CN-121995745-A - Robust self-adaptive track tracking control method based on nonlinear extended observer

CN121995745ACN 121995745 ACN121995745 ACN 121995745ACN-121995745-A

Abstract

A robust self-adaptive track tracking control method based on a nonlinear extended observer belongs to the technical field of intelligent control and nonlinear self-adaptive robustness. The method comprises the steps of establishing a dynamics model of a nonlinear system, obtaining tracking error dynamics, constructing a hybrid performance function, mapping a constrained track tracking error into an equivalent unconstrained conversion variable, carrying out real-time estimation and feedforward compensation on system lumped disturbance by a nonlinear extended state observer, combining a nominal system design self-adaptive evaluation neural network weight update law with an optimal control strategy under the nominal system, constructing a time-varying gain mechanism with preset time characteristics, and constructing a composite optimal controller. The invention can ensure that the disturbed nonlinear system converges the tracking error to a steady-state limit in the preset time, and the whole process meets the preset transient performance envelope, thereby obviously improving the track tracking precision and robustness under complex disturbance.

Inventors

ZHANG HONGXU
RONG WEI
WANG ZHENHUA
WANG HONGGUI

Assignees

哈尔滨理工大学

Dates

Publication Date: 20260508
Application Date: 20251223

Claims (7)

1. A robust self-adaptive track tracking control method based on a nonlinear extended observer is characterized by comprising the following steps: s1, establishing a dynamics model of a nonlinear system, and combining a reference signal to obtain tracking error dynamics; s2, constructing a mixed performance function fusing preset time and preset performance attributes; s3, mapping the constrained track tracking error into an equivalent unconstrained conversion variable through an error conversion mechanism; S4, designing a fixed time convergence nonlinear expansion state observer with a multi-power composite feedback structure, and carrying out real-time estimation and feedforward compensation on the lumped disturbance of the system; s5, designing an adaptive evaluation neural network weight update law and an optimal control strategy under a nominal system by combining the nominal system; S6, constructing a time-varying gain mechanism with preset time characteristics, and constructing a composite optimal controller.
2. The robust adaptive trajectory tracking control method based on a nonlinear extended observer according to claim 1, wherein the step S1 comprises the steps of: s101, establishing a state space of a continuous time nonlinear system dynamic model with external disturbance: (1) In the formula (1): system state variables that are continuous-time nonlinear system dynamic models; Is a system state variable Is the first derivative of (a); to describe the inherent dynamic nonlinear unknown function of the internal state of the system; A control input matrix for reflecting the relationship of the control inputs to the system state; A control input for a continuous time nonlinear system; A disturbance input matrix for describing the action relation of external disturbance to the system state; Unknown bounded perturbations that are continuous-time nonlinear systems; S102, given a reference signal track: (2) in the formula (2): A system state variable which is a reference signal dynamic model; Is a system state variable Is the first derivative of (a); to describe a nonlinear function of a reference signal system; S103, establishing a tracking error system dynamics equation: (3) in the formula (3): is the original tracking state error; Is the original tracking state error Is a first derivative of (a).
3. The robust adaptive trajectory tracking control method based on a nonlinear extended observer according to claim 2, wherein the specific form of the mixing performance function of S2 is as follows: (4) in the formula (4): Is the original tracking state error Is defined as a function of the performance boundary of the (c), for any time Meets the preset performance control condition , wherein, The initial time of the system; Performance boundary function for constraining the original tracking state error magnitude Is defined by a set of values; performance boundary function for determining final steady state error accuracy of system Is a steady state boundary value of (1), the boundary value satisfies ; Is a decay function; A preset convergence time independent of the initial conditions; As a function of performance boundary Attenuation rate adjusting parameters of (a); Is a terminal smoothness parameter; To be irrational number An exponential function of the base.
4. The robust adaptive trajectory tracking control method based on a nonlinear extended observer according to claim 3, wherein the step S3 comprises the steps of: s301, constructing an error conversion mechanism: (5) in formula (5): The state variable is converted unconstrained system state variable; is an inverse hyperbolic tangent function; To be irrational number Natural logarithm of the base; s302, obtaining a converted unconstrained system: (6) in formula (6): a first derivative of the converted unconstrained system state variable; A nonlinear function of a post-conversion unconstrained system, wherein: As a function of performance boundary Is used as a first derivative of (a), Is a function of a hyperbolic cosine, As a hyperbolic tangent function; A control input matrix for the converted unconstrained system; The matrix is input for the disturbance of the unconstrained system after conversion.
5. The robust adaptive trajectory tracking control method based on a nonlinear extended observer according to claim 4, wherein the step S4 comprises the steps of: S401 defining a nonlinear function : (7) In the formula (7): Is a nonlinear power parameter; is a linear interval threshold; as a function of absolute value; is a standard sign function; S402, defining a lumped disturbance that the conversion system contains unknown nonlinearities and unknown disturbances: (8) s403, designing a fixed time converged nonlinear extended state observer with a multi-power composite feedback structure: (9) in the formula (9): as converted unconstrained system state variables Is used for the estimation of the (c), For estimating the value Is the first derivative of (a); For lumped disturbance Is used for the estimation of the (c), For estimating the value Is the first derivative of (a); is a nonlinear power parameter to be designed and satisfies And (3) with ; All are nonlinear observer gains; s404, constructing a feedforward compensation term based on a nonlinear extended state observer: (10) In the formula (10): control input matrix for post-conversion unconstrained system Is the generalized inverse of (a).
6. The robust adaptive trajectory tracking control method based on a nonlinear extended observer according to claim 5, wherein the step of S5 comprises the steps of: S501, constructing a nominal system of the unconstrained system after conversion: (11) in the formula (11): as a state variable of the nominal system, Is a state variable Is the first derivative of (a); A control input matrix for a nominal system; is a control input to the nominal system; s502, constructing a value function and an optimal value function in a finite time domain: (12) (13) In formulae (12) - (13): State variables for nominal systems Is a transpose of (2); Control input for nominal system Is a transpose of (2); Is that A cost function of the time of day, Is that An optimal value function of time; a constraint function is used for the terminal; a state weight matrix is positively determined; Inputting a weight matrix for positive control; As a function of the minimum value; s503, utilizing the evaluation neural network to function the optimal value Approximation is performed: (14) In formula (14): A weight vector for evaluating the neural network between the hidden layer and the output layer; the number of neurons being hidden layers; Is a weight vector Is a transpose of (2); Is a time-varying activation function; is the remaining time; approximation error for neural network; S504, designing an approximate optimal control law of a nominal system : (15) In formula (15): Input weight matrix for positive control An inverse matrix of (a); Control input matrix for nominal system Is a transpose of (2); Is the partial derivative Is to be used in the present invention, State variables for time-varying activation functions with respect to nominal systems Is a partial derivative of (2); to evaluate the weight of a neural network Is a function of the estimated value of (2); S505, designing and evaluating a weight update law of the neural network based on a gradient descent method: (16) In formula (16): for estimating the value Is the first derivative of (a); Is the learning rate of the neural network; Is the HJB residual error; Is HJB residual error Is a transpose of (2); the activation function value is the terminal moment; Function value for activation at terminal time Is a transpose of (2); Constraint errors for the terminal; constraining errors for terminals Is a transpose of (2); for estimating the value Is a transpose of (2); Weighting coefficients of the HJB residual error item, the terminal constraint item and the regularization item are respectively adopted; time for time-varying activation functions Is a partial derivative of (2); Is the partial derivative Is a transpose of (a).
7. The robust adaptive trajectory tracking control method based on a nonlinear extended observer according to claim 6, wherein the step S6 comprises the steps of: S601, constructing a time-varying gain control term with preset time convergence characteristics : (17) In formula (17): A time-varying gain parameter to be designed; s602 feedforward compensation term in combination with S404 Approximately optimal control law of S504 Time-varying gain control term of S601 Obtaining a final composite optimal controller: (18)。

Description

Robust self-adaptive track tracking control method based on nonlinear extended observer Technical Field The invention relates to a robust self-adaptive track tracking control method based on a nonlinear extended observer, and belongs to the technical field of intelligent control and nonlinear self-adaptive robustness. Background With the rapid development of industrial automation and intelligent manufacturing, in the mission-critical fields of aerospace, precision machining, minimally invasive surgery and the like, unprecedented stringent requirements are put forward on the track tracking control of a nonlinear system. These systems typically have strong coupling, nonlinear, and multivariate characteristics, and their control systems not only need to achieve error convergence within a preset time, but also must ensure that transient performance of the system state is severely constrained throughout to avoid overshoot and collision. However, such systems are often subject to a combination of model uncertainty, parametric perturbation, and external perturbation, making it extremely difficult to meet the dual objectives of both pre-set time convergence and overall process pre-set performance constraints. Traditional methods (such as PID control and sliding mode control) can only ensure asymptotic or exponential convergence, and convergence time depends on initial conditions, so that the explicit deadline requirement is difficult to meet. The preset performance control can restrict the transient and steady state boundaries of errors, but generally can not guarantee the convergence in a limited time based on an infinite time frame, and the preset time control can realize the convergence in a designated time, but often ignores the transient waveform restriction, is easy to cause overshoot and needs extremely large initial control energy. In addition, aiming at the system lumped uncertainty, the existing disturbance rejection technology (such as a linear expansion state observer) is easy to generate phase lag and amplitude attenuation when dealing with rapid time-varying disturbance, and the convergence speed and noise suppression capability near the balance point are difficult to be combined by the conventional finite time observer. Therefore, aiming at an uncertain nonlinear system under strong nonlinear disturbance, how to design a control method which can realize high-precision convergence within a preset time of a user, strictly follow transient performance constraint of the whole process and accurately compensate time-varying disturbance in real time is a key technical problem to be broken through in the field of robust control. Disclosure of Invention In order to solve the problems in the background technology, the invention provides a robust self-adaptive track tracking control method based on a nonlinear extended observer. The invention realizes the aim, and adopts the following technical scheme that the robust self-adaptive track tracking control method based on the nonlinear extended observer comprises the following steps: s1, establishing a dynamics model of a nonlinear system, and combining a reference signal to obtain tracking error dynamics; s2, constructing a mixed performance function fusing preset time and preset performance attributes; s3, mapping the constrained track tracking error into an equivalent unconstrained conversion variable through an error conversion mechanism; S4, designing a fixed time convergence nonlinear expansion state observer with a multi-power composite feedback structure, and carrying out real-time estimation and feedforward compensation on the lumped disturbance of the system; s5, designing an adaptive evaluation neural network weight update law and an optimal control strategy under a nominal system by combining the nominal system; S6, constructing a time-varying gain mechanism with preset time characteristics, and constructing a composite optimal controller. Further, the step S1 includes the following steps: s101, establishing a state space of a continuous time nonlinear system dynamic model with external disturbance: (1) In the formula (1): system state variables that are continuous-time nonlinear system dynamic models; Is a system state variable Is the first derivative of (a); to describe the inherent dynamic nonlinear unknown function of the internal state of the system; A control input matrix for reflecting the relationship of the control inputs to the system state; A control input for a continuous time nonlinear system; A disturbance input matrix for describing the action relation of external disturbance to the system state; Unknown bounded perturbations that are continuous-time nonlinear systems; S102, given a reference signal track: (2) in the formula (2): A system state variable which is a reference signal dynamic model; Is a system state variable Is the first derivative of (a); to describe a nonlinear function of a reference signal system; S103, establishing a t