trajectory comparison chart, (b) is a controller trajectory comparison chart, (c) is an adaptive parameter trajectory comparison chart, and (d) is a virtual control performance comparison chart.

[0073] Figure 5 This is a robustness verification diagram of the RBF neural network in Embodiment 1 of the present invention, wherein (a) is Disturbed trajectory diagram, (b) is Disturbed trajectory diagram, (c) is Disturbed trajectory diagram, (d) is Disrupted trajectory diagram;

[0074] Figure 6 This is a state tracking performance diagram of the jet engine compressor model in Embodiment 2 of the present invention, where (a) represents the state. The tracking performance graph, (b) shows the state. Tracking performance graph;

[0075] Figure 7 This is a state tracking performance diagram of the second-order nonlinear system in Embodiment 3 of the present invention, where (a) represents the state. The tracking performance graph, (b) shows the state. Tracking performance graph;

[0076] Figure 8 The control performance comparison charts for Embodiment 3 of the present invention are shown below, where (a) is an error trajectory comparison chart, (b) is a controller trajectory comparison chart, (c) is an adaptive parameter trajectory comparison chart, and (d) is a virtual control performance comparison chart.

[0077] Figure 9 This is a state tracking performance diagram of the system under strong disturbance in Embodiment 4 of the present invention, where (a) is the state The tracking performance graph, (b) shows the state. Tracking performance graph;

[0078] Figure 10 The diagram shows a comparison of control performance in Embodiment 4 of the present invention, wherein (a) is a comparison diagram of error trajectories, (b) is a comparison diagram of controller trajectories, (c) is a comparison diagram of adaptive parameter trajectories, and (d) is a comparison diagram of virtual control performance. Detailed Implementation

[0079] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described below in conjunction with specific embodiments and accompanying drawings. This embodiment uses a second-order disturbed strictly feedback nonlinear system as an example for illustration, but the invention is also applicable to higher-order systems. The design parameters for each embodiment are shown in Table 1.

[0080]

[0081] Example 1: Second-order disturbed strictly feedback nonlinear system

[0082] like Figure 1-2 As shown, this embodiment includes the following steps:

[0083] S1: Construct a second-order disturbed strict feedback nonlinear system model as a strict feedback nonlinear system model with full-state time-varying dynamic constraints, unknown nonlinearity, and external disturbance, as shown in the following formula:

[0084] (13)

[0085] The unknown nonlinear function is: , , , ;

[0086] The given function is: , ;

[0087] External disturbances: , The perturbation is Gaussian distributed.

[0088] All states must satisfy time-varying dynamic constraints:

[0089] , ;

[0090] The desired tracking signal is: ;

[0091] The initial state is: , ;

[0092] The initial parameter estimates are: , .

[0093] To further verify the robustness of the proposed control method under enhanced disturbances, the enhanced disturbance term is defined as follows:

[0094]

[0095] in, It is an unknown bounded constant.

[0096] S2: The novel logarithmic barrier function is designed as follows:

[0097]

[0098] (14).

[0099] S3: Design a radial basis function (RBF) neural network to approximate the aggregated unknown nonlinear terms in each subsystem online, specifically:

[0100] The design parameters are set as follows: , , , , , , Select the Gaussian function for the RBF neural network. Center 3 Grid, width Approximating the aggregated unknown nonlinear term , ;

[0101] S4: Based on the unconstrained variable definition of tracking error after barrier transformation, virtual controllers at each level and adaptive iterative adjustment functions are designed through backstepping recursion to complete the online estimation of neural network weights and unknown system parameters;

[0102] S5: Select the optimal gain Construct positive definite matrix-valued functions Design auxiliary controller And obtain the inverse robust optimal controller:

[0103] (15)

[0104] Design the adaptive law as follows: .

[0105] The simulation results of this embodiment are as follows: Figure 3-5 As shown, Figure 3 The state is displayed under the control of the method of the present invention. , It always remains strictly within the preset time-varying constraint boundaries, without any exceeding of the limits; Figure 4 The method of this invention shows that the tracking error converges rapidly to within 0.03, with no overshoot and a convergence time of only 2.5s, which is far superior to the existing inverse optimal control method (convergence time 4.0s, steady-state error 0.07) and the standard adaptive method (convergence time 5.2s, steady-state error 0.11). Figure 5 The results show that even with the application of enhanced perturbations... , The RBF neural network can still accurately approximate unknown nonlinearities, and the system tracking performance does not degrade significantly, demonstrating excellent robustness.

[0106] Example 2: Strict Feedback System for Aircraft Engine Compressors

[0107] This embodiment uses an aerodynamic thermodynamic model of an axial compressor in an aero-engine. This model is a typical strongly nonlinear, strongly coupled, and strictly feedback structure with time-varying state constraints. During the control process, it is necessary to strictly limit key states such as pressure ratio and mass flow rate to avoid surge and stall failures, thus verifying the actual control effect of the present invention in high-end aero-equipment.

[0108] S1: Construct a second-order disturbed strictly feedback nonlinear system model, state Defined as compressor pressure ratio, state Defined as compressor mass flow rate, the unknown nonlinear function is determined by the compressor's variable operating condition aerodynamic characteristics. External disturbances include inlet total temperature and pressure pulsations, mechanical vibrations, and equivalent disturbances from fuel fluctuations. The system satisfies time-varying asymmetric dynamic constraints in all states. , The desired tracking signal is The initial state is set to , ;

[0109] S2: Design a novel logarithmic barrier function;

[0110] S3: The unknown aerodynamic nonlinearity of the compressor is approximated online using a radial basis function neural network;

[0111] S4: Design a virtual controller and adaptive iterative adjustment function through backstepping recursion;

[0112] S5: Select the optimal gain Design an inverse robust optimal controller.

[0113] The simulation results of this embodiment are as follows: Figure 6 As shown, the compressor pressure ratio mass flow rate Throughout the entire process, the system remained strictly within the preset constraint boundaries without any exceedances. The tracking error converged rapidly to within 0.02 within 1.8 seconds, with no overshoot. The control input was smooth and stable, with no risk of surge triggering, fully meeting the safety operation specifications for aero-engines. Compared with the traditional BLF control method, this invention eliminates the feasibility limitations of virtual controllers, can adapt to more stringent time-varying constraints, and significantly improves control response speed and stability.

[0114] Example 3: Second-order reference nonlinear system

[0115] This embodiment employs a standard second-order strictly feedback nonlinear system. The core objective is to rigorously verify the inverse optimality of the designed controller and prove that this method can minimize the control cost without solving the HJB equation.

[0116] S1: Construct the system model, the specific expression is as follows: , , ,in , For bounded time-varying external disturbances, asymmetric, zero-crossing time-varying dynamic constraints are set for the system state, and the desired tracking signal is... The control objectives are to satisfy state constraints, achieve accurate trajectory tracking, and verify the cost functional minimization property.

[0117] S2: Design a novel logarithmic barrier function;

[0118] S3: Using a radial basis function neural network to approximate unknown nonlinear terms online;

[0119] S4: Design a virtual controller and adaptive iterative adjustment function through backstepping recursion;

[0120] S5: Select the optimal gain Design an inverse robust optimal controller.

[0121] The simulation results of this embodiment are as follows: Figure 7-8 As shown, simulation results indicate that the system tracking error converges rapidly within 1.5 seconds, and the steady-state error is less than 0.01. The constructed cost functional... Converging to the theoretical minimum It strictly satisfies the inverse optimality condition. Compared with traditional ADP and LQG optimal control methods, this invention eliminates the need to solve complex HJB equations, reducing the computational load by more than 80%, achieving optimal allocation of control inputs, lower energy consumption, and eliminating chattering.

[0122] Example 4: Robustness Verification under Strong Disturbances and Unknown Control Gain

[0123] This embodiment verifies the strong robustness and generalization ability of the invention under harsh operating conditions with strong unmatched external disturbances and completely unknown control gain.

[0124] S1: Construct a second-order disturbed, strictly feedback nonlinear system model. The unknown nonlinear term remains consistent with that in Example 1. The control gain is set as a completely unknown time-varying function, satisfying only the sign-invariant condition. The external disturbance is set as a strong disturbance. , Simultaneously, abnormal disturbances are superimposed to simulate extreme operating conditions, and the system state is set with fast time-varying tight constraints, with the desired tracking signal being... .

[0125] S2: Design a novel logarithmic barrier function;

[0126] S3: Using a radial basis function neural network to approximate unknown nonlinear terms online;

[0127] S4: Design a virtual controller and adaptive iterative adjustment function through backstepping recursion;

[0128] S5: Select the optimal gain Design an inverse robust optimal controller.

[0129] The simulation results of this embodiment are as follows: Figure 9-10 As shown, even under the dual adverse conditions of strong disturbances and completely unknown control gain, the system does not exceed its limits in any state, the steady-state tracking error is less than 0.02, and the convergence time is less than 2.2s. The RBF neural network and adaptive law can quickly and accurately estimate the unknown nonlinearity and upper bound of the disturbance. Compared with traditional robust control methods, the present invention improves the disturbance rejection capability by more than 60%, and the system exhibits no chattering or divergence, fully verifying the control reliability under complex and uncertain operating conditions.

[0130] To fully demonstrate the technical advantages of this invention, four typical existing technologies—the traditional BLF method, the standard inverse optimal control method, the ADP / LQG / H∞ optimal control method, and the conventional adaptive control method—are selected for a comprehensive comparative analysis from the dimensions of constraint handling capability, robust disturbance rejection performance, computational complexity, and engineering practicality.

[0131] 1. Compared with the traditional BLF method: The traditional BLF requires strict feasibility conditions to be imposed on the virtual controller, which cannot handle asymmetric and zero-crossing time-varying constraints. It has strong design conservatism and is prone to control infeasibility problems when the constraints are tight. The present invention adopts a novel logarithmic barrier function, which completely eliminates the feasibility condition restriction. It can handle arbitrary time-varying, asymmetric, and zero-crossing full-state constraints. The constraint handling is not conservative and the versatility is greatly improved.

[0132] 2. Comparison with standard inverse optimal control method: Standard inverse optimal control is only applicable to unconstrained or simple constraint scenarios, and it is difficult to be compatible with strong uncertainty and full-state dynamic constraints; This invention combines barrier transformation with relaxation inverse optimal conditions to simultaneously achieve state constraint satisfaction, robust disturbance rejection and optimal allocation of control variables.

[0133] 3. Comparison with ADP / LQG / H∞ optimal control methods: Traditional optimal control requires solving HJB / HJI equations, which suffers from a serious dimensionality curse problem, highly depends on an accurate system model, and is extremely difficult to implement in engineering; This invention does not require solving HJB equations, significantly reduces computational complexity, can be calculated online in real time, and has stronger engineering applicability.

[0134] 4. Compared with conventional adaptive control methods: Conventional adaptive control has weak robustness. When faced with strong disturbances and unknown nonlinearities, it has large tracking errors and slow convergence speed. This invention combines the universal approximation characteristics of RBF neural networks with adaptive parameter estimation, which can efficiently compensate for unknown nonlinearities and mismatched disturbances, and significantly optimize transient and steady-state performance.

[0135] Comprehensive performance data shows that the present invention reduces the average tracking error by more than 90%, reduces the average control input by 60%-70%, and improves the convergence speed by 40%-60%. It can adapt to more stringent and complex state constraints and can be widely used in high-end equipment control scenarios such as robotic arms, aero engines, hypersonic aircraft, and ship autopilot.

[0136] Results Verification: Table 2 shows the performance comparison between the present invention and existing methods. The method of the present invention can achieve strict state constraint satisfaction, high-precision trajectory tracking, inverse optimal optimization of control quantity and robustness under strong disturbances. Moreover, the control input is smooth without singularities, and the average control input and tracking error are better than those of existing methods.

[0137]

[0138] In summary, the state-constrained inverse robust control method for disturbed strict feedback systems provided by this invention does not rely on an accurate system model or require solving the HJB equations. It can handle arbitrary time-varying asymmetric full-state dynamic constraints, exhibits strong robustness to parameter uncertainties, unknown nonlinearities, and external disturbances, and achieves a unity of stability, constraint satisfaction, accurate tracking, and optimal control. It successfully solves several problems in the prior art and has significant progress and extremely high industrial application value.

[0139] This invention can be directly applied to the controller design of various strictly feedback nonlinear systems, such as robotic arm trajectory tracking control, aero-engine pressure control system, ship heading autopilot, and hypersonic vehicle attitude control, providing stable and reliable technical support for improving the operational safety and energy efficiency of nonlinear systems under complex working conditions.

[0140] This application also provides a state-constrained inverse robust optimal control system for a disturbed strict feedback system, including:

[0141] Status acquisition module: used to acquire the status of the controlled object;

[0142] Control module: Used to execute the methods described above and output the optimal control quantity;

[0143] Execution module: Used to apply control quantities to the controlled object;

[0144] Communication module: Used for real-time data transmission.

[0145] This application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

[0146] The method provided by this invention has been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are merely for the purpose of helping to understand the core ideas of this invention. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. A state-constrained inverse robust control method for a disturbed strict feedback system, characterized in that, Includes the following steps: S1: Establish a rigorous feedback nonlinear system model subject to unmatched external disturbances and full-state time-varying dynamic constraints; S2: Construct a logarithmic barrier function to equivalently transform the system model into an unconstrained barrier nonlinear system model; S3: Using a radial basis function neural network, the unknown nonlinear dynamics in the barrier nonlinear system model are approximated online; S4: Design a virtual controller and adaptive iterative adjustment function based on the backstepping method, and estimate the neural network weights and unknown system parameters online; S5: Based on the control Lyapunov function and the relaxation inverse optimal condition, design an inverse robust optimal controller and construct its minimized cost functional to achieve robust stabilization and trajectory tracking of the system.

2. The method according to claim 1, characterized in that, The strictly feedback nonlinear system model described in step S1 is as follows: （1） in, Let i be the i-dimensional state sub-vector formed by the first i states of the system. for System No. Item state vector, This is an unmatched external disturbance. Let n be the n-dimensional full-state vector consisting of all n states of the system. To control the input gain term, This is the external disturbance gain term. For the nth unmatched external disturbance, For system control input, For system output, , , For a smooth, unknown, nonlinear function, Moreover, times change. For a smooth, known nonlinear function; The system satisfies time-varying dynamic constraints in all states. ,in , It is a continuous and bounded upper and lower constraint function.

3. The method according to claim 1, characterized in that, The logarithmic barrier function mentioned in step S2 is: (2) in, Let i be the unconstrained variable after the barrier transformation of the i-th state. The transformed state function, , These are the transformed upper and lower bound constraint functions, respectively. This barrier function ensures the key property that states do not exceed limits. The barrier function satisfies the following condition: ;when hour, ;when hour, .

4. The method according to claim 1, characterized in that, The form of the radial basis function neural network approximation of the unknown nonlinear term in step S3 is as follows: (4) in, For the unknown nonlinear term to be approximated, For the ideal weight vector, These are Gaussian radial basis function vectors. For bounded approximation error, This is the parameter vector of the neural network.

5. The method according to claim 1, characterized in that, Step S4, the backstepping design, includes: determining error variables based on the unconstrained variables after barrier transformation and the previous-order virtual controller; designing a virtual controller based on the error variables; the virtual controller includes state feedback, neural network compensation, and adaptive adjustment terms, and neural network weight estimates. The adaptive update law is ,in >0 is a human-defined constant. This is an adaptive iterative adjustment function.

6. The method according to claim 1, characterized in that, The relaxation inverse optimal condition described in step S5 is one of three types: the existence of a lower bound on the error, an upper bound on the error, and a perturbation threshold. Class function; functions that control the upper and lower bounds of the Lyapunov function matching error variable magnitude; When the magnitude of the error variable is greater than or equal to the threshold function corresponding to the magnitude of the total disturbance, the control input takes the minimum value to satisfy the system stability judgment condition.

7. The method according to claim 1, characterized in that, The inverse robust optimal controller mentioned in step S5 is: (8) in, For optimal gain; For the basic control law, a Sontag-type formula is used: (9) in, To control the derivative term of the Lyapunov function, As a preset positive constant, The barrier function is transformed into a state gain function. Let be the perturbation gain function. For estimating the unknown control gain, This is a composite term that includes neural network estimation; when Valid at the time; when hour, .

8. The method according to claim 1, characterized in that, The cost functional to be minimized in step S5 is: (11) in, This is the system's comprehensive disturbance term, including all unmodeled effects such as external mismatch disturbances, neural network approximation errors, and parameter uncertainties. For the perturbation allowed set, For time variables, The preset disturbance adjustment parameters have a range of values. , The positive definite penalty function is constructed from the control Lyapunov function. It is a positive definite weight matrix. For integration variables, for Class functions are used to penalize disturbances in the worst-case scenario; When control input When the inverse robust optimal controller is used, the cost functional reaches its minimum value.

9. A state-constrained inverse robust optimal control system for a disturbed strict feedback system, characterized in that, include: Status acquisition module: used to acquire the status of the controlled object; Control module: used to execute the method according to any one of claims 1-8 and output the optimal control quantity; Execution module: Used to apply control quantities to the controlled object; Communication module: Used for real-time data transmission.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-8.

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