Research On Sliding Mode Control Of Uncertain Switched Systems

As an important class of hybrid dynamical systems, switched systems are consisted of a series of continuous-time subsystems or discrete-time subsystems and a switching signal among them. In the past two decades, the stability analysis and stabilization of switched systems have received an increasing attention. The reasons can be seen in the following two aspects. Firstly, switched systems have been used widely in practice. In physical world, many plants may subejet to abrupt variations in their structures, due to sudden changes of the environment, system components aging and changing of subsystem’s struture, which can be described as switched systems; Secondly, the dynamic analysis of switched systems is complex. Due to the existence of the switching signal, the sability analysis of switched systems is complex. A common example is that the dynamical performance of switched systems is not the simple superposition of the subsystems.It is well known that, sliding mode control (SMC) has many desirable properties, such as fast response, simple design and strong robustness against both uncertain parameters and matched disturbances. Therefore, SMC strategy has been an important robust control method and attracted a lot of attentions since its appearance in the1950s. In recent years, SMC method has been used to analyze switched systems and many constructive results have been developed. However, it is worth noting that the aforementioned works were considered under the assumptions that the input channels were the same, the system state was available, the actuator or sensor worked normally, or the system signals could be successfully transmitted to the controller/actuator. Theorefore, when the above conditions are not satisfied, the sliding mode controller design of switched systems may have important theoretical and practical significance in developing control performance of switched systems.For switched systems with different input matrices, a weighted sum of the input matrices is proposed. This thesis has discussed SMC of switched systems under the following cases: unavailable states, actuator nonlinearities, actuator faults, non-fragile observer and incomplete state information, and some meaningful results have been obtained.The main contribution in this thesis is as follows:(1) Considering the SMC for a calss of uncertain switched systems. Firstly, a weighted sum of the input matrices is proposed such that a common slidng surface is designed. Construct a switching signal depending on the state and time. Then, by employing the multiple Lyapunov function theory, the asymptotical stability of the sliding mode dynamics is analyzed. Moreover, a SMC law is designed to ensure the reachability of the sliding surface. Furthermore, when the system states are unmearable, by introducing a state observer, the output feedback control of switched systems is considered;(2) Considering the problem of SMC for switched systems with actuator nonlinearities. Firstly, by means of the weighted sum approach, a common integral sliding surface is designed. And then, the efficient condition on the exponential stability of the sliding mode dynamics is geiven based on the average dwell time method. In the cases that the control input contains both sector nonlinearities and deadzones, a special sliding mode controller depending on the switched function is designed, by which the reachability of the specified sliding surface is guaranteed;(3) Considering the reliable control of SMC for switched systems subject to actuator fualts. Firstly, the model of actuator faults with different degradation channels is proposed. And then, based on the theory of passive reliable control, a robust slidng mode controller is presented such that the closed-loop systems is exponentially stable despite the presence of actuator faults, external disturbances and uncertain parameters;(4) Considering the adaptive sliding mode control of switched systems. By estimating the actuator failures online, the controller’s parameters are updated adaptively. It not only reduce the conservatism compared with some existing approaches which only utilize the bound of the actuator gain variation, but also compensate effectively the effects of the gain variation of the actuators on the system performance. Finally, by designing a switching signal depending on the average dwell time, sufficient conditions on stability of the closed-loop systems were given;(5) Considering the non-fragile control for switched systems with unmearable state. Firstly, to estimate the unmearable state, a state observer is introduced, in which the uncetrtain parameters exist. And then, an observer-based sliding mode controller is designed such that the reachability of the sliding surface can be ensured. Finally, by menas of the multiple Lyapunov function method, the exponential stability of the closed-loop systems is analyzed;(6) Considering the SMC for discrete switched systems subject to incomplete state information. Firstly, a compensator is introduced such that the lost data can be estimated. A common sliding surface depending on the dropout-probability is constructed. And then, a compensator-dependent sliding mode law is designed. Thus, the augmented system consisted of system state and slidng variable is obtained. By employing the stochastic stability theory, it is shown that the sliding mode dynamics is mean square exponentially stable in a neighborhood of the origion. Meanwhile, the state trajectories are driven (with mean square) into a band of the sliding surface.