Hybrid Systems And Its Applications In Nonlinear Control Systems

Study of hybrid systems originates from engineering practice. The hybrid systems' theories concern with the development of systematic modeling, analysis and synthesis methods for a class of complicated systems which incorporate the continuous variable dynamical parts and discrete event dynamical components simultaneously into a single system, and in which these two kind of the system components interact with each other. Studies of hybrid systems enrich and extend the control theories and hence control theories will be used to solve successfully and effectively a large number of complex engineering problems.In the past decade, scientists from the field of system and control science and also from computer science have conducted much research work in hybrid system and its applications in many engineering problems, and make a series of satisfied achievements. But, because of the difficulty and the popularity of the hybrid system (i.e. hybrid system is essentially a non-smooth and even non-continuous nonlinear system and hybrid system has a extensive engineering background), up to today, the topic of hybrid system and its applications is one of the most difficult research work and also one of the hot spots of studies in the field of system and control science.On the basis of summarizing and reviewing previous research work, this dissertation makes some further research work and explorations in hybrid system and its applications in nonlinear systems. The research work of this thesis consists of following three aspects:● Study of the theories for hybrid systems. Particularly, developing optimal control approaches for hybrid systems with states and control inputs constraints.● Application of hybrid systems in nonlinear systems I : By using hybrid systems' MLD model and optimization approach, developing optimal control method for a class of non-smooth and even non-continuous nonlinear systems.● Application of hybrid systems in nonlinear systems II: By using hybrid systems' PWA model and multi-parametric programming techniques, developing methods for stability and feasibility analysis of closed-loop model predictive system (MPC), which is essentially a complex nonlinear system.The detailed research work and the main achievements in this dissertation are asfollowings:(1) The concept and the background of the development of hybrid systems, theimportance and necessity of studies of hybrid systems are explained. Various widely used modeling approaches for hybrid systems, their characteristics and the equivalences of typical hybrid models are summarized. The developments of theories for hybrid systems, specially the stability analysis and the optimal control of hybrid systems, are reviewed. Typical examples of the applications of hybrid systems in engineering practice are also illustrated.(2) Discrete time mixed logical dynamical model based optimal control of hybridsystems with states and control inputs constraints are studied. In order to reduce online computational burden of the optimal control problem, and at the same time, to maintain good control performance and as largest as possible feasible region, a mixed integer model predictive control strategy with dynamic control horizon is purposed.(3) Mixed logical dynamical model for a class of nonlinear systems with typicalnon-smooth and non-continuous components is established. By using the optimal control techniques developed for hybrid systems, a new method for optimal control of nonlinear systems is developed.(4) Based upon branch and bound, genetic algorithm and evolutionary strategyrespectively, the principles, the procedures and its implementation for solution of mixed integer nonlinear programming (MINLP) problems are studied. As another important application of evolutionary algorithms based solution of MINLP problems, a new method for solving the job shop scheduling problems is developed.(5) Based upon the explicit solution of the constrained linear quadratic optimal controlproblems, which is obtained by using the multi-parametric quadratic programming (MPQP) tech...