Data-Driven Adaptive LQR for Completely Unknown LTI Systems

In this paper, a data-driven on-policy optimal control design is proposed for continuous-time linear time invariant (LTI) systems with completely unknown dynamics. An online system identifier and control gain parameter estimator, which use past and current data together with standard gradient descent update laws, facilitate the design of an adaptive optimal controller that guarantees parameter convergence without the need of persistence of excitation (PE). Unlike the classical approach of enforcing the restrictive PE condition on the regressor, the data-driven approach is verifiable online and establishes parameter convergence from information rich past stored data simultaneously with the current data. A state feedback controller is designed using a dynamic gain parameter which is shown to converge to the neighborhood of the optimal LQR gain. Semi-global uniformly ultimately bounded (UUB) stability of the overall system is established using Lyapunov-based analysis. Simulation results further validate the developed result. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.