Research On Control Of High-Order Stochastic Systems

Because high-order stochastic systems are widely used in engineering,traffic,management,economy,and aerospace,their control design has attracted much attention from researchers.Inspired by the above,in this paper,the control problem of high-order stochastic systems is explored by using the method of backstepping method and high-gain homogeneous dominance.The main contents include the following four parts:1.For high-order stochastic systems with time-varying powers and Markov switching,the control problem is discussed.Specifically,by constructing a new dimension reduction observer with dynamic gain and using the infinitesimal generator of the Markov switching system,the output-feedback controller is designed to ensure that the closed-loop system has an almost surely unique solution and the states are regulated to the origin almost surely.Finally,by simulation,the feasibility of the design method is verified.2.For high-order stochastic systems with time-varying powers and unknown covariance,the control problem is discussed.Specifically,the adaptive law function is constructed by reasonable estimation.Then,by using the backstepping method,we design a state-feedback controller to ensure the closed-loop system is globally stable in probability and the states are regulated to the origin almost surely.Finally,the feasibility of this design method is verified by two examples.3.The decentralized control problem for large-scale high-order stochastic systems with unknown covariance and time-varying powers is investigated.Unlike the existing results,a more general system is considered,that is,the system is large-scale,and its bounds are not needed to be considered when dealing with unknown timevarying covariance,but use the estimator to design an adaptive law function.Then,by using the backstepping method,we construct a controller to ensure that the closedloop system is globally stable in probability and that the states are regulated to the origin almost surely.Finally,by simulation,the feasibility of the design method is verified.4.The decentralized output-tracking problem for high-order stochastic systems.Firstly,we study the nominal system of the original system,and the unknown state information is estimated.Then,by using the high-gain homogeneous dominance technique and the backstepping method,the controller is designed to prove all the signals of the closed-loop system bounded in probability,and the output-tracking error can be adjusted to a small neighborhood of the origin.Finally,the feasibility of the design method is verified by simulation.Finally,summarize the full text and look ahead.