Neural-network-based finite horizon optimal control for partially unknown linear continuous-time systems

In this paper, we establish a neural-network-based online learning algorithm to solve the finite horizon linear quadratic regulator (FHLQR) problem for partially unknown continuous-time systems. To solve the FHLQR problem with partially unknown system dynamics, we develop a time-varying Riccati equation. A critic neural network is used to approximate the value function and the online learning algorithm is established using the policy iteration technique to solve the time-varying Riccati equation. An integral policy iteration method and a tuning law are used when the algorithm is implemented without the knowledge of the system drift dynamics. We give a simulation example to show the effectiveness of this algorithm.