Control of Switched Hybrid Systems Based on Disjunctive Formulations

This contribution addresses the task of computing optimal control trajectories for hybrid systems with switching dynamics. Starting from a continuous-time formulation of the control task we derive an optimization problem in which the system behavior is modelled by a hybrid automaton with linear discrete-time dynamics and discrete as well as continuous inputs. In order to transform the discrete dynamics into an equation-based form we present and compare two different approaches: one uses the ‘traditional’ M-formulation and one is based on disjunctive formulations. The control problem is then solved by mixed integer programming using a moving horizon setting. As illustrated for an example, the disjunctive formulation can lead to a considerable reduction of the computational effort.