Approximate Optimal Adaptive Control of Partially Unknown Linear Continuous-time Systems with State Delay

Abstract

In this paper, an approximate optimal adaptive control of partially unknown linear continuous time systems with state delay is introduced by using integral reinforcement learning. A quadratic cost function over infinite time horizon is considered and a value function is defined by considering the delayed state. It has been shown that the optimal control input makes the system asymptotically stable when, given dynamics, the time delay is greater than zero. A novel delay modified algebraic Riccati equation is derived to confirm the stability of the system. Then, to overcome the need for drift dynamics, an actor-critic framework is introduced based on the integral reinforcement learning approach for approximate optimal adaptive control. A novel value function is defined and update law for tuning the parameters of the critic/value function is derived. Lyapunov theory is employed to demonstrate the boundedness of the closed-loop system. A simulation example is included to verify the effectiveness of the proposed approach.