Finite horizon optimal tracking control of partially unknown linear continuous-time systems using policy iteration

In this study, a neural-network-based online learning algorithm is established to solve the finite horizon linear quadratic tracking (FHLQT) problem for partially unknown continuous-time systems. An augmented problem is constructed with an augmented state which consists of the system state and the reference trajectory. The authors obtain a solution for the augmented problem which is equivalent to the standard solution of the FHLQT problem. To solve the augmented problem with partially unknown system dynamics, they develop a time-varying Riccati equation. A critic neural network is used to approximate the value function and an online learning algorithm is established using the policy iteration technique to solve the time-varying Riccati equation. An integral policy iteration method and an online tuning law are used when the algorithm is implemented without the knowledge of the system drift dynamics and the command generator dynamics. A simulation example is given to show the effectiveness of the established algorithm.