Data‐Driven Optimal Output Tracking of Electrostatic Micromirrors: A Guaranteed Convergence Rate Approach

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This article proposes a data‐driven optimal output tracking algorithm for electrostatic micromirror systems, which guarantees the convergence rate of the tracking error without relying on precise model knowledge. By embedding a convergence rate requirement into the performance index, the tracking problem is reformulated as an optimal tracking problem with guaranteed transient performance. To solve the associated algebraic Riccati equation (ARE) online, an improved hybrid iteration (HI) method is developed, which requires neither an accurate system model nor an initially stabilizing control policy, while converging faster than conventional value iteration (VI) methods. Moreover, different internal model structures are adopted in the learning phase and the control phase, so that the learning dynamics are decoupled from the control dynamics. This design reduces the number of unknowns in the data equation, alleviates the computational burden, and relaxes the rank conditions required for data collection. Finally, simulation results on an electrostatic micromirror system demonstrate the effectiveness of the proposed method in achieving optimal output tracking with a guaranteed convergence rate.