Optimal stochastic control of discrete-time systems subject to total variation distance uncertainty

This paper presents another application of the results in, where existence of the maximizing measure over the total variation distance constraint is established, while the maximizing pay-off is shown to be equivalent to an optimization of a pay-off which is a linear combination of L₁ and L_∞ norms. Here emphasis is geared towards to uncertain discrete-time controlled stochastic dynamical system, in which the control seeks to minimize the pay-off while the measure seeks to maximize it over a class of measures described by a ball with respect to the total variation distance centered at a nominal measure. Two types of uncertain classes are considered; an uncertainty on the joint distribution, an uncertainty on the conditional distribution. The solution of the minimax problem is investigated via dynamic programming.