Stochastic Nonlinear Systems Control Problems And Applications

In recent years, the fruitful theoretical achievements and extensive prac-tical applications in controller design and stability analysis for stochastic non-linear systems have been achieved. For a few classes of important stochastic nonlinear systems, this dissertation will study controller design, analysis a,nd practical applications. The main contents are as follows:(â… ) Control effort reduction in output-feedback stabilization for stochastic nonlinear systemsFor a class of stochastic nonlinear systems in which the drift and diffu-sion vector fields depend on the unmeasurable states besides the measurable output, the research purpose of this part is to find the maximum value in-terval of observer gain for the desired control performance. For this interval, the designed output-feedback controller ensures that the equilibrium at the origin is globally asymptotically stable in probability, and the inverse optimal stabilization in probability is achieved.(â…¡) State-feedback control of high-order stochastic nonlinear systems with SiISS inverse dynamicsThis part considers a class of high-order stochastic nonlinear systems with stochastic integral input-to-state stability (SilSS) inverse dynamics and drift and diffusion terms depending upon the stochastic inverse dynamics and all the states. A new design and analysis approach to the problem of state-feedback global regulation is developed to guarantee that all the signals of the closed-loop system are bounded almost surely and the states can be regulated to zero almost surely.(â…¢) Output-feedback control using small-gain conditions for stochastic nonlinear systems with SiISS inverse dynamics This part further discusses output-feedback control for stochastic nonlin-ear systems with stochastic integral input-to-state stability (SiISS) inverse dynamics. Based on the stochastic LaSalle theorem and small-gain type conditions on SiISS, an output-feedback controller using the backstepping method is constructively designed to guarantee that all the closed-loop signals are bounded almost surely and the stochastic closed-loop system is globally asymptotically stable in probability.(â…£) Output tracking of high-order stochastic nonlinear systems with application to benchmark mechanical systemThis part considers output tracking of high-order stochastic nonlinear systems without imposing any restriction on the high-order and the drift and diffusion terms. By using the backstepping design technique, a smooth state-feedback controller is given to guarantee that the solution process is bounded in probability and the error signal between the output and the reference signal can be regulated into a small neighborhood of the origin in probability. A practical application of stochastic benchmark mechanical system are provided at last.