Analysis And Design For High-order Stochastic Nonlinear Systems

This paper mainly focuses on the problem of stability analysis and controller design for high-order stochastic nonlinear systems. The systems we studied here usually contain some uncertainties,such as uncertain parameters, time delays and random interference, which makes this model a goodway to describe the systems in real life. Based on the stochastic nonlinear systems’ stability theo-ries, by combining with the adding a power integrator technique, the Back-stepping design technique,the certainty equivalence principle, the inequality transformation techniques, the homogeneous dom-ination technology and the decentralized control method for large scale systems, we construct statefeedback controllers and output feedback controllers for the systems and get less conservative results,which can render the closed-loop systems globally asymptotically stability in probability. The maincontent of the study can be divided into the following three parts:Part1, the state feedback controller design for a class of high-order stochastic nonlinear systemsis considered in this part. By using the technique of adding a power integrator, and choosing properLyapunov-Krasovskii functional, we finally construct a state feedback controller, it renders the closed-loop system globally asymptotically stability in probability and the state can be regulated to the originalmost surely. Compared with the existing research, this paper studies a class of much more generalsystems because the power order restriction is completely removed, the nonlinear growth condition islargely relaxed and a much weaker condition is given here.Part2, based on the study in the first part, we consider the output feedback controller design forthe high-order stochastic nonlinear systems in order to reduce the impact of the condition that not allof the state vectors are measurable. By applying the results obtained above, combining the certaintyequivalence principle and the homogeneous domination technology, we construct an output feedbackcontroller which renders the closed-loop system globally asymptotically stability in probability andthe output can be regulated to the origin almost surely.Part3, since that many systems in our daily life are large-scale systems, and their control prob-lems cannot be solved by centralized control methods dealt with single systems. We extend the studyin this part by extending the controlled objects to a class of high-order stochastic nonlinear large-scalesystems. By developing a decentralized high gain homogeneous domination approach, it is shown thatunder some general conditions, the closed-loop system can be proved to be globally asymptoticallystable in probability.