We first identify the phenomena that arise in such real-world systems. Then, we introduce a mathematical model of "hybrid systems" as interacting collections of dynamical systems, evolving on continuous-variable state spaces, and subject to continuous controls and discrete transitions.
We develop tools for analyzing hybrid systems, encompassing limit cycle existence, perturbation robustness, and stability. These tools represent a departure from previous ad hoc methods like extensive simulation. As a demonstration, we prove global asymptotic stability for a typical aircraft controller that logically switches between two conventional controllers.
We develop tools for synthesizing hybrid controllers for hybrid plants in an optimal control framework. In particular, we demonstrate existence of optimal (chattering) and near optimal (non-chattering) controls and derive "generalized quasi-variational inequalities" that the associated value function satisfies. We outline algorithms for solving these inequalities based on a generalized Bellman equation, impulse control, and linear programming. Several illustrative examples are solved.
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Modified: Jun 25, 1997|
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