Explicit solutions for multivariate, discrete-time control problems under uncertainty

We consider discrete time control problems, where only the support sets 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 problem of the stochastic setting, we present a problem that admits an explicit analytic solution. In particular, we characterize a property of compatibility between the system dynamics and the norms of the spaces, that is crucial to obtain the analytic solution also in the general multidimensional case.