| In this dissertation, new methodologies to solve important control problems in hybrid systems have been developed. Our work is motivated by the need to address challenging problems in the control and coordination of modern complex engineering applications such as autonomous vehicles, chemical and manufacturing plants, and multiple robotic systems. The research contributions of this dissertation impact the areas of analysis, verification, and synthesis of piecewise linear hybrid systems. Piecewise linear hybrid dynamical systems is an important class of systems with many practical applications. A novel methodology for of the continuous dynamics is presented. The main characteristic of the approach is that the available control inputs are taken into consideration in order to simplify the continuous dynamics. Typical control specifications investigated in this dissertation are formulated with respect to a partition of the state space of the system. Examples include safety and reachability specifications. The main advantage of the approach is that it provides a convenient general framework not only for analysis, but more importantly for controller synthesis. In particular, the regulator problem for hybrid systems is formulated as a systematic methodology for controller design.; Additionally, the stability of piecewise linear hybrid systems using piecewise linear Lyapunov functions is investigated. A large class of stabilizing switching sequences for switched linear systems is characterized by computing conic partitions of the state space.; Significant progress is also made in the representation of hybrid control systems using Petri nets. A special class of timed Petri nets was used for modeling and supervisory control of hybrid systems. It was shown that Petri nets offer advantages over finite automata when model complexity and concurrency issues are of concern. |
