Randomized, Several Control Problem Of Uncertain Nonlinear Systems Is Studied

Ever since the stochastic stability theory is established and improved, the controllerdesign and stability analysis for stochastic nonlinear systems have achieved remarkable the-oretical results. Due to time-delay phenomena existing in many practical systems, and theexistence of time-delay being often a significant cause of instability and deteriorative per-formance, the study on stochastic nonlinear time-delay systems has received much attentionin recent years. This paper investigated problems of controller design and stability analysisfor several classes of important stochastic、uncertain nonlinear systems. The main contri-butions include:1. For a class of stochastic high-order nonlinear systems with stochastic inverse dynam-ics, this chapter investigates state-feedback control problem. Under the assumption thatthe inverse dynamics of the subsystem is stochastic input-to-state stable, by extending theadding a power integrator technique, choosing an appropriate Lyapunov function and usingthe idea of changing supply function, a smooth state-feedback controller is constructed toensure that the equilibrium at the origin of the closed-loop system is globally asymptoticallystable in probability and the states can be regulated to the origin almost surely.2. This chapter investigates output-feedback control for a class of stochastic high-ordernonlinear systems with time-varying delay for the first time. By introducing the adding apower integrator technique in the stochastic systems and a rescaling transformation, andchoosing an appropriate Lyapunov-Krasoviskii functional, an output-feedback controller isconstructed to render the closed-loop system globally asymptotically stable in probability,the output can be regulated to the origin almost surely.3. The homogeneous domination approach is introduced to solve the state feedback sta-bilization problem for a class of stochastic high-order nonlinear systems with time-varyingdelay. Under the weaker conditions on the drift and difusion terms, by using the homo-geneous domination approach and solving several troublesome obstacles in the design andanalysis procedure, a state feedback controller is constructed to render the closed-loop systemglobally asymptotically stable in probability.4. This chapter further discusses the output feedback stabilization problem for stochas-tic high-order nonlinear systems with time-varying delay. Under the weaker conditions onnonlinearities in drift and difusion vector fields, by using the idea of homogeneous dom- ination approach, skillfully choosing an appropriate Lyapunov-Krasoviskii functional, andsuccessfully solving several troublesome obstacles in the design and analysis procedure, anoutput feedback controller is constructed to render the closed-loop system globally asymp-totically stable in probability.5. This chapter investigates a class of stochastic feedforward nonlinear systems withtime-varying delay. By introducing the homogeneous domination approach to stochasticsystem, a state feedback controller is constructed to render the closed-loop system globallyasymptotically stable in probability.6. This paper studies the problem of decentralized adaptive output feedback stabiliza-tion for a class of interconnected systems with dynamic input and output interactions andnonlinear interactions by using MT-filters and the backstepping design method. It is shownthat the closed-loop decentralized system based on MT-filters is globally uniformly bounded,all the signals except for the parameter estimates can be regulated to zero asymptotically,and the L2and L∞norms of the system outputs are also be bounded by functions of designparameters.7. This chapter investigates the problem of adaptive output feedback stabilizationusing MT-filters and the backstepping design method for a class of nonlinear systems withunknown input and output time-delay. It is shown that all the signals in the closed-loopsystem are globally uniformly bounded, and the output can be regulated to zero.