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In this paper, we investigated the optimal tracking control problem of flexible-joint robotic manipulators in order to achieve trajectory tracking, and at the same time reduced the energy consumption of the feedback controller. Technically, optimization strategies were well-integrated into backstepping recursive design so that a series of optimized controllers for each subsystem could be constructed to improve the closed-loop system performance, and, additionally, a reinforcement learning method strategy based on neural network actor-critic architecture was adopted to approximate unknown terms in control design, making that the Hamilton-Jacobi-Bellman equation solvable in the sense of optimal control. With our scheme, the closed-loop stability, the convergence of output tracking error can be proved rigorously. Besides theoretical analysis, the effectiveness of our scheme was also illustrated by simulation results.
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