Finite-time Control Research Of Stochastic Nonlinear Switched System Based On Constraint

In actual engineering,the controlled object often has nonlinearity,uncertainty,boundedness of state variables,and time-varying structure,and is often disturbed by random disturbances from the outside world.Therefore,it has certain theoretical and application value to study the tracking problem and calming problem of stochastic nonlinear switched systems with constrained conditions.Therefore,based on backstepping technology,dynamic surface control method,Lyapunov stability theory,fuzzy system control theory and finite time control theory,this paper studies the finite time tracking control of stochastic nonlinear switched systems.The main content is divided into the following two parts:(1)A problem of fuzzy adaptive finite-time prescribed performance control for a class of stochastic nonlinear switched systems with input saturation is studied.Firstly,the performance function is introduced to convert the limited tracking error of stochastic nonlinear switched system into an equivalent unconstrained system,and a first-order dynamic system is used to approximate the input saturation function.Then,based on the Lyapunov theory,a finite-time backstepping controller is designed,at the same time,the comparison theorem and the mean value theorem of integral are used to establish a finite-time mean square error stability criterion to analyse the stability of the system.Finally,the effectiveness of this design method is verified by simulation.Through theoretical analysis and simulation,it can be known that this design method can not only effectively reduce the influence of input saturation on system performance,but also control the convergence speed and overshoot of the tracking error while ensuring that the tracking error of the system converges in a finite time.(2)The stabilization problem of a class of unmeasurable stochastic nonlinear switched systems with quantized inputs,full state constraints and external disturbances is studied.Firstly,a nonlinear hysteresis quantizer is used to quantize the input,which effectively avoids the occurrence of chattering.Then,the unmeasured state of the system is estimated by constructing a linear observer,and the unknown smooth nonlinear function in the system is approximated by the fuzzy inference system.Next,the barrier Lyapunov function is used to realize the constraints on the system state,and the dynamic surface control method is used to avoid the phenomenon of "differential explosion".Finally,the effectiveness of the above method is verified by simulation.Through theoretical analysis and simulation,it can be known that the control strategy proposed in this paper can not only ensure that the state of the system is bounded by probability under any switching rule,but also can ensure that the output of the system converges to a small neighborhood near the steady-state value.