Adaptive optimal output regulation: a parametric Lyapunov equation approach

This article delves into a data-driven approach for solving the adaptive optimal output regulation problem in continuous-time linear systems with uncertain dynamics. Employing a class of parametric Lyapunov equations in conjunction with a nominal system model, the initial stabilizing feedback gain is determined to initiate the iterative method. Then, by utilizing a policy-iteration-based technique, we design an optimal control policy to achieve precise output tracking and disturbance rejection. The prescribed convergence characteristics of the closed-loop system directly result from the properties embedded within the solution of the parametric Lyapunov equation. The applicability and performance of the proposed method are demonstrated through a numerical example involving an input-constrained double integrator system.