Optimistic minimax search for noncooperative switched control with or without dwell time

• Published in: Automatica (Oxford) Vol. 112; p. 108632
• Main Authors: Buşoniu, Lucian, Rejeb, Jihene Ben, Lal, Ioana, Morărescu, Irinel-Constantin, Daafouz, Jamal
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2020; Elsevier
• Subjects: Automatic Control Engineering; Computer Science; Noncooperative optimal control; Nonlinear systems; Optimistic search; Switched systems; Switched systems; Optimistic search; Noncooperative optimal control; Nonlinear systems; nonlinear systems; optimistic search; noncooperative optimal control
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2019.108632

We consider adversarial problems in which two agents control two switching signals, the first agent aiming to maximize a discounted sum of rewards, and the second aiming to minimize it. Both signals may be subject to constraints on the dwell time after a switch. We search the tree of possible mode sequences with an algorithm called optimistic minimax search with dwell time (OMSd), showing that it obtains a solution close to the minimax-optimal one, and we characterize the rate at which the suboptimality goes to zero. The analysis is driven by a novel measure of problem complexity, and it is first given in the general dwell-time case, after which it is specialized to the unconstrained case. We exemplify the framework for networked control systems where the minimizer signal is a discrete time delay on the control channel, and we provide extensive simulations and a real-time experiment for nonlinear systems of this type.