Output Feedback Q-Learning for Linear-Quadratic Discrete-Time Finite-Horizon Control Problems

An algorithm is proposed to determine output feedback policies that solve finite-horizon linear-quadratic (LQ) optimal control problems without requiring knowledge of the system dynamical matrices. To reach this goal, the Q-factors arising from finite-horizon LQ problems are first characterized in the state feedback case. It is then shown how they can be parameterized as functions of the input-output vectors. A procedure is then proposed for estimating these functions from input/output data and using these estimates for computing the optimal control via the measured inputs and outputs.