Optimal Control of Linear Continuous-time Systems in the Presence of State and Input Delays with Application to a Chemical Reactor

In this paper, the optimal regulation of linear continuous-time systems with state and input delays is introduced by utilizing a quadratic cost function and state feedback. The Lyapunov-Krakovskii functional incorporating state and input delays is defined as a value function. Next, the Bellman type equation is formulated, and a delay Algebraic Riccati equation (DARE) over infinite time horizon is derived. By using the stationarity condition for the Bellman type equation, the optimal control input is obtained. It is demonstrated that the proposed optimal control input makes the closed-loop system asymptotically stable. Finally, simulation results confirm the theoretical claims by applying the proposed approach to a chemical reactor.