Data-Driven Online Adaptive Optimal Control for Linear Systems with Completely Unknown Dynamics

This paper develops a novel method to address the optimal control problem of systems with unknown dynamics. An adaptive identifier is first constructed based the the vectorization operator and Kronecker products, where we can reconstruct the unknown system dynamics based on the measurable input and output data. A recently proposed adaptive law is used to guarantee the convergence of the identifier parameters. Then, a data-driven technology is applied to online solve the derived algebraic Riccati equation (ARE). For this purpose, we apply the Kronecker's products on the ARE such that another adaptive law is employed to online estimate the parameters involved in the ARE with guaranteed convergence. Simulation results are given to illustrate the effectiveness of the proposed method.