Study On Stabilization And Tracking Control Of High-order Stochastic Time-delay Nonlinear Systems

In real life,many practical models are nonlinear systems and usually suffer from time-delays and random disturbances.Therefore,stochastic time-delay nonlinear systems can be adopted to describe this kind of models.As one of the general models,the research of high-order stochastic time-delay nonlinear system is of great realistic significance and theoretical value which provides the basis to the research of mechanical system,power system and biological system.For such kind of systems,based on the Lyapunov-Krasovskii stability theory,the stabilization and tracking control problems are considered here.The main work includes several aspects:First,by combining the adding a power integrator method,the tracking control and stability problems are considered for a class of systems with the same power.This part gives an output tracking controller which guarantees that all the states of the closed-loop system are bounded in probability and the mean square of the tracking error can be adjusted as small as possible.The results are further extended to system with stochastic input-to-state stable(SISS)-like inverse dynamics.Simulation examples are provided to show the effectiveness of the theory.Then,for a class of stochastic time-delay nonlinear systems with different powers,the tracking control problem is studied.Different from the above results,the powers of the nonlinear terms are relaxed to a certain interval rather than a precisely known point.More general results are obtained by constructing a new Lyapunov-Krasovskii functional and by using the modified adding a power integrator method.In addition,systems with unknown parameters,intricate stochastic drift terms and unknown time-delay are investigated.Based on the adaptive control strategy and the adding a power integrator method,an adaptive controller is proposed to ensure that the closed-loop system is globally asymptotically stable in probability.By modifying the method,an adaptive output tracking controller is designed to achieve the expected tracking performance.Numerical and practical examples are provided to show the effectiveness of the theory.At last,the global stabilization problem of non-triangular system is studied.Different from the existing results,the system here contains state delay and input delay.The nonlinear growing condtions are also more general.By using a gain-scaling method and a homogeneous domain control strategy,a delay-independent controller is constructed to ensure that the equilibrium of the closed-loop system is globally asymptotically stable in probability.