Adaptive Finite-Time Tracking Control For A Class Of Nonlinear Systems With Constraints

Since the 1980 s,the theory of linear control analysis and design marked by state space method has becoming mature.However,most of the actual industrial systems are nonlinear systems,thus the control research on the nonlinear systems has become a mainstream issue in the control field.With the development and maturity of science and technology,nonlinear terms,external disturbances,unmeasurable states and uncertainty problems generally exist in most practical engineering systems.Such as dead zones,saturations,etc.,are common in servo drivers,hydraulic brakes,and sensors.Their existences may severely degrade system performance,lead to instability and undersirable inaccuracy or oscillation.Therefore,the study of nonlinear systems with input nonlinearities is of great significance,and it has received much attention in control field.Besides,in practical system research,in order to achieve a certain performance,the state/output of the system is often subject to the certain constraints.Therefore,the control design of such system should not only ensure the expected performance of the system,but also keep the state/output of the system within the predefined constraints.Although some effective control schemes have been consecutively done,there are still some problems to be solved.Based on the current research status,in this paper,by using adaptive backstepping technique and neural network approximation method,the following research designs will be carried out for a class of nonlinear systems with constraints:Chapter 2 considers the influence of two factors,output constraint and input saturation,in the continuous nonlinear system,and presents the adaptive neural network finite-time tracking control scheme.In the framework of adaptive backstepping technique,neural networks are used to estimate the desired virtual signals.The designed barrier Lyapunov functions are designed and based on the finite-time stability theory,the stable system performance can be obtained.Finally,the simulation results are given to verify the correctness and effectiveness of the proposed method in this chapter.In chapter 3,the controller of nonlinear system with full state constraints and dead zone is devised.Based on the backstepping design method,with the help of the transformation expression of dead-zone model,the stability of the controlled system is analyzed by designing the appropriate barrier Lyapunov functions and combining with Lyapunov stability theorem.Finally,the simulation results verify the effectiveness of the proposed method,which can ensure that all signals in the closed-loop system are bounded in finite-time and the tracking error converges to a small neighborhood near the zero point.In chapter 4,considering the influence of time-varying full state constraints and dead zone factors in the robotic manipulators system,an adaptive finite-time tracking control method is designed.This chapter uses neural networks approximation method to estimate unknown functions,combining the finite-time control theory and the constructed time-varying barrier Lyapunov functions,a finite-time tracking controller is designed,so as to achieve control of the system,and makes the system obtain the finite-time stability,all closed-loop signals are bounded,the tracking error is small enough and all system states are in preset constrained boundaries.Furthermore,the effectiveness of the proposed control method is verified by some simulation results.