Model Reference Adaptive State Tracking Control For Switched Systems

As a particular class of hybrid systems, switched systems are of great significance both in theoretical research and engineering applications, and have received much of the focus in recent years. Since uncertainties such as the modeling error, environment noise and load changing often exist in a dynamical system; traditional control methods usually cannot guarantee desirable performances of systems with uncertainties, in particular for switched systems. Therefore, it is important to investigate uncertain switched systems from both theoretical and practical point of view. Due to the co-existence of discrete dynamics, continuous dynamics and uncertainties which are also interact with each other, behaviors of an uncertain switched system become very complicated; and the mechanism that triggers those behaviors of such a system is far from clear. Thus, issues on this subject remain fully studied, and deserve more attention. This dissertation studies the model reference adaptive state tracking control problem for switched systems by designing switching signals, switched controllers and switched adaptive laws. Actuator failures, controller failures and asynchronous switching are also considered in the dissertation. The main contributions of this thesis are as follows.(1) The state tracking problem of the model reference adaptive control for switched systems is investigated. We consider a class of linear systems with unknown constant parameters, and suppose none of the given adaptive controllers can achieve control targets. Differing from the traditional control method, we introduce switched mechanism into those adaptive controllers, rather than redesign them completely. The stabilizing switching signal is identified by the convex combination technique, under which the state tracking problem of the close-loop system is solved.(2) We study the state tracking problem for a class of model reference adaptive control systems with intermittent failures of all actuators. Considering the actuator failures, the error system is modeled as a switched system. Then, some sufficient conditions are provided to guarantee the global practical stability of the error system. The proposed method differs from the existing ones which are all based on the assumption that failures affect a certain subset of actuators and the remaining actuators can achieve a desired control objective. Thus, it is still valid for the system with a signal actuator.(3) We study the state tracking problem for a nonlinear uncertain systems in the presence of controller temporary failure. We give some sufficient conditions, under which the model reference adaptive state tracking control problem is solvable. The tracking problem of the system in the presence of controller temporary failure is transformed into the stability issue of an error switched system. Then, the switched adaptive law is designed subsequently. The global practical stability of the error switched system can be ensured by dwell time technique.(4) The H∞ state tracking problem for a class of uncertain switched systems is investigated for the first time. We provide a solution to the state tracking problem of switched systems with both parametric uncertain and external disturbance input. We first study a switched reference model and give a stability criterion for such a system. Then, an H∞ adaptive controller is designed for the error switched system with external disturbance input. By using the average dwell time method, sufficient conditions are given to guarantee the global practical stability of the error switched system, and thus, the H∞ state tracking model reference adaptive control problem is solved.(5) The state tracking model reference adaptive control problem for an uncertain switched system with asynchronous switching is concerned for the first time. For the phenomenon of asynchronous switching between a subsystem and its corresponding controller, we proposed a sufficient condition such that the switched reference model is bounded input bounded state stability. Then, we convert the state tracking problem into the stability problem of an error switched system. A parameter projection adaptive law is designed, and a novel method is proposed to estimate the convergence and divergence rates of the state tracking error. A class of switching signal is identified to guarantee the global practical stability of the error switched systems by the dwell time technique. Furthermore, we reveal the interaction between the asynchronous switching and the "slowly" switching in sense of dwell-time, and the effect on the tracking performance.Finally, the results of the dissertation are summarized and further research topics are pointed out.