Finite-time Stabilization Of A Class Of Stochastic High-order Nonlinear Systems With Nonsmooth Input

In recent years,as nonlinear characteristic,non-smooth inputs,and external stochastic disturbances are common in engineering systems,many deterministic models cannot be applied in high-performance command engineering.In view of this,the control problem of stochastic high-order nonlinear systems has been extensively studied.Moreover,compared to asymptotical stability in Lyapunov,closed-loop systems with finite-time control law usually not only demonstrate higher accuracy and better disturbance rejection properties,but also fully considers the system's transient performance,so the finite time stabilization problem has become a research hotspot.Based on finite-time stability theory,adding a power integrator technique and the homogeneous systems theory,this paper researches the finite-time stabilization problem for a class of stochastic high-order nonlinear systems with non-smooth input systems.The main work of this paper includes the following three aspects.Firstly,the almost surely finite-time state feedback control problem for a class of stochastic nonlinear systems is studied.A smooth state feedback controller is designed to make the system studied almost surely stable for a limited time.The adding a power integrator method is employed to construct a state feedback stabilizer.The closed-loop system is almost surely global finite time stable with any initial.Finally,a set of numerical simulations is carried out to verify the effectiveness of the design in this chapter.Secondly,the global finite-time stabilization for a class of time-varying stochastic high-order system with the nonlinear characteristics are low order is studied.First the constraint of the nonlinear function term is given.Next,the adding a power integrator method is employed to construct a continuous state feedback stabilizer and it protects the system is global finite-time stable in probability for any initial.Finally,two sets of simulation examples are carried out to demonstrate the effectiveness of the proposed control method.Finally,the global finite-time output feedback stabilization method of a class of stochastic high-order nonlinear systems with dead zone input characteristics is studied.In this chapter,the unknown dead zone input is first modeled.In the design process of output feedback control,the output feedback controller is designed first in the nominal system.The second step is to establish the global finite-time output feedback control of the nominal system based on the homogeneous system theory and the adding a power integrator technique.The third step is to introduce a scale gain to offset the effects of drift and diffusion terms,which proved the closed-loop system composed of the original system can be global stabilized in finite time.Finally,a set of numerical simulations is given to show the effectiveness of the conclusions of this chapter.