Automatic synthesis of a swing-up controller for the pendulum.

摘要

In this thesis we study the automatic synthesis of optimal controllers using hybrid system theory. We use these automatic synthesis techniques to find control switch enabling conditions for time optimal swing-up of the pendulum, which appear not to have been published to date. The method used is to partition the hybrid state space into cells, which become nodes of a finite automaton A, and perform a shortest path computation over A. The resulting minimum cost control for each node is translated into optimal enabling conditions for control switches in the hybrid system. We present an algorithm for computing the edges between nodes of A, using a variant of existential quantifier elimination methods.