An extension of the minimum principle with application to switched linear systems

In this paper we address the problem of optimal switching for switched linear systems. The uniqueness of our approach lies in casting the switching action as multiple control inputs. This allows us to apply the concept of Pontryagin´s minimum principle in solving the optimal control problem. There is no restriction on the switching sequence or the number of switchings although the later is bound by the sampling interval. This is in contrast to search based algorithms where a fixed number of switchings is set a priori. We solve the optimization problem using an iterative scheme where a two point boundary value problem is solved. Simulation results are provided to support the proposed method