Optimal Timing Control of Switched Linear Systems Based on Partial Information

Optimal switch-time control is an area that investigates how best to switch between different control modes. In this paper we present an algorithm for solving the optimal switch-time control problem for single-switch, linear systems where the state of the system is only partially known through the outputs. A method is presented that both guarantees that the current switch-time remains optimal as the state estimates evolve, and that ensures this in a computationally feasible manner, thus rendering the method applicable to real-time applications. An extension is moreover considered where constraints on the switch-time provides the observer with sufficient time to settle. The viability of the proposed method is illustrated through a number of examples.