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In this paper, a novel theoretic formulation based on adaptive dynamic programming (ADP) is developed to solve online the optimal tracking problem of the continuous-time linear system with unknown dynamics. First, the original system dynamics and the reference trajectory dynamics are transformed into an augmented system. Then, under the same performance index with the original system dynamics, an augmented algebraic Riccati equation is derived. Furthermore, the solutions for the optimal control problem of the augmented system are proven to be equal to the standard solutions for the optimal tracking problem of the original system dynamics. Moreover, a new online algorithm based on the ADP technique is presented to solve the optimal tracking problem of the linear system with unknown system dynamics. Finally, simulation results are given to verify the effectiveness of the theoretic results.
Qin et al. (2013) studied this question.