Finite-horizon and infinite-horizon linear quadratic optimal control problems: A data-driven Euler scheme

In this paper, we devote our focus to studying finite-horizon and infinite-horizon linear quadratic optimal control (LQOC) problems in continuous time. We focus on algorithms for approximating optimal controls of these two problems without the knowledge of all system coefficients. Firstly, we transform the backward differential Riccati equation (DRE) corresponding to the finite-horizon LQOC problem into a forward ordinary differential equation. Then, we discretize the forward equation by the Euler method. Subsequently, we use the collected state and input data to calculate all discretized points of the forward equation. At the same time, we obtain the optimal control of the finite-horizon LQOC problem. Moreover, we approximate the optimal control of the infinite-horizon LQOC problem by virtue of an asymptotic behavior between the DRE and an algebraic Riccati equation (ARE) arising in the infinite-horizon LQOC problem. Finally, we validate the obtained results via two practically motivated examples.