Abstract. We formulate a robust optimal control problem for a general nonlinear system with finitely many admissible control settings and with costs assigned to switching of controls. We formulate the problem both in an L 2 -gain/dissipative system framework and in a game-theoretic framework. We show that, under appropriate assumptions, a continuous switching-storage function is characterized as a viscosity supersolution of the appropriate system of quasivariational inequalities (the appropriate generalization of the Hamilton-Jacobi-Bellman-Isaacs equation for this context), and that the minimal such switching-storage function is equal to the continuous switching lower-value function for the game. Finally we show how a prototypical example with one-dimensional state space can be solved by a direct geometric construction.
DEDICATED TO PROFESSOR GEORGE LEITMANN WITH RESPECTIn this paper we prove a comparison principle between a viscosity sub-and supersolution for a system of quasivariational inequalities and apply it to show that a continuous lower value vector function of an optimal switching-cost control problem is characterized as the minimal, nonnegative, continuous, viscosity supersolution of the SQVI. ᮊ
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.