Quantized optimal control of discrete-time systems

In this paper we consider a quantized discrete-time linear quadratic regulator (DLQR) problem, namely a DLQR problem where the input u may only take values in a given finite set 14. Eased on our previous results on the optimal control of hybrid systems we show that the optimal control law for the quantized DLQR problem takes the form of a feedback control law, that can be obtained from a partition of the state space C, computed off-line. The numerical simulations carried out enabled us to observe a particular structure of C, related to the solution of the non-quantized DLQR problem. The lines of our future research in this topic are described in details in the last section, devoted to conclusions and future work