Memory-Efficient Filter-Based Approximate Optimal Regulation of Unknown LTI Systems Using Initial Excitation

This paper proposes a memory-efficient approx-imate/adaptive optimal control (AOC) design of completely unknown continuous-time (CT) linear time invariant (LTI) systems, without requiring the restrictive persistence of excitation (PE) condition for parameter convergence. The AOC algorithm utilizes two layers of filtering - the first layer filters strategically eliminate the need for state derivative information, while the second layer filters provide suitable algebraic relations for iteratively obtaining the optimal policy under a milder online-verifiable initial excitation (IE) assumption. Unlike past literature, the proposed method does not require memory intensive delayed-window integrals, intelligent data-storage and restrictive PE assumption. The intermediate policies are proved to be stabilizing and converging to the optimal policy. Simulation results validate the efficacy of the proposed adaptive/approximate linear quadratic regulator (LQR) algorithm.