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In this technical note, an online learning algorithm is developed to solve the linear quadratic tracking (LQT) problem for partially-unknown continuous-time systems. It is shown that the value function is quadratic in terms of the state of the system and the command generator. Based on this quadratic form, an LQT Bellman equation and an LQT algebraic Riccati equation (ARE) are derived to solve the LQT problem. The integral reinforcement learning technique is used to find the solution to the LQT ARE online and without requiring the knowledge of the system drift dynamics or the command generator dynamics. The convergence of the proposed online algorithm to the optimal control solution is verified. To show the efficiency of the proposed approach, a simulation example is provided.
Modares et al. (Fri,) studied this question.