| Abstract: | In this paper, we propose a novel approach to the linear quadratic (LQ) optimal control of unknown discrete‐time linear systems. We first describe an iterative procedure for minimizing a partially unknown static function. The procedure is based on simultaneous updates in the estimation of unknown parameters and in the optimization of controllable inputs. We then use the procedure for control optimization in unknown discrete‐time dynamic systems—we consider applications to the finite‐horizon and the infinite‐horizon LQ control of linear systems in detail. To illustrate the approach, an example of the pitch attitude control of an aircraft is considered. We also compare our proposed approach to several other approaches to finite/infinite‐horizon LQ control problems with unknown dynamics from the literature, including extremum seeking and adaptive dynamic programming/reinforcement learning. Our proposed approach is competitive with these approaches in speed of convergence and in implementation and computational complexity. |
