The Study Of Analysis And Synthesis For Hybrid Systems

With the development of information technology, computer, robotic and so on, a class of man-made systems have appeared which reflect technique trend in the area such as communication, manufacture, traffic management, military command, etc., and prompt the development of the theory of discrete event dynamical systems(DEDS). DEDS theory reflects dynamical law of all kinds of man-made systems. Hybrid systems consist of the discrete event interacting with continuous dynamic, and the theory and application of hybrid systems have attracted many researchers. Unlike the conventional continuous variable control system and discrete event dynamical system, hybrid system contains not only continuous dynamical systems subject to Newton's law of causation but also discrete event system satisfied the optimal decision logic principle, and both of them accord with the same strong interaction condition. In general, the differential or difference equations describe the continuous subsystem of hybrid systems, while the discrete event subsystem is described by Petri net model, automata and max/min algebra model. In this dissertation, automata model is applied to study hybrid systems.The main contents contain the analysis and design of hybrid systems. Analysis of hybrid systems mainly contains Zeno problem, stable problem and fault diagnosis, while in the design of hybrid systems, the strategies mainly contain u calculus combined with game theory, method based on Zeno reachable specification, optimal control problem based on a kind of mixed dynamical programming. In this dissertation, the main contributions are as follows.1) Prompt a kind of modified hybrid game automata model. Since u, calculus can describe the system character as fixed point operator in the state space, and the method of game theory characterized the different effect to hybrid systems between controller and environment, the game theory and u calculus are combined to study control problem of hybrid systems, and the game control strategy is prompted based on u calculus.2) Based on the results of analysis and control design of Zeno hybrid systems, the reachable problem of hybrid systems got deep into study, the new notations such as Zeno reachable and some basic properties are given, then the shortage of prior synthesis strategy are studied and a kind of control method based on Zeno reachable specification is presented.3) For the optimal control problem of hybrid systems whose continuous location duration is deterministic, the model is first given. Then a kind of new method, that is, mixed dynamical programming is applied to study optimal control problem of hybrid systems, at same time, two implement strategies are obtained. At last, based on multiple Lyapunov functions, the stability of the resulting closed-loop hybrid system is analyzed.4) For the stability problem of hybrid systems whose continuous dynamical subsystems are supervised by discrete event, the shortage of prior results by using multiple Lyapunov functions is described. An example is applied to show the stability of hybrid systems could be analyzed by using multiple Lyapunov function when the switching hypersurface becomes sliding mode. Based on Filipov theory, a viable stability is studied and the quadratic stabilization of hybrid systems whose continuous subsystems is linear time invariant system is studied.5) Timed DBS is applied to modeling hybrid systems. In order to solve the model complexity problem of hybrid systems supervise and design because of time property of discrete event, a kind of combined modeling method based on timed DBS is presented. Then the active diagnosis algorithm is given based on this model.