Stability Control For Several Classes Of Stochastic Systems

Stochastic control has always been one of the most challenging control problems in the field of control theory.Random disturbance is the main controlled factor of stochastic control.It will deteriorate the performance of the systems and even affect the stability of the systems.In order to achieve better performance and cost saving of the controlled system,the stability control of stochastic systems has become a hot research area in the field of control theory.Therefore,the stability of stochastic systems is of great significance to practical engineering systems.Based on the stability theory of stochastic systems,the control problems of stochastic discrete-time mean-field systems,stochastic nonlinear systems with time-varying delays and asymmetric output constraints are considered in this thesis.The specific research contents are as follows:1.For a class of discrete-time mean-field systems with Poisson process driven by Brownian motion,the problem of stochasticH₂/H_∞control is studied.Firstly,a mean-field stochastic bounded real lemma（SBRL）is derived in this thesis.Secondly,a sufficient condition for the solvability of Poisson jump-diffusion linear quadratic（LQ）optimal control of discrete-time mean-field type is presented.Finally,based on the results of SBRL and LQ optimal control,the sufficient conditions for the existence of stochasticH₂/H_∞control of discrete-time mean-field systems with Poisson process are established by the solvability of the coupled matrix value equations.2.For a class of stochastic nonlinear systems with time-varying delays,the problem of output feedback stabilization with an unknown output function is investigated.A remarkable feature of the system to be considered is the simultaneous presence of a continuous unknown sensitivity function and the random disturbances,which have not been treated together before.A new observer is designed by using a dynamic gain without using the information on unknown time-varying delay and nonlinearities.With the aid of the observer,an output feedback controller is constructed by the stochastic double-domination method,where two gains are used to handle the unknown output function and nonlinearities.The performance of the systems is analyzed in detail via two integral Lyapunov functions.3.For a class of high-order stochastic nonlinear systems,the finite-time state feedback stabilization problem with asymmetric output constraints is studied.In the presence of the systems with uncertain control coefficients,a novel asymmetric barrier Lyapunov function is constructed to manipulate the output constraint for the systems.By adding a power integrator method and sign function technique,this thesis designs a state-feedback controller by recursive method for the high-order stochastic nonlinear systems.While guaranteeing output constraint,the finite-time state-feedback stabilization is achieved for the proposed stochastic nonlinear systems.Finally,the efficiency of the control strategy is illustrated by a simulation example.