Nash Strategies for Discrete-Time Linear Systems with Multirate Controllers

This paper explores a new aspect of discrete-time linear systems in a game-theoretic context. We consider a class of multirate, linear shift-invariant systems with two controllers or Decision Makers (DMs). We assume that the underlying dynamic system is evolving at a fast rate and that one of the two DMs is operating at this rate. The other DM is constrained to operate at a slower rate. The fast rate is an integral multiple of the slow rate. Under these conditions, we formulate and solve a multirate, noncooperative game problem where the cost functionals are Linear Quadratic (LQ). Linear feedback Nash strategies are obtained and the main results are summarized. Computational aspects of solving LQ Nash games are explored which results in a numerical algorithm suitable for computer implementation. An example illustrates the preceding ideas and highlights the features of multirate games that are not present in single rate discrete-time systems.