An Optimal Control Approach to Mode Generation in Hybrid Systems

Digital Object Identifier: 10.1016/j.na.2005.07.044NOTICE: this is the author’s version of a work that was accepted for publication in Nonlinear Analysis: Theory, Methods and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nonlinear Analysis: Theory, Methods and Applications, Vol. 65, No. 5, pp. 963-983, Sept. 2006. Digital Object Identifier: 10.1016/j.na.2005.07.044Copyright © 2005 Elsevier Ltd All rights reserved.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