Understanding the difference between robust control and optimal control in a linear discrete-time system with time-varying parameters

Robust control has been a very popular area of research in the last two decades. The goal of this paper is to investigate the assumptions implicit in the “nonprobabilistic nature” of the a priori information used to derive the linear-quadratic robust control in discrete-time. This is done by comparing robust control with the optimal control for a linear system with time-varying parameters. First the theoretical differences between the two approaches are discussed. Then they are used in two numerical examples: a simple model with one control, one state and a time horizon of two periods, which is suitable for hand calculations, and the permanent income model. The main conclusion is that the decision maker applying robust control is indeed assuming a very restricted class of true, unknown models.