Trajectory tracking control method based on extended adaptive terminal sliding mode observer

Abstract

The invention discloses a trajectory tracking control method based on an extended adaptive terminal sliding mode observer. The method comprises the following steps: establishing an extended state-space equation for a control system; constructing a sliding mode surface equation containing a saturation function integral term; constructing an extended adaptive terminal sliding mode observer; the terminal stability of the observer is ensured based on a Lyapunov function; and a disturbance compensation model and a trajectory tracking controller are established for the control system to perform trajectory tracking control on a controlled object. According to the method, the extended self-adaptive terminal sliding mode observer is designed, so that the time-varying lumped disturbance can be accurately estimated in finite time; and by designing a disturbance compensation control strategy, the stability and the anti-interference capability of the control system can be effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to an automatic control system and the technical field thereof, in particular to a trajectory tracking control method based on an extended adaptive terminal sliding mode observer. BACKGROUND

[0002] Trajectory tracking control is crucial in robotic, aircraft and other automation and mechatronic systems, and its performance directly affects the task execution effect. In engineering practice, the controlled object generally has model parameter uncertainty and unknown external disturbance. These factors cause significant deviation between the actual dynamic model and the nominal model of the control system. If not compensated effectively, it will directly cause the tracked trajectory to deviate from the expected value, reduce the response speed, and even cause system instability, making it difficult to meet the high-precision control requirements.

[0003] To address the above challenges, compensation control schemes based on disturbance observers are widely used. Considering the strong robustness of sliding mode control to matching disturbances and parameter changes, related technologies often combine sliding mode observers to estimate and feed-forward compensate the total disturbance of the system in order to further improve the anti-disturbance performance of the controlled system. However, the existing technical solutions still have limitations: on the one hand, traditional sliding mode observers rely on pre-set and fixed switching gains, which are usually conservatively set according to the possible maximum upper bound of the disturbance. When the actual disturbance amplitude is low or presents a slow-changing characteristic, it will cause large observation error and insufficient precision, thereby affecting the compensation effect. Moreover, the fixed switching gain lacks adaptability when the disturbance characteristics change in real time, and cannot achieve optimal estimation performance; on the other hand, standard terminal sliding mode control may have a significantly reduced convergence speed when the initial state of the system is far from the sliding mode surface. More importantly, the discontinuous switching terms of the controller and the observer will inject high-frequency chattering signals into the system, which not only excites unmodeled high-frequency dynamics of the system, causing oscillation, but also accelerates the wear and even destroys the structure of the physical system.

[0004] Although some research attempts to adjust the gain through an adaptive law or introduce high-order sliding mode structures to suppress chattering, when dealing with time-varying compound disturbances, there is still a lack of integrated control schemes that can dynamically optimize disturbance observation accuracy, accurately compensate disturbance components, and balance fast convergence and low chattering performance. Given the characteristic of terminal sliding mode control that the system state converges to an equilibrium point in a finite time, its core advantages can be integrated into the design of the disturbance observer to solve the technical contradiction between fast convergence and chattering suppression. SUMMARY

[0005] The present application aims to provide a trajectory tracking control method based on an extended adaptive terminal sliding mode observer, to solve the influence of parameter perturbation and external disturbance of the control system on the tracking effect of the controller during the trajectory tracking control process, and to achieve adaptive anti-interference and accurate trajectory tracking of the control system.

[0006] This invention provides a trajectory tracking control method based on an extended adaptive terminal sliding mode observer, comprising the following:

[0007] S1. Establish extended state-space equations for the control system;

[0008] S2. Construct the equation of the sliding surface containing the integral term of the saturated function;

[0009] S3. Construct an extended adaptive terminal sliding mode observer;

[0010] S4. The terminal stability of the observer is guaranteed based on the Lyapunov function;

[0011] S5. Establish a disturbance compensation model for the control system and a trajectory tracking controller to perform trajectory tracking control on the controlled object.

[0012] The specific process of step S1 is as follows:

[0013] For a linear system described by state-space equations Where X and Let A and B represent the system's state variables and their first derivatives, respectively; u represents the system's control input variables; and A and B are the state transition matrix and input matrix, respectively. Due to system complexity and errors in actual measurement or estimation, system modeling usually involves some deviations (i.e., model uncertainty). Furthermore, physical systems are more or less affected by external environmental disturbances. These uncertainties constantly impact the system's stability and robustness. To enhance the system's anti-interference capability and response performance, the impact of these uncertainties on the control system must be fully considered.

[0014] Generally, the lumped disturbance d, consisting of model uncertainty and external disturbances, is added to the control system model, that is, the linear system model is modified as follows:

[0015]

[0016] The lumped disturbance d is first-order differentiable with respect to time t (denoted as ). If it is a state variable, then it can also be considered as such. Therefore, the modified system model described above can be extended to the following state-space equation:

[0017]

[0018] in, To expand the state vector, To expand the state transition matrix, To expand the input matrix, Let I be the perturbation coefficient matrix, and let I be the identity matrix.

[0019] According to the experience of modeling physical systems, it can also be assumed that the rate of change of the lumped disturbance is bounded but the bound is unknown, i.e. (where ||·||2denotes the 2-norm of a vector, and σ is an unknown normal number). Then, obviously, holds.

[0020] As a preference, in the step S2, the error of the extended state variable is defined as where is the estimated value of ; X represents the state variable of the system, is the extended state vector; d represents the lumped disturbance, represents the estimated value of the lumped disturbance. Thus, the sliding mode surface equation can be designed as:

[0021]

[0022] where δ, α and ε are normal numbers, and α ∈ (0, 1), and ||·||1denotes the 1-norm of a vector. is a self-defined saturation function, and satisfies the following inequality relationship:

[0023] For a general column vector and a normal number ε, the following saturation function relationship is defined: where

[0024]

[0025] then (where μ = 0.25), thus

[0026] As a preference, in the step S3, the extended adaptive terminal sliding mode observer designed for the extended state space equation has the following form:

[0027]

[0028] where is the extended state transition matrix, is the estimated value of the extended state vector, is the extended input matrix, and u represents the input variable of the system control, is the error of the extended state variable, δ, α and ε are normal numbers, and α ∈ (0, 1), and ||·||1denotes the 1-norm of a vector, is a self-defined saturation function, and s is the sliding mode surface equation.

[0029] The corresponding adaptive update law of the disturbance upper bound is:

[0030]

[0031] where, is the estimation of unknown normal quantity σ; ρ and λ are both normal numbers.

[0032] As preferred, in the step S4, considering that the sliding mode control generally contains two sub-processes of approaching and sliding, only if each sub-process satisfies the terminal stability, the terminal stability of the whole system can be ensured. Therefore, the terminal stability of the approaching process and the sliding process of the above-mentioned observer needs to be proved respectively.

[0033] S401, proving the terminal stability of the sliding process of the extended adaptive terminal sliding mode observer designed in the step S3.

[0034] that is, proving that the observation error quantity falling on the sliding surface can always converge to a small neighborhood containing the steady state in a finite time.

[0035] Based on the modern control theory, the positive definite Lyapunov function (Liapunov function) is constructed as:

[0036]

[0037] It is noted that on the sliding surface s = 0, there is always Therefore, there is Substituting it into the first order derivative of the Lyapunov function, the following equation can be obtained:

[0038]

[0039] where,

[0040] Therefore, based on the finite time practical stability theorem, the trajectory of the system is finite time practical stable, that is, the observation error can slide to a small neighborhood containing the origin in a finite time t sl , and the finite time t sl satisfies:

[0041]

[0042] S402, proving the terminal stability of the approaching process of the extended adaptive terminal sliding mode observer designed in the step S3.

[0043] ​That is, to prove that the sliding state variable starting from any point in space can always reach a small neighborhood containing the sliding surface s=0 in a finite amount of time.

[0044] From the sliding stability of the sliding surface mentioned above, it can be seen that as long as s→0, there must be... Therefore, it is only necessary to prove Outside the sliding surface, i.e., when s≠0, the positive definite Lyapunov function is constructed as follows:

[0045]

[0046] in, Substituting the extended state-space equations and the designed extended adaptive terminal sliding mode observer expression into the first derivative of V2, and based on Jensen's inequality, we obtain:

[0047]

[0048] in,

[0049] Therefore, based on the practical stability theorem for finite time, it can be known that the sliding mode s can be maintained in a finite time t. re Reaching a small neighborhood containing the sliding surface s=0 Within, and at that finite time t re satisfy:

[0050]

[0051] Therefore, the sliding mode state variables starting from any point in space can always reach a small neighborhood containing the sliding surface s=0 in a finite time, thereby determining the terminal stability of the approach process of the extended adaptive terminal sliding mode observer.

[0052] Under the action of the perturbation observer designed in step S3, the perturbation observation error is practically stable in finite time, and the corresponding convergence time t c It has a finite upper bound, that is:

[0053]

[0054] Preferably, in step S5, the observer designed in step S3 can accurately obtain the estimated value of the lumped disturbance d. The impact of disturbances on the control system can then be eliminated through the following disturbance compensation strategy:

[0055]

[0056] Among them, u c K is the output of the tracking controller to be designed. cis a compensation control gain. In order to eliminate the disturbance from the input channel, a simple and effective compensation gain can be taken as the negative inverse matrix of the control matrix B (i.e. c =-B -1 , if B is nonsingular) or the negative pseudo-inverse matrix (if B is not full rank).

[0057] Therefore, the disturbance compensation model of the original linear system is:

[0058] wherein A is a state transition matrix, and X is a state variable of the system.

[0059] The disturbance compensation model of the corresponding extended observation system is:

[0060] wherein is an extended state transition matrix, is an estimation of the extended state vector, is an extended input matrix, and u represents an input variable of the system control, is an error of the extended state variable, and δ, α and ε are all normal numbers, and α is in (0, 1), ||·||1 represents a 1-norm of a vector, is a self-defined saturation function, s is a sliding surface equation, and I is a unit matrix

[0061] Based on the stability analysis in step S4, the disturbance observation error can converge to the origin (i.e. d →0) in a finite time, so that the compensation model of the above linear system can be equivalent to the nominal model Then, a suitable feedback controller u c is designed for the nominal model, for example, PID control, fuzzy control, neural network control, etc., so that a better trajectory tracking effect can be achieved.

[0062] Compared with the prior art, the present application has the beneficial effects that:

[0063] The present application proposes a novel disturbance observer based on an extended adaptive terminal sliding mode, which can accurately estimate the lumped disturbance composed of model uncertainty and external disturbance in a finite time, and eliminate the influence of the disturbance on the control system through the design of a compensation controller.

[0064] Meanwhile, compared with the disturbance observation compensation and the disturbance compensation control method based on the extended state observer, the trajectory tracking control method based on the extended adaptive terminal sliding mode observer designed by the present application can more accurately estimate the time-varying disturbance, and then implement an accurate compensation control strategy, so that the stability and anti-interference ability of the control system can be effectively improved. BRIEF DESCRIPTION OF DRAWINGS

[0065] In order to more clearly illustrate the technical solutions in the present application and the embodiments, the following briefly introduces the drawings required in the present application or the embodiments. It should be understood that the following introduced drawings are merely for the convenience of clearly expressing the technical solutions in the present application and some embodiments, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0066] Figure 1 A structure diagram of the trajectory tracking control method based on the extended adaptive terminal sliding mode observer is shown in the present application.

[0067] Figure 2 An effect comparison diagram based on different methods for estimating time-varying disturbance in the embodiments of the present application is shown.

[0068] Figure 3 An effect comparison diagram based on different control methods for tracking a reference trajectory in the embodiments of the present application is shown.

[0069] Figure 4 An error comparison diagram based on different control methods for tracking a reference trajectory in the embodiments of the present application is shown. DETAILED DESCRIPTION

[0070] In order to make those skilled in the art better understand the content of the present application, the technical solutions proposed by the present application are further explained in combination with the drawings and specific embodiments.

[0071] It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present application and are not intended to limit the present application. It should also be understood that when used in the present specification and the appended claims, the term "comprising" indicates the presence of the described features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or sets thereof. It should be further understood that the terms used in the present specification are merely for the purpose of describing specific embodiments and are not intended to limit the present application. As used in the present specification and the appended claims, the singular forms "a", "an" and "the" are intended to include the plural forms unless the context clearly indicates otherwise. The term "and / or" used in the present specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations thereof, and includes these combinations. The term "if" used in the present specification and the appended claims can be interpreted as "when" or "upon" or "in response to determining" or "in response to detecting" depending on the context.

[0072] The present embodiment discloses a trajectory tracking control method based on an extended adaptive terminal sliding mode observer for a tracked chassis, which refers to Figure 1In the embodiment, the track tracking control of the tracked chassis comprises the following steps:

[0073] S1, an extended state space equation is established for the control system.

[0074] Specifically, first, the kinematic equation of the tracked mobile chassis in the plane reference coordinate system {Σ OXYZ} is established:

[0075]

[0076] wherein, is the linear velocity of the mass center of the tracked chassis moving in the plane reference system, is the angular velocity of the tracked chassis rotating around the Z axis of the plane reference system; ω l and ω r are the rotational speeds of the left and right drive wheels; r is the radius of the drive wheel; and L is the wheelbase of the left and right sides.

[0077] A variable P is defined as the pose (x, y, θ) of the tracked chassis in the plane reference system, that is, x is the front-back displacement of the mass center of the tracked chassis, y is the left-right displacement of the mass center of the tracked chassis, and θ is the included angle between the mass center of the tracked chassis and the OXY plane; a variable ω is defined as the rotational speed (ω l , ω r ) of the left and right drive wheels, that is, Therefore, the kinematic equation of the tracked chassis can be approximated as the following linear equation:

[0078]

[0079] wherein, and are the expected pose trajectory and the expected drive wheel rotational speed, respectively; f is the high-order infinitesimal in the Taylor expansion; and there is:

[0080]

[0081] Let X: = P d -P, u: = M ω (ω d -ω), A: = M P , and B: = I, and the above linear equation can be written in the form of a state space equation: Due to the errors in the sensor measurement data and the complexity of the real environment, the actually measured pose of the tracked chassis and the rotational speed of the drive wheel always have some deviations, that is, the expression (P+ΔP) and (ω+Δω) containing the measurement errors should be used to replace P and ω in the original equation, and thus the above state space equation can be modified as:

[0082]

[0083] Definitions Let d be the lumped disturbance containing model uncertainty and measurement error, then the linear system model for the tracked trajectory motion of the tracked chassis can be obtained as follows:

[0084]

[0085] In order to eliminate the influence of the disturbance on the stability of the control system, measures need to be taken to suppress the disturbance, and one feasible method is to design an extended state observer to estimate the disturbance term, and then design a disturbance compensation controller to ensure the stability and robustness of the control system.

[0086] Specifically, assuming that the lumped disturbance d is first-order differentiable with respect to time t (denoted as ), it can also be regarded as a state variable. Therefore, the above linear system model can be extended to the following state space equation:

[0087]

[0088] wherein, I is a unit matrix.

[0089] According to the experience of modeling physical systems, it can also be assumed that the rate of change of the lumped disturbance is bounded but the limit is unknown, that is (wherein ||·||2 represents the 2-norm of a vector, and σ is an unknown normal number). Then, it is obvious that holds.

[0090] Next, the present application will design an extended adaptive terminal sliding mode observer based on the "separation principle" to estimate the lumped disturbance, and then design a trajectory tracking controller based on disturbance compensation to weaken the disturbance to ensure the robustness of the system and the accuracy of the trajectory tracking.

[0091] S2, construct a sliding surface equation containing a saturated function integral term.

[0092] Specifically, in order to design an effective sliding mode observer, an effective sliding surface needs to be constructed first. For this purpose, the error of the extended state variable is defined as wherein is the estimated value of . Therefore, the following sliding surface equation can be designed:

[0093]

[0094] wherein δ, α and ε are normal numbers, and α ∈ (0, 1), and ||·||1 represents the 1-norm of a vector. is a self-defined saturated function, and satisfies the following inequality relationship:

[0095] For a general column vector and a positive constant ε, define the saturation function as follows: where,

[0096]

[0097] Then, (where μ = 0.25), so that

[0098] S3, construct an extended adaptive terminal sliding mode observer.

[0099] Specifically, the extended adaptive terminal sliding mode observer designed for the extended state space equation has the following form:

[0100]

[0101] The corresponding adaptive update law of the disturbance upper bound is:

[0102]

[0103] where, is the estimated value of the unknown positive constant σ; ρ and λ are both positive constants.

[0104] Before using the observer to estimate the disturbance, the effectiveness of the observer should be theoretically proved, that is, the stability of the designed observer should be proved.

[0105] S4, prove the terminal stability of the observer based on Lyapunov function.

[0106] Specifically, considering that the sliding mode control generally includes two sub-processes of approaching and sliding, only by ensuring that each sub-process satisfies the terminal stability can the terminal stability of the entire system be ensured. Therefore, the terminal stability of the approaching process and the sliding process of the above observer should be proved respectively.

[0107] S401, prove the terminal stability of the sliding process of the extended adaptive terminal sliding mode observer designed in step S3.

[0108] That is, it is proved that the sliding mode surface designed in step S2 satisfies the terminal sliding stability, that is, it is proved that the observation error quantity falling on the sliding mode surface can always converge to a small neighborhood containing the stable state in a finite time.

[0109] Specifically, based on modern control theory, a positive definite Lyapunov function is constructed as follows:

[0110]

[0111] Note that on the sliding surface s=0, there is always Therefore, there is Substituting this into the first derivative of the Lyapunov function, we get:

[0112]

[0113] in,

[0114] Therefore, based on the finite-time practical stability theorem, the system The trajectory is practically stable in a finite time, meaning the observation error is... Can be done in a finite time t sl Slide inward to a small area containing the origin. Within, and at a finite time t sl satisfy:

[0115]

[0116] S402. Prove the terminal stability of the approaching process of the extended adaptive terminal sliding mode observer designed in step S3 above.

[0117] That is, to prove that the sliding state variable starting from any point in space can always reach a small neighborhood containing the sliding surface s=0 in a finite amount of time.

[0118] Specifically, based on the sliding stability of the sliding surface mentioned above, it can be seen that as long as s→0, there must be... Therefore, it is only necessary to prove Outside the sliding surface, i.e., when s≠0, the positive definite Lyapunov function is constructed as follows:

[0119]

[0120] in, Substituting the extended state-space equations and the designed extended adaptive terminal sliding mode observer expression into the first derivative of V2, and based on Jensen's inequality, we obtain:

[0121]

[0122] in,

[0123] Therefore, based on the practical stability theorem for finite time, it can be known that the sliding mode s can be maintained in a finite time t. re Reaching a small neighborhood containing the sliding surface s=0 Within, and at that finite time t re satisfy:

[0124]

[0125] Thus, under the action of the disturbance observer designed in step S3, the disturbance observation error is finite-time practically stable, and the corresponding convergence time t c with a finite upper bound, i.e.,

[0126]

[0127] S5, establish a disturbance compensation model for the control system and design a trajectory tracking controller.

[0128] Specifically, based on the observer designed in step S3, the estimated value of the lumped disturbance d can be accurately obtained Then, the influence of the disturbance factor on the control system can be eliminated by the following disturbance compensation strategy:

[0129]

[0130] where u c is the output of the tracking controller to be designed, K c is the compensation control gain. In order to eliminate the disturbance from the input channel, a simple and effective compensation gain can be taken as the negative inverse matrix of the control matrix B (i.e., K c = -B -1 , if B is nonsingular) or the negative pseudo-inverse matrix (if B is not full rank).

[0131] Therefore, the disturbance compensation model of the original linear system is:

[0132]

[0133] The disturbance compensation model of the corresponding extended observation system is:

[0134]

[0135] Based on the stability analysis in step S4, the disturbance observation error can converge to the origin (i.e., e d → 0) in finite time, so the compensation model of the above linear system can be equivalent to the nominal model Next, a suitable feedback controller u c is designed for the nominal model, which can achieve good trajectory tracking effect.

[0136] More specifically, for the trajectory tracking control problem of the tracked chassis, based on the nominal model the following PID controller can be designed:

[0137]

[0138] where eX : = X d -X represents that the state variable X deviates from its expected value X d error (note that X: = P d -P is the error of the track of the tracked chassis, so here X d = 0), and respectively represent the integral and differential of e X .

[0139] The beneficial effects of the present application are illustrated below based on simulation experiments.

[0140] Specifically, as shown in Figure 2 , whether it is a continuous time-varying disturbance or a step disturbance, the extended adaptive terminal sliding mode observer (EATSMO) designed by the present application can estimate the time-varying disturbance more quickly and accurately than the general extended state observer (ESO).

[0141] More specifically, as shown in Figure 3 and Figure 4 , the control method based on observer compensation has better trajectory tracking effect than the control method without compensation; compared with the PID controller without disturbance compensation and the PID controller based on ESO compensation (ESO-PID), the PID controller based on EATSMO compensation (EATSMO-PID) designed by the present application has smaller tracking error when tracking the time-varying pose trajectory. It can be seen that the trajectory tracking controller based on the extended adaptive terminal sliding mode observer designed by the present application has good stability and robustness.

[0142] The above-described embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the content of the present application. Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or make equivalent replacements to some technical features; and these modifications or replacements made according to the technical solutions and inventive concept of the present application should be included in the protection scope of the claims of the present application.

Claims

1. A trajectory tracking control method based on extended adaptive terminal sliding mode observer, characterized in that, The method comprises the following steps: establishing an extended state space equation for the control system; constructing a sliding surface equation containing a saturated function integral term; constructing an extended adaptive terminal sliding mode observer; guaranteeing terminal stability of the observer based on a Lyapunov function; establishing a disturbance compensation model for the control system and performing trajectory tracking control on the controlled object by a trajectory tracking controller.

2. The method of claim 1, wherein, The step of establishing an extended state space equation for the trajectory tracking control system comprises: Establish state-space equations for a linear system Where X and Let A represent the system's state variables and their first derivatives, respectively; let u represent the system's control input; let A be the state transition matrix; and let B be the input matrix. The aggregated disturbance d consisting of model uncertainty and external disturbance is added to the control system, and the linear system model is modified as: The first derivative of the lumped disturbance d with respect to time t is denoted as The modified system model can then be transformed into the following extended state space equations: wherein, is the extended state vector, is the extended state transition matrix, is the extended input matrix, is the disturbance coefficient matrix, i is the identity matrix; The rate of change of the lumped perturbation is bounded, i.e. where || · ||2denotes the 2-norm of a vector, σ is an unknown positive constant, and obviously has 3. The method of claim 1, wherein, The step of constructing a sliding surface equation containing a saturated function integral term comprises: Define the error in the extended state variable as where is an estimate of where X denotes the state variable of the system, is the extended state vector; d denotes the lumped disturbance, is the estimate of the lumped disturbance. The sliding surface equation is designed as: where δ, a and ε are all normal numbers, and a e (0, 1), ||·||1 represents the 1-norm of a vector; is a self-defined saturation function, and satisfies the following inequality relationship: For a column vector and a positive number ε, define the saturation function relation where, Then we have where μ = 0.25, so that 4. The method of claim 1, wherein, The step of constructing an extended adaptive terminal sliding mode observer comprises: The extended adaptive terminal sliding mode observer designed for the extended state space equation has the following form: wherein, is an extended state transition matrix, is an estimate of the extended state vector, is an extended input matrix, u represents the input variable of the system control, is an error of the extended state variable, δ, α and ε are all normal numbers, and α ∈ (0, 1), ||·||1 represents the 1-norm of a vector, is a self-defined saturation function, s is a sliding mode surface equation; The adaptive update law of the corresponding disturbance upper bound is: where is an estimate of the unknown normal quantity σ; both p and λ are normal numbers.

5. The method of claim 4, wherein, The step of guaranteeing terminal stability of the observer based on a Lyapunov function comprises: The step of determining terminal stability of the sliding process of the extended adaptive terminal sliding mode observer comprises: The positive definite Lyapunov function is constructed as: On the sliding surface s = 0, there is always Thus, we have Substituting it into the first derivative of Lyapunov function, we have wherein, Therefore, based on the finite-time practical stability theorem, the system The trajectory is practically stable in a finite time, meaning the observation error is... Can be done in a finite time t sl Slide inward to a small area containing the origin. Within, and at a finite time t sl satisfy: Thus, the observed error quantity falling on the sliding surface is always able to converge in a small neighborhood containing the steady state of the terminal sliding stability; The step of determining terminal stability of the approaching process of the extended adaptive terminal sliding mode observer comprises: From the sliding stability of the above sliding surface, it is known that as s→0, there must be Therefore, it is only necessary to prove Outside the sliding surface, i.e. when s≠0, a positive definite Lyapunov function is constructed as wherein, Substituting the extended state-space equation and the designed extended adaptive terminal sliding-mode observer expression into the first derivative of V2, and based on the Jensen inequality, we have: wherein Therefore, based on the finite-time practical stability theorem, the sliding mode s can reach a small neighborhood containing the sliding surface s = 0 in finite time t re , and the finite time t re satisfies:​ Therefore, the sliding mode state quantity starting from any point in space can always reach a small neighborhood containing the sliding surface s=0 in a finite time, thereby determining the terminal stability of the approaching process of the extended adaptive terminal sliding mode observer; Under the action of the observer, the disturbance observation error is finite-time practically stable, and the corresponding convergence time t c has a finite upper bound, that is:

6. The method of claim 1, wherein, The step of establishing a disturbance compensation model for the control system and performing trajectory tracking control on the controlled object by a trajectory tracking controller comprises: The observer accurately obtains an estimated value of the lumped disturbance d The influence of the disturbance factor on the control system can then be eliminated by the following disturbance compensation strategy: wherein u c is the output of the tracking controller to be designed, K c is a compensation control gain; in order to eliminate the disturbance from the input channel, a simple and effective compensation gain can be taken as the negative inverse matrix of the non-singular control matrix B, that is, K c = -B -1 , or the negative pseudo-inverse matrix of the non-full-rank control matrix B; The disturbance compensation model of the original linear system is: Wherein, A is a state transition matrix, and X is a state variable of the system; The disturbance compensation model of the corresponding extended observation system is: wherein, is the extended state transition matrix, is the estimation of the extended state vector, is the extended input matrix, u represents the input variable of the system control, is the error of the extended state variable, δ, α and ε are all normal numbers, and α ∈ (0, 1), ||·||1 represents the 1-norm of the vector, is a self-defined saturation function, s is the sliding mode surface equation; I is the unit matrix.

7. The method of claim 1, wherein, The step of establishing a disturbance compensation model for the control system and performing trajectory tracking control on the controlled object by a trajectory tracking controller comprises: Disturbance observation error Converge to the origin in finite time, i.e. e d → 0, so the compensated model of the linear system can be equivalent to the nominal model wherein A is a state transition matrix, X is a state variable of the system, B is an input matrix, u c is the output of the tracking controller to be designed; For trajectory tracking control of tracked chassis, based on nominal model A trajectory tracking controller can be designed as follows: where e X : = X d - X denotes the error of the state variable X from its desired value X d : = P d - P is the error of the tracked chassis trajectory, P d is the desired tracked chassis pose trajectory, P is the actual tracked chassis pose trajectory, denotes the integral of e X , denotes the derivative of e X .

8. The method of claim 1 or 7, wherein, The control method of the trajectory tracking controller is a PID control method, a fuzzy control method or a neural network control method.

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