Finite-time Control For Stochastic Systems

In recent years, the problems on finite-time control have attracted muchattention and become a popular research. The main problems on this respectare concerned on stability analysis and controller design. In this dissertation,the finite-time stability and stabilization and the corresponding robust controland filtering for stochastic systems have been studied. Some primary resultsare obtained. The details are given as follows:1. Based on the practical engineering problems, the novel concept offinite-time stability is proposed, which formalizes the characteristics of sys-tems in more detail. This leads to the diffculties of designing feedback con-troller to make the closed-loop system finite-time stable. This section stud-ies the stochastic systems with state and control dependent on noise, givesout a concept of finite-time stochastic stability and an equivalent propositionwhich provides an easier method to check the system finite-time stochasticstable. Moreover, finite-time stochastic stabilization is studied. Consideringfull state information and partial information, the two classes of controllers:state-feedback controller and dynamic output-feedback controller are designed.The corresponding algorithm is given to explore the scope of existence of thetwo controllers.2. The non-fragile finite-time stabilization for nonlinear stochastic sys-tems is studied. Using neural network and linear interpolation method, thenonlinear stochastic system is transformed to linear differential inclusion.Based on this model, by means of stochastic differential equation theory andmatrix analysis theory, a suffcient condition for the existence of this stabilizingcontroller is given.3. The finite-time guaranteed cost control for linear stochastic systems isproposed. A suffcient condition for the existence of the controller is given andan optimal guaranteed cost bound which is independent on exact initial value is obtained. Moreover, the finite-time guaranteed cost control withδ-stabilityconstraint is studied and a corresponding suffcient condition is given.4. The finite-time H_∞control for linear stochastic systems is given. Inthe sequence, by constructing Lyapunov-Krasoviskii function and using linearmatrix inequality approach, a suffcient condition for finite time H_∞controlof a class of linear stochastic systems is presented. Furthermore, the problemis reduced to the optimization problem under the constraint of linear matrixinequality and give the corresponding solving algorithm.5. The problem of non-fragile robust finite-time H_∞control for a classof uncertain nonlinear stochastic systems is investigated. Applying multi-layer feedback neural networks, the nonlinearity is approximated by lineardifferential inclusion(LDI) under state-space representation. Then, a suffcientcondition is proposed for the existence of non-fragile state feedback finite-timeH_∞controller. Furthermore, the optimal non-fragile control is studied and adetailed solving algorithm is given. Finally, an example is given to illustratethe effectiveness of the developed method.6. The finite-time H_∞filtering problem for a class of nonlinear stochas-tic uncertain systems is considered and the difference from finite horizon H_∞filtering is explained. Then, by Lyapunov function and matrix inequality ap-proach, a suffcient condition for finite-time H_∞filter of a class of nonlinearstochastic uncertain systems is presented, and the relationship with infinitehorizon H_∞filtering is explained.