Optimal Control Of Hybrid Systems

As an important research direction to explore complex systems, researches on hybrid systems have become a hot issue in system control fields. This paper is devoted to optimal control of hybrid systems. Optimality conditions at the continuous part and juming instants are investigated for several important classes of hybrid systems: switching systems, impulsive systems, impulsive and switching systems. The main contributions in this dissertation can be summarized as follows.Necessary optimality conditions for a class of switching systems with non-smooth cost function are investigated. By introducing a new time variable, the original switching optimal control problems are transformed into classical optimal control problems. Based on the classical optimal control theory and knowledge of generalized differential, nonsmooth necessary optimality conditions for this switching control problem are obtained. Finally, one example is given to illustrate the efficiency of the main results.An optimal control problem is discussed for a class of hybrid systems, where the impulsive instants are state-dependent. Instead of relying on the usual technique of ariational approach, necessary optimality conditions of this hybrid system are obtained by parameterizing the impulsive instants. Then, the optimal control problem is transformed into a boundary value problem, which can be solved by numerical method or analytic method. Moreover, taking advantage of the theory of generalized differential, necessary optimality conditions are extended to generalized differential form. Finally, two examples are presented to illustrate validity of the methods.An optimal control problem is investigated for a class of hybrid systems with unfixed impulsive switching points. The mixed constraints with state and control are considered in this problem. By defining the variable intervals between jumping instants as part of an extended state, necessary optimality conditions and sufficient optimality conditions of this impulsive and switching optimal control problem are derived. According to the conditions satisfied by the constraints, the Legendre-Clebsch condition and Riccati matrix equations in sufficient conditions are simplified. Finally, the obtained results are applied to a model of output value growth.An optimal control problem is discussed for a class of impulsive switching systems, where the impulses depend on the state and the switching costs are contained in the cost functional. According to the character of the switching function, we transform the event-driven hybrid control problem into time-driven problem in variable time intervals, optimality conditions for the hybrid optimal control problems are obtained. Moreover, the conditions for normality of multiplier in necessary optimality conditions are also formulated. The obtained results generalized the existing results in the literature.