Research On Sliding Mode Control Of Stochastic Markovian Jumping Systems

Markovian jumping systems (MJSs) have recently received considerable attention, since they may effectively represent a class of plants with abrupt variations in their structures. These changes can be due, for instance, to sudden environmental disturbances, component failures or repairs, changes in subsystems interconnections, etc. Examples of these situations can be found in economic systems, aircraft control systems, robotic manipulator systems, etc. On the other hand, it is known that stochastic modeling (especially the Markov process) has played an important role in many real-world systems, and Ito differential equation is one of the most useful stochastic models in applications. Hence, Ito stochastic MJSs may be the representative model for systems subject to both abrupt changes in their structures and the random factors.It is well known that sliding mode control (SMC) is an effective robust control approach for uncertain systems. The main strengths of SMC systems are its robustness to variations of systems parameters and external disturbances, fast response, simple design and reduced-order sliding mode dynamics. In recent years, considerable applications on SMC for stochastic MJSs have been developed, which have shown the effectiveness of SMC. However, it is worth noting that the aforementioned works were considered under the assumptions that the system state was available, the actuator or sensor worked normally, or the system signals could be successfully transmitted to the controller/actuator, which may result in limited application fields, and are usually difficult to satisfy in actual physical systems.By analyzing the features and the design methods of sliding function for stochastic MJSs, this thesis has discussed the SMC of stochastic MJSs under the following cases:unavailable states/actuator nonlinearities/actuator degradation/incomplete state information, and some meaningful results have been obtained. The effectiveness of these proposed methods has been theoretically validated and supported by numerical simulation.The main contribution in this thesis is as follows:(1) Considering the output feedback control for stochastic MJSs via sliding mode design. Firstly, a state observer is constructed to estimate the unmeasured states. And then, sliding functions are constructed in the estimation space, in which a set of specified matrices are employed to establish the connections among sliding functions corresponding to different modes, and the analysis on the stability of sliding motions is made. Moreover, a state estimate-based sliding mode controller is synthesized, and the reachability of the specified sliding surface is attained.(2) Considering the problem of SMC for stochastic MJSs with actuator nonlinearities. The integral sliding functions are designed firstly, by means of Lyapunov function, sufficient conditions are derived such that the sliding motion on the specified sliding surface is globally asymptotically stable with probability one. And then, considering the control input may contain both sector nonlinearities and deadzones, a sliding mode controller depending on the transition rates is synthesized such that the reachability of the specified sliding surface can be ensured.(3) Considering the reliable problem of SMC for stochastic MJSs subject to actuator degradation. Firstly, the model of actuator degradation is presented, and then, both the sliding function and reliable sliding mode controller are designed, respectively. By means of Lyapunov theory, the analysis on both the reachability and the stability of the closed-loop system are made simultaneously, and sufficient conditions are derived to ensure the stochastic stability, and the reachability of the specified sliding surface is guaranteed.(4) Based on the previous work, an adaptive sliding mode control strategy is proposed for stochastic MJSs with actuator degradation, which not only ensures the reachability of the specified sliding surface, but also effectively compensates the effect of actuator degradation on the system performance by adaptively updating the controller’s parameters. Finally, the sufficient conditions for the stability of the closed-loop systems are derived.(5) Considering the SMC for T-S fuzzy stochastic MJSs. By introducing some defined matrices and linear matrix inequalities conditions, the assumption that each nominal local system model shares the same input channel is removed, which is usually required in some existing works on SMC of T-S fuzzy systems. Hence, the present method has less conservativeness. The integral sliding function and sliding mode controller involving in the transition rates from one mode to another are designed. It is shown that both the reachability of sliding surfaces and the stability of sliding mode dynamics can be ensured.(6) Considering the SMC for discrete MJSs subject to incomplete state information. An estimation method is introduced to compensate the lost data, based on which the integral-like sliding functions are designed, and the sufficient conditions for the stability of the sliding mode dynamic are derived. Moreover, a dropout-probability-dependent SMC law is designed. By means of the stochastic Lyapunov method dependent on sliding mode variable and system state, the analysis on the reachabiltiy is made, simultaneously, with the stability of the closed-loop system, which means that the state trajectories will be driven (with mean square) into the band of the sliding surface.