Robust optimal switching control for nonlinear systems


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Siam Publications


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. e 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 quasi-variational 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.



running cost, switching cost, worst-case disturbance attenuation, differential game, state-feedback control, nonanticipating strategy, storage function, lower-value function, system of quasi-variational, inequalities, viscosity solution, h-infinity control, viscosity solutions, differential-games, strategies, equations, automation & control systems, mathematics, applied


Ball, J. A.; Chudoung, J. A.; Day, M. V., "Robust optimal switching control for nonlinear systems," SIAM J. Control Optim., 41(3), 900-931, (2002). DOI: 10.1137/s0363012900372611