Memory-Efficient Filter Based Novel Policy Iteration Technique for Adaptive LQR

This paper proposes a novel memory-efficient double-filtered policy iteration (PI) algorithm for adaptive optimal control of continuous-time (CT) linear time invariant (LTI) systems. The first layer filters strategically eliminate the need for state derivative information, while the second layer filters provide suitable algebraic relation for solving the intermediate policies under the excitation assumption. Unlike past literature, the proposed method does not require memory intensive delayed-window integrals and intelligent data-storage, and hence, is an on-policy PI algorithm. In addition to guaranteeing the intermediate policies to be stabilizing and their convergence to the optimal policy, the present work rigorously establishes global asymptotic stability of the overall (switched) closed-loop system. Simulation results validate the efficacy of the proposed adaptive linear quadratic regulator.