Optimal backstepping based active suspension control method

Abstract

This invention discloses an active suspension control method based on optimal backstepping, comprising the following steps: Step 1: Introducing a performance index function into the backstepping control framework, and solving the HJB equation and HJB estimation equation based on an Actor-Critic structure reinforcement learning method; Step 2: Designing an adaptive update law using the negative gradient of the squared Bellman residuals, constructing an Actor network to execute control behavior and a Critic network to evaluate system performance, and designing the virtual control law and the actual control law as optimal solutions; Step 3: Designing a Lyapunov function based on tracking error. This invention introduces a performance index function into the backstepping control framework, solves the HJB equation based on an Actor-Critic structure reinforcement learning method, and constructs an Actor network to execute control behavior and a Critic network to evaluate system performance, enabling both the virtual control law and the actual control law to approximate the optimal solution of the subsystem, thus achieving optimal control of the active suspension system under Lyapunov stability.

Description

Technical Field

[0001] This invention belongs to the field of vehicle suspension system control technology, and relates to an active suspension control method based on optimal backstepping. Background Technology

[0002] In vehicle suspension systems, existing active suspension control methods mainly include LQR, sliding mode, H∞ control, predictive control, etc. They have certain theoretical advantages in terms of stability assurance and constraint handling, but they cannot systematically incorporate performance index functions into the control law design framework, thus making it difficult to achieve global optimization of control performance.

[0003] In contrast, optimal control strategies place greater emphasis on the trade-offs in control performance, aiming to optimize system performance by designing appropriate control strategies. For optimization problems, the solution method based on the HJB equations provides a theoretical framework for achieving optimal control of nonlinear systems. However, due to the inherent curse of dimensionality in the HJB equations, analytical solutions for high-order nonlinear systems are often difficult to achieve in practice. Summary of the Invention

[0004] In order to overcome at least one deficiency of the prior art, the present invention provides an active suspension control method based on optimal backstepping.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: an active suspension control method based on optimal backstepping, comprising:

[0006] Step 1: Introduce the performance index function into the backstepping control framework, and solve the HJB equation and the HJB estimation equation based on the reinforcement learning method of the Actor-Critic structure. Step 2: Design an adaptive update law using the negative gradient of the squared Bellman residuals, construct the Actor network to execute the control behavior and the Critic network to evaluate the system performance, and design the virtual control law and the actual control law as the optimal solution. Step 3: Design based on tracking error Lyapunov functions; Step 4: Analyze the stability of the active suspension system based on Lyapunov; Step 5: Analyze the unsprung mass displacement and speed The stability of the zero-dynamic subsystem constituted; Step 6: Simulation verification: This step verifies the dynamic performance of the control method under typical road surface excitation.

[0007] Furthermore, step 1 includes Step 11: Set the vertical motion of sprung and unsprung mass in a 1 / 4 vehicle semi-active suspension model; The state-space equations for the 1 / 4 vehicle semi-active suspension model are expressed as follows: (3) (4) Equation (3) is the state-space equation for the suspension model with sprung mass; Equation (4) is the state-space equation for the suspension model without sprung mass. in, For the spring-loaded mass displacement variable, For the sprung mass velocity variable, The displacement is not that of the spring-loaded mass. The velocity is not that of the sprung mass; the sprung velocity variable is subject to an asymmetric state. Constraints, among which and These are the constraint limits; Step 12: Based on the backstepping control framework, set the tracking error of the suspension system. ; Tracking error Represented as: (5) in Represents the desired trajectory. The virtual control law representing the subsystem; Step 13: Based on tracking error Set performance index function ; Step 14: Based on tracking error and performance index functions The HJB equation and the HJB estimation equation are defined.

[0008] Furthermore, step 2 includes Step 21: Define the Bellman residual function based on the HJB equation and the HJB estimation equation. ; Step 22: Design the adaptive law of the Critic network and the weight update law of the Actor network based on the gradient update method, so that the Bellman residual function... .

[0009] Furthermore, step 3 includes Step 31: Design based on tracking error Lyapunov functions And obtain its time derivative. ; (29) (30) in, These are estimated values ​​for the weights of the Critic network. These are estimates of the Actor network weights. and This indicates the parameter estimation error. Represents the ideal weight matrix. It is a basis function matrix. This refers to the estimation error, and there exists a positive number. satisfy , This represents the derivative of the expected trajectory. It is a positive constant. It is a positive constant. It is an intermediate variable. For learning rate, For learning rate; Step 32: Design based on tracking error Lyapunov functions And obtain its time derivative. ; (48) (49) in, These are estimated values ​​for the weights of the Critic network. These are estimates of the Actor network weights. and This indicates the parameter estimation error. Represents the ideal weight matrix. It is a basis function matrix. This refers to the estimation error, and there exists a positive number. satisfy , This represents the derivative of the expected trajectory. It is a positive constant. It is a positive constant. It is an intermediate variable. For learning rate, This refers to the learning rate.

[0010] Furthermore, step 4, based on the Lyapunov method, analyzes the stability of the active suspension system as follows: Based on Lyapunov functions time derivative and Lyapunov functions time derivative This yields the final time derivative of the Lyapunov function. : (50) The upper bound of the residual term Convergence gain Convergence gain Convergence gain , Control parameters , as well as The following conditions must be met (51) Therefore, (50) can be represented as (52) in V For Lyapunov functions, the convergence rate parameter , for The smallest eigenvalue, for The smallest eigenvalue In time interval Perform an exponential function on both sides of (55). The points are obtained. (53) Therefore, we can conclude that , , The displacement of the sprung mass is semi-globally uniform and ultimately bounded. ,speed and tracking error and Both can guarantee convergence.

[0011] Furthermore, step 13 includes Step 131: Based on tracking error Set performance index function ; Tracking error Its time derivative is (6) By using the backstep control method, Considered as the optimal virtual control law ,Right now , Performance index function Defined as (7) in Let cost function be yes The permissible control set, It is a compact set that includes the origin. It is a virtual control law. and It is a positive constant. It is an integral variable.

[0012] Step 132: Based on tracking error Set performance index function ; Tracking error The time derivative is ,in , It is the time derivative of the estimate of the optimal virtual control law; By using the backstep control method, Considered as the optimal virtual control law ; Performance index function Defined as (8) in and It is a positive constant. It is an integral variable.

[0013] Furthermore, as stated above.

[0014] Furthermore, step 14 includes Step 141: Based on tracking error and performance index functions Set the HJB equation ; (9) in, It is a performance index function Regarding tracking error The partial derivatives; Step 142: Solve for the optimal virtual control law ; Step 143: Optimal virtual control law obtained based on Step 142 Update HJB equations ; Step 144: Design a Critic network to evaluate control performance metrics and an Actor network to execute the virtual controller, obtaining estimates through iterative updates. as well as ; Step 145: Based on the estimated value as well as Set the HJB estimation equation ; Step 146: Based on tracking error Performance index function Following steps 141-145, the HJB equation is obtained. and HJB estimation equation .

[0015] Furthermore, the optimal virtual control law in step 142 The solution method is as follows Setting HJB equations If it holds true and there exists a unique solution, then According to (6) and (9), we get (10) From (10), we get ; Set auxiliary variables , performance index function Defined as (11) in, It is a positive constant, from (11) we get (12) in In the set For an unknown continuous function on the π / 2, RBFNN is used to estimate it; (13) in Represents the ideal weight matrix. It is a basis function matrix. This refers to the estimation error, and there exists a positive number. satisfy .

[0016] From (13), we get (14).

[0017] Furthermore, step 144 includes The Critic network used for estimating performance metrics is designed as follows: (16) in These are estimated values ​​for the weights of the Critic network; Optimal Virtual Control Law Based on Actor Network Make an estimate (17) in These are the estimated values ​​of the Actor network weights.

[0018] Furthermore, step 22 includes Step 221: Based on Design the adaptive law of the Critic network and the weight update law of the Actor network ; Adaptive Law of Critic Network for (25) Wherein, error function intermediate variables , For learning rate, For Bellman residuals, This represents the estimation error of the Critic network.

[0019] Weight update law of Actor network for (26) in For learning rate, It is the estimation error of the Actor network.

[0020] Step 222: Based on Design the adaptive law of the Critic network and the weight update law of the Actor network ; Adaptive Law of Critic Network for (27) Weight update law of Actor network for (28) Where parameters , Positive constants, intermediate variables .

[0021] Step 3: Design based on tracking error The Lyapunov function.

[0022] In summary, the advantages of this invention are: This invention introduces a performance index function into the backstepping control framework, solves the HJB equations using a reinforcement learning method based on an Actor-Critic structure, and designs an adaptive update law using the negative gradient of the Bellman residual square. It then constructs an Actor network to execute control behavior and a Critic network to evaluate system performance, enabling both the virtual and actual control laws to approximate the optimal solution of the subsystem. This achieves optimal control of the active suspension system under Lyapunov stability. The control method of this application can significantly improve the vibration suppression capability and ride comfort of the active suspension system, providing an effective technical solution for high-performance suspension control. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of a 1 / 4 scale vehicle semi-active suspension model of the present invention.

[0024] Figure 2 The sprung displacement of the Class B random road surface of the present invention Schematic diagram.

[0025] Figure 3 The sprung speed of Class B random road surface of the present invention Schematic diagram.

[0026] Figure 4 This is a schematic diagram of the sprung acceleration of the Class B random road surface according to the present invention.

[0027] Figure 5 This is a schematic diagram of tire dynamic displacement on a Class B random road surface according to the present invention.

[0028] Figure 6 This is a schematic diagram of the suspension dynamic deflection for a Class B random road surface according to the present invention.

[0029] Figure 7 This is a schematic diagram of the control signals for the Class B random road surface of the present invention.

[0030] Figure 8 The spring displacement of the impact machine road surface of the present invention Schematic diagram.

[0031] Figure 9 The sprung speed of the impact random road surface of the present invention Schematic diagram.

[0032] Figure 10 This is a schematic diagram of the control signal for impacting random road surfaces according to the present invention. Detailed Implementation

[0033] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0034] Example: like Figures 1-10 As shown, the active suspension control method based on optimal backstepping includes the following steps: Step 1: Introduce the performance index function into the backstepping control framework, and solve the HJB equation and the HJB estimation equation based on the reinforcement learning method of the Actor-Critic structure. Step 2: Design an adaptive update law using the negative gradient of the squared Bellman residuals, construct the Actor network to execute the control behavior and the Critic network to evaluate the system performance, and design the virtual control law and the actual control law as the optimal solution. Step 3: Design based on tracking error Lyapunov functions; Step 4: Analyze the stability of the active suspension system based on Lyapunov; Step 5: Analyze the unsprung mass displacement and speed The stability of the zero-dynamic subsystem constituted; Step 6: Simulation verification: This step verifies the dynamic performance of the control method under typical road surface excitation.

[0035] To facilitate control over the design, some necessary assumptions and lemmas are proposed as follows: Assumption 1: In the interval The following conditions must be met for continuous incentive: (1) in , and It is a positive number. Represents the identity matrix.

[0036] Step 1 specifically includes: Step 11: Set the vertical motion of sprung and unsprung mass in a 1 / 4 vehicle semi-active suspension model; The dynamic equations of the 1 / 4 vehicle semi-active suspension model are as follows: (2) in For the sprung mass, For unsprung mass, To reduce suspension stiffness, For suspension damping, For tire damping, For tire stiffness, and These represent the vertical displacements of the sprung mass and the unsprung mass, respectively. For road surface excitation, This refers to the controllable damping force of the suspension.

[0037] Define the system's state variables , , , , These are the spring forces and damping forces of the suspension. Given the spring force and damping force of the tires, the state-space equations of the suspension model are expressed as follows: (3) (4) Equation (3) is the state-space equation for the suspension model with sprung mass; Equation (4) is the state-space equation for the suspension model without sprung mass.

[0038] in, For the spring-loaded mass displacement variable, For the sprung mass velocity variable, The displacement is not that of the spring-loaded mass. The velocity is not that of the sprung mass; the sprung velocity variable is subject to an asymmetric state. Constraints, among which and These are the constraint limits.

[0039] Step 12: Based on the backstepping control framework, set the tracking error of the suspension system. ; Tracking error Represented as: (5) in Represents the desired trajectory. This represents the virtual control law of the subsystem.

[0040] Step 13: Based on tracking error Set performance index function ; Step 13 includes: Step 131: Based on tracking error Set performance index function ; Tracking error Its time derivative is (6) By using the backstep control method, Considered as the optimal virtual control law ,Right now , Performance index function Defined as (7) in Let cost function be yes The permissible control set, It is a compact set that includes the origin. It is a virtual control law. and It is a positive constant. It is an integral variable.

[0041] Step 132: Based on tracking error Set performance index function ; Tracking error The time derivative is ,in , It is the time derivative of the estimate of the optimal virtual control law; By using the backstep control method, Considered as the optimal virtual control law ; Performance index function Defined as (8) in and It is a positive constant. It is an integral variable; Step 14: Based on tracking error and performance index functions Define the HJB equation and the HJB estimation equation; Step 14 includes the following steps: Step 141: Based on tracking error and performance index functions Set the HJB equation ; (9) in, It is a performance index function Regarding tracking error The partial derivatives of .

[0042] Step 142: Solve for the optimal virtual control law ; Setting HJB equations If it holds true and there exists a unique solution, then According to (6) and (9), we get (10) From (10), we can obtain that ; because The nonlinearity makes it difficult to directly calculate. The analytical solution. To effectively solve for the optimal virtual control law. Set auxiliary variables , performance index function Defined as (11) in, It is a positive constant, which can be obtained from (11). (12) in In the set For an unknown continuous function on the π / 2, RBFNN is used to estimate it; (13) in Represents the ideal weight matrix. It is a basis function matrix. This refers to the estimation error, and there exists a positive number. satisfy .

[0043] From (13), we can obtain that (14) Step 143: Optimal virtual control law obtained based on Step 142 Update HJB equations ; Substituting (13) and (14) into (9), we update the HJB equation and obtain... (15) in It is a positive number. ; Step 144: Design a Critic network to evaluate control performance metrics and an Actor network to execute the virtual controller, obtaining estimates through iterative updates. as well as ; Ideal weight matrix and estimation error It is unknown, and the optimal virtual control law cannot be obtained directly. Therefore, a reinforcement learning method based on the Actor-Critic structure is adopted for solving the problem. A Critic network is designed to evaluate control performance, and an Actor network is used to execute the virtual controller. Estimates are obtained through iterative updates. as well as

[0044] The Critic network used for estimating performance metrics is designed as follows: (16) in These are estimated values ​​for the weights of the Critic network; Optimal Virtual Control Law Based on Actor Network Make an estimate (17) in These are estimates of the Actor network weights; Step 145: Based on the estimated value as well as Set the HJB estimation equation ; HJB Estimation Equation for (18) During the above process, the Critic network will adjust the current virtual control law. The evaluation is performed, and the estimated value of the HJB equation is updated iteratively to reach the optimal solution, i.e. The Actor network improves the control strategy based on the Critic network's evaluation, thereby ultimately optimizing control performance.

[0045] Step 146: Based on tracking error Performance index function Following steps 141-145, the HJB equation is obtained. and HJB estimation equation ; (19) in, , , It is a positive constant. Represents the ideal weight matrix. It is a basis function matrix. This refers to the estimation error, and there exists a positive number. satisfy , ; A Critic network is designed to evaluate control performance metrics, and an Actor network is designed to execute a virtual controller. Estimates are obtained through iterative updates. as well as ; The Critic network used for estimating performance metrics is designed as follows: , (20) in These are estimated values ​​for the weights of the Critic network; Optimal Virtual Control Law Based on Actor Network Make an estimate (twenty one) in These are estimates of the Actor network weights; Based on the estimated value as well as Set the HJB estimation equation ; (twenty two) Step 2: Design an adaptive update law using the negative gradient of the squared Bellman residuals, construct the Actor network to execute the control behavior and the Critic network to evaluate the system performance, and design the virtual control law as the optimal solution. Step 2 includes Step 21: Define the Bellman residual function based on the HJB equation and the HJB estimation equation. ; Step 211: Based on HJB equations and HJB estimation equation Define the Bellman residual function ; (twenty three) in ; Step 212: Based on HJB equations and HJB estimation equation Define the Bellman residual function ; (twenty four) in,

[0046] Step 22: Design the adaptive law of the Critic network and the weight update law of the Actor network based on the gradient update method, so that the Bellman residual function... ; Step 221: Based on Design the adaptive law of the Critic network and the weight update law of the Actor network ; Adaptive Law of Critic Network for (25) Wherein, error function intermediate variables , For learning rate, For Bellman residuals, This represents the estimation error of the Critic network.

[0047] Weight update law of Actor network for (26) in For learning rate, It is the estimation error of the Actor network.

[0048] Step 222: Based on Design the adaptive law of the Critic network and the weight update law of the Actor network ; Adaptive Law of Critic Network for (27) Weight update law of Actor network for (28) Where parameters , Positive constants, intermediate variables .

[0049] Step 3: Design based on tracking error Lyapunov functions; Step 3 includes Step 31: Design based on tracking error Lyapunov functions And obtain its time derivative. ; (29) in, and This indicates the parameter estimation error; (30) time derivative The method to obtain it is as follows: according to From the definition, we can obtain (31) Combining (17) and (25)-(26), The time derivative is (32) according to The following relation is obtained. (33) (34) Substituting (33) and (34) into (32), we get (35) According to Young's inequality, the following relationship can be obtained. (36) (37) (38) Based on (36)-(38) and (25), (35) can be rewritten as (39) According to (15), the following relation can be obtained. (40) Substituting (40) into (39), we can obtain (41) according to and The following relationship can be obtained. (42) (43) Substituting (42) and (43) into (41), we get (44) According to Young's inequality, we can obtain (45) (46) (47) Substituting (45)-(47) into (44), we get (30) Step 32: Design based on tracking error Lyapunov functions And obtain its time derivative. ; (48) in and This indicates the parameter estimation error. Based on the previous analysis and the derivation steps (33)-(47), we can obtain the following about The expression for the time derivative is: (49) Among them, intermediate variables .

[0050] Step 4: The method for analyzing the stability of the active suspension system based on Lyapunov is as follows. Based on Lyapunov functions time derivative and Lyapunov functions time derivative This yields the final time derivative of the Lyapunov function. : (50) The upper bound of the residual term Convergence gain Convergence gain Convergence gain .

[0051] Based on the above analysis, control parameters , as well as The following conditions must be met (51) Therefore, (50) can be further expressed as (52) in V For Lyapunov functions, the convergence rate parameter , for The smallest eigenvalue, for The smallest eigenvalue.

[0052] In time interval Perform an exponential function on both sides of (55). The points can be obtained. (53) Therefore, we can conclude , , The displacement of the sprung mass is semi-globally uniform and ultimately bounded. ,speed and tracking error and Both can guarantee convergence.

[0053] The stability analysis method in step 5 is as follows: The optimal virtual control law will be based on the Actor network. The estimated value for estimation (48) Substituting into the unsprung state-space equation (4), we get (54) Among them, system variables State matrix State matrix Based on the boundedness of state variables, intermediate variables can be obtained. It is also bounded.

[0054] Define Lyapunov functions Its time derivative is (55) in It is a positive definite matrix. Because the matrix... If it is a Hurwitz matrix, then there exists a positive definite matrix. ,satisfy Using Young's inequality, we can obtain (56) Where the positive constant Substituting (42) into equation (41), we get (57) in and These represent the minimum and maximum eigenvalues, respectively. By appropriately selecting the parameters... The exponential convergence rate is obtained. Moreover, the upper bound of the residual term Therefore, it can be Further expressed as (58) In time interval Internal (39) on the integral factor Integrating, we get (59) Based on the above zero-dynamic analysis, the vertical displacement of the unsprung mass... With speed It remains bounded at all times. Therefore, the active suspension control method based on optimal backstepping proposed in this application can guarantee the stability of the overall suspension system.

[0055] Step 6 verifies the effectiveness of the Optimized Backstepping Control (OBC) method proposed in this application by conducting system simulation studies based on a quarter-suspension model. The dynamic performance of the proposed control method under typical road surface excitation is comprehensively evaluated by comparing it with traditional passive suspension and the classic Sky Hook Control (SHC) method.

[0056] For a quarter-suspension system, set the sprung mass Unsprung mass The stiffness coefficient is and The damping coefficient is and System initial conditions To comprehensively evaluate the performance of the control strategy under different operating conditions, the following two typical road surface excitations were selected: (1) Random road surface Random road surfaces are used to simulate the random vibration response of vehicles under typical urban road conditions. According to the international standard ISO 8608, the time-domain signal of road surface excitation can be expressed as follows: (60) in Indicates road surface excitation, This represents Gaussian white noise. This is the lower limit of the cutoff frequency. Power spectral density of Class B road surface, using the reference spatial frequency. .

[0057] (2) Impact on the road surface Impact surfaces are used to simulate sudden road surface changes such as speed bumps and potholes. A typical road surface profile can be described as follows: (61) Among them, the height of the speed bump Speed ​​reduction band .

[0058] Vehicle speed The simulation results of the suspension system are shown below. Vertical displacement of the sprung mass on a Class B random road surface. and speed like Figure 2 and Figure 3 As shown, under OBC and It can converge quickly, effectively ensuring the suspension's vibration damping performance. Figure 4-6 The spring acceleration of the suspension system was shown respectively. Tire dynamic deformation and suspension travel . Figure 7 The optimal signal for this control scheme is shown. Under impact road surface conditions, Figure 8-10 The sprung displacements of the suspension system were shown respectively. ,speed and control signals To comprehensively evaluate the suspension system performance, Tables 1 and 2 show the root mean square values ​​of various evaluation indicators under random and impact road conditions, respectively. Compared to passive suspension, OBC reduces acceleration (representing comfort) by 39% and 53%, and tire dynamic deformation (representing handling) by 31% and 37%. OBC significantly reduces vehicle vibration and tire dynamic displacement, thus the suspension bears more relative motion, resulting in a slight increase in suspension dynamic deflection, but it remains within the safe travel range.

[0059] Table 1 Random pavement performance indicators

[0060] Table 2 Impact pavement performance indicators

[0061] Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.

Claims

1. An active suspension control method based on optimal backstepping, characterized in that: include Step 1: Introduce the performance index function into the backstepping control framework, and solve the HJB equation and the HJB estimation equation based on the reinforcement learning method of the Actor-Critic structure. Step 2: Design an adaptive update law using the negative gradient of the squared Bellman residuals, construct the Actor network to execute the control behavior and the Critic network to evaluate the system performance, and design the virtual control law and the actual control law as the optimal solution. Step 3: Design based on tracking error Lyapunov functions; Step 4: Analyze the stability of the active suspension system based on Lyapunov; Step 5: Analyze the unsprung mass displacement and speed The stability of the zero-dynamic subsystem constituted; Step 6: Simulation verification: This step verifies the dynamic performance of the control method under typical road surface excitation.

2. The active suspension control method based on optimal backstepping according to claim 1, characterized in that: Step 1 includes Step 11: Set the vertical motion of sprung and unsprung mass in a 1 / 4 vehicle semi-active suspension model; The state-space equations for the 1 / 4 vehicle semi-active suspension model are expressed as follows: （3） （4） Equation (3) is the state-space equation for the suspension model with sprung mass; Equation (4) is the state-space equation for the suspension model without sprung mass. in, For the spring-loaded mass displacement variable, For the sprung mass velocity variable, The displacement is not that of the spring-loaded mass. The velocity is not the sprung mass velocity; the sprung velocity variable is subject to an asymmetric state. Constraints, among which and These are the constraint limits; Step 12: Based on the backstepping control framework, set the tracking error of the suspension system. ; Tracking error Represented as: （5） in Represents the desired trajectory. The virtual control law representing the subsystem; Step 13: Based on tracking error Set performance index function ; Step 14: Based on tracking error and performance index functions The HJB equation and the HJB estimation equation are defined.

3. The active suspension control method based on optimal backstepping according to claim 1, characterized in that: Step 2 includes Step 21: Define the Bellman residual function based on the HJB equation and the HJB estimation equation. ; Step 22: Design the adaptive law of the Critic network and the weight update law of the Actor network based on the gradient update method, so that the Bellman residual function... .

4. The active suspension control method based on optimal backstepping according to claim 1, characterized in that: Step 3 include Step 31: Design based on tracking error Lyapunov functions And obtain its time derivative. ; （29） （30） in, These are estimated values ​​for the weights of the Critic network. These are estimates of the Actor network weights. and This indicates the parameter estimation error. Represents the ideal weight matrix. It is a basis function matrix. This refers to the estimation error, and there exists a positive number. satisfy , This represents the derivative of the expected trajectory. It is a positive constant. It is a positive constant. It is an intermediate variable. For learning rate, For learning rate; Step 32: Design based on tracking error Lyapunov functions And obtain its time derivative. ; （48） （49） in, These are estimated values ​​for the weights of the Critic network. These are estimates of the Actor network weights. and This indicates the parameter estimation error. Represents the ideal weight matrix. It is a basis function matrix. This refers to the estimation error, and there exists a positive number. satisfy , This represents the derivative of the expected trajectory. It is a positive constant. It is a positive constant. It is an intermediate variable. For learning rate, This refers to the learning rate.

5. The active suspension control method based on optimal backstepping according to claim 1, characterized in that: Step 4, which uses the Lyapunov-based method to analyze the stability of the active suspension system, is as follows: Based on Lyapunov functions time derivative and Lyapunov functions time derivative This yields the final time derivative of the Lyapunov function. : （50） The upper bound of the residual term Convergence gain Convergence gain Convergence gain , Control parameters , as well as The following conditions must be met （51） Therefore, (50) can be represented as （52） in V For Lyapunov functions, the convergence rate parameter , for The smallest eigenvalue, for The smallest eigenvalue In time interval Perform an exponential function on both sides of (55). The points are obtained. （53） Therefore, we can conclude that , , The displacement of the sprung mass is semi-globally uniform and ultimately bounded. ,speed and tracking error and Both can guarantee convergence.

6. The active suspension control method based on optimal backstepping according to claim 2, characterized in that: Step 13 includes Step 131: Based on tracking error Set performance index function ; Tracking error Its time derivative is （6） By using the backstep control method, Considered as the optimal virtual control law ,Right now , Performance index function Defined as （7） in Let cost function be yes The permissible control set, It is a compact set that includes the origin. It is a virtual control law. and It is a positive constant. It is an integral variable; Step 132: Based on tracking error Set performance index function ; Tracking error The time derivative is ,in , It is the time derivative of the estimate of the optimal virtual control law; By using the backstep control method, Considered as the optimal virtual control law ; Performance index function Defined as （8） in and It is a positive constant. It is an integral variable.

7. The active suspension control method based on optimal backstepping according to claim 2, characterized in that: Step 14 includes Step 141: Based on tracking error and performance index functions Set the HJB equation ; （9） in, It is a performance index function Regarding tracking error The partial derivatives; Step 142: Solve for the optimal virtual control law ; Step 143: Optimal virtual control law obtained based on Step 142 Update HJB equations ; Step 144: Design a Critic network to evaluate control performance metrics and an Actor network to execute the virtual controller, obtaining estimates through iterative updates. as well as ; Step 145: Based on the estimated value as well as Set the HJB estimation equation ; Step 146: Based on tracking error Performance index function Following steps 141-145, the HJB equation is obtained. and HJB estimation equation .

8. The active suspension control method based on optimal backstepping according to claim 7, characterized in that: The optimal virtual control law in step 142 The solution method is as follows Setting HJB equations If it holds true and there exists a unique solution, then According to (6) and (9), we get （10） From (10), we get ; Set auxiliary variables , performance index function Defined as （11） in, It is a positive constant, from (11) we get （12） in In the set For an unknown continuous function on the π / 2, RBFNN is used to estimate it; （13） in Represents the ideal weight matrix. It is a basis function matrix. This refers to the estimation error, and there exists a positive number. satisfy ; From (13), we get （14）。 9. The active suspension control method based on optimal backstepping according to claim 7, characterized in that: Step 144 includes The Critic network used for estimating performance metrics is designed as follows: （16） in These are estimated values ​​for the weights of the Critic network; Optimal Virtual Control Law Based on Actor Network Make an estimate （17） in These are the estimated values ​​of the Actor network weights.

10. The active suspension control method based on optimal backstepping according to claim 3, characterized in that: Step 22 includes Step 221: Based on Design the adaptive law of the Critic network and the weight update law of the Actor network ; Adaptive Law of Critic Network for （25） Wherein, error function intermediate variables , For learning rate, For Bellman residuals, This represents the estimation error of the Critic network; Weight update law of Actor network for （26） in For learning rate, It is the estimation error of the Actor network; Step 222: Based on Design the adaptive law of the Critic network and the weight update law of the Actor network ; Adaptive Law of Critic Network for （27） Weight update law of Actor network for （28） Where parameters , Positive constants, intermediate variables ; Step 3: Design based on tracking error The Lyapunov function.

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