EXPLICIT SOLUTIONS FOR MULTIVARIATE, DISCRETE-TIME CONTROL-PROBLEMS UNDER UNCERTAINTY

We consider discrete time control problems, where only the support set s of the initial condition and of the disturbances are known. We study the applicability of the DP method and, as a counterpart of the LQ pr oblem of the stochastic setting, we present a problem that admits an e xplicit analytic solution. In particular, we characterize a property o f compatibility between the system dynamics and the norms of the space s, that is crucial to obtain the analytic solution also in the general multidimensional case. (C) 1998 Elsevier Science B.V. All rights rese rved.