Design And Application Of Variable Structure Control Of Uncertain Distributed Parameter Systems And Stochastic Systems

The variable structure control appeared in the 1950s and the great progresses have been made for 50 years. At present, it is an independent research branch and has become an important designed method in control theory. Under certain conditions, the designed variable structure control law makes the sliding mode along a specified sliding manifold invariable to the system perturbation and external disturbances. Due to these good properties, many researchers have paid attention to this method. In this paper, the variable structure control problems of the uncertain distributed parameter systems and stochastic systems are studied, and the variable structure control theory is applied to study the nonlinear ship'course-keeping control system with actuator dynamics.In the first chapter, we briefly introduce the variable structure control theory and its developing history, the survey of variable structure control of uncertain distributed parameter systems and stochastic systems, and the background knowledge of ship'course-keeping control systems.In the second chapter, the variable structure control problem of a class of uncertain distributed parameter system is studied. Because the research methods based on operator semi-group theory usually lose some of the features of the system itself and then major errors arise, the characteristic of the systems itself is directly used to study the variable structure control problem of a class of distributed parameter system. The existence of uncertainties and time-varying delay makes the problem more complex and difficult. The two methods of the design of variable structure control laws with delay term and without delay term are presented, respectively. These control laws not only guarantee the system's trajectories to reach the sliding mode in finite time, but also ensure the sliding mode to be exponentially asymptotically stable. Simulation examples are given to illustrate the effectiveness of the proposed design method.In the next two chapters, the variable structure control problem of It(o|^) type stochastic systems is studied. As stochastic control systems can accurately describe the uncertain factors surrounding system, their theoretical research has been highly thought by many scholars. In the third chapter, the variable structure control problems of It(o|^) type stochastic systems with centralized parameters are thoroughly studied. The system model contains multiple factors such as time-varying delay, parameter perturbation and nonlinear. Using mean, variance conceptions in the definition of the sliding mode reachability can better reflect the stochastic characteristics of the systems. The sufficient conditions of sliding mode mean stability are given, and the variable structure control law can guarantee the sliding mode to have reachability.As the control problems of the stochastic systems with distributed parameters are more difficult, these systems have not been studied still in a deepgoing way by now. The reasons probably arise from their double complexity of distributed parameters and stochastic factors. In the fourth chapter, the research methods in centralized parameter stochastic systems and the variable structure control techniques are applied to the distributed parameter stochastic systems, and the variable structure control problems of two classes of It(o|^) type stochastic systems with distributed parameter are studied. The variable structure control laws are designed to ensure the sliding mode to have reachability. The numerical simulation results are given to verify the effectiveness of the proposed control law.In the fifth chapter, the variable structure control methods of nonlinear systems are used in the ship's course-keeping system with actuator dynamics. The mathematic model of these system has the form of triangular system. The necessary and sufficient conditions for feedback linearization of this triangular system are more easily testified than the involutivity conditions for the feedback linearization theory. The designed control law can force a ship to exponentially asymptotically stabilize to a specified course. The simulation results on a far going experimental ship named'YuLong'of Delian Maritime University show that the designed methods to be proposed is very effective.In the sixth chapter, the full paper is summarized, and some greatly significant research directions are proposed.