Adaptive Fuzzy Finite-time Control For Stochastic Nonlinear Systems

The stochastic disturbance is ubiquitous in nonlinear systems of the real world.The stochastic nonlinear systems represented by It(?) calculus are the main form of describing systems with disturbance.In recent years,the research of stochastic nonlinear systems has attracted extensive attention and is one of the hot topics in nonlinear control theory.It is difficult and challenging to stability analysis of stochastic nonlinear systems because they cannot be calculated by Riemann calculus.In addition,many practical stochastic nonlinear systems(such as robot systems,chemical production processes,and intelligent transportation systems)have high requirements on the convergence performance of the controlled object,and the research on the finite-time control of this kind of nonlinear system needs to be further improved.Therefore,it has important theoretical significance and application value for studying the stability and finite-time control for stochastic nonlinear systems.Based on the adaptive fuzzy control method and Lyapunov stability theory,this paper starts from the control problem of deterministic nonlinear systems and extends to the control problem of stochastic nonlinear systems using stochastic calculus Ito formula and infinitesimal operators.Furthermore,based on Lyapunov finite-time stability theory,the finite-time control problem is studied.The main work is as follows:1.The stability and finite-time control problems of nonlinear systems with full state constraints are studied.The median value theorem is used to transform the nonlinear system with pure-feedback form into strict-feedback form,the obstacle Lyapunov function is constructed to meet the requirements of state constraints,the fuzzy logic system is used to approximate the unmatched uncertainty in the controlled system,and the adaptive backstepping control method is integrated to design the controller satisfying the state constraints.Dynamic surface technology is used to reduce the derivation process of the virtual controller and the complexity of the controller algorithm.Furthermore,based on Lyapunov finite-time stability theory,a finite-time stability controller satisfying state constraints is designed.2.The stability and finite-time control of high-order stochastic nonlinear systems are studied.The order of the high-order stochastic system is reduced by the inequality scaling technique,the unknown nonlinear dynamics of the controlled system is approximated by the fuzzy logic system,the high-order Lyapunov undetermined function is constructed according to the characteristics of the high-order stochastic system,and the controller of the high-order stochastic system is designed based on adaptive backstepping control method.Furthermore,considering both the transient performance index and the steady-state convergence index of the system,the exponential transient index is integrated into the state space equation of the stochastic system by using the state transformation reconstruction method.Combining Lyapunov finite-time stability theory,a higher-order finite-time controller with both transient and steady-state performance is designed.3.The finite-time fault-tolerant control problem of stochastic nonlinear systems with undetectable states and actuator faults is studied.The fuzzy state observer is designed by using the system output to observe the unmeasured state of the controlled system.The fuzzy adaptive law is used to approximate the unknown nonlinear dynamics and the fault adaptive law is constructed to approximate the partial failure degree of the system actuator.Considering unknown nonlinear dynamics and actuator fault characteristics,merging fuzzy adaptive law and fault adaptive law,and combing quartic barrier Lyapunov function and Lyapunov finite-time stability theory,a finitetime fault-tolerant controller is designed for stochastic nonlinear systems based on output feedback.4.On the basis of the finite-time control research,the fixed-time control of stochastic nonlinear systems is further studied.By using the fixed-time control theory and the stability theorem of stochastic systems,the fixed-time convergence conditions of stochastic systems are solved by increasing the power of the controller to remove the initial state limit.Combining convergence conditions and It(?) calculus infinitesimal operator,an adaptive fuzzy fixed-time controller with stronger convergence performance is designed by using the Cauchy Schwartz inequality and absolute value inequality scaling method.5.Matlab simulation software is used to carry out simulation verification of the above research problems.Simulation results show that the designed control strategy can ensure that the controlled system tends to be semi-globally uniformly ultimately bounded,satisfy the given control requirements.Compare with the existing results,the proposed methods which achieve good control performances have ability of fault tolerance and improve convergence rate of the system.In this paper,the adaptive fuzzy control methods are proposed to achieve the finite time stability for nonlinear systems and stochastic nonlinear systems by combining the stochastic system stability theory and the finite time stability theorem.An output feedback fault-tolerant controller is designed to improve the fault-tolerant capability for stochastic nonlinear systems.The dependence limits of the convergence time on the initial state is released.The fixed time control strategy of stochastic nonlinear system is obtained.Aforementioned provide theoretical support for the application in engineering practice.