<p>This paper concentrates on the problem of adaptive optimal prescribed-time prescribed performance control based on the reinforcement learning algorithm in a pioneering way for nonlinear systems with error constraints. After developing the prescribed-time performance function and the transformation error function, together with the barrier function, a neural-based adaptive transformation error-constrained optimal controller is derived by employing the fuzzy approximation and the optimal backstepping technique. Compared with the traditional prescribed performance control, the constructed performance function is predetermined based on the prescribed time that remains independent of initial conditions and controller design parameters. Moreover, the transformation error constraint can be handled in the control structure through a barrier function, which restricts the transformation error while further enhancing the tracking error convergence performance. Under the proposed controller, it is proven that all signals within the closed-loop system remain bounded, and the transformation error constraint is achieved. This means that the output tracking error converges to a prescribed, arbitrarily small region within a prescribed time interval, while the convergence time is not influenced by the initial state. Simulation results on the numerical example and the single-link robot manipulator system demonstrate the merits of the proposed control scheme.</p>

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Prescribed-Time-Based Adaptive Optimal Control for Nonlinear Systems with Error Constraint

  • Yan Qin,
  • Yang Liu,
  • Yingnan Pan,
  • Liang Cao,
  • Guohuai Lin

摘要

This paper concentrates on the problem of adaptive optimal prescribed-time prescribed performance control based on the reinforcement learning algorithm in a pioneering way for nonlinear systems with error constraints. After developing the prescribed-time performance function and the transformation error function, together with the barrier function, a neural-based adaptive transformation error-constrained optimal controller is derived by employing the fuzzy approximation and the optimal backstepping technique. Compared with the traditional prescribed performance control, the constructed performance function is predetermined based on the prescribed time that remains independent of initial conditions and controller design parameters. Moreover, the transformation error constraint can be handled in the control structure through a barrier function, which restricts the transformation error while further enhancing the tracking error convergence performance. Under the proposed controller, it is proven that all signals within the closed-loop system remain bounded, and the transformation error constraint is achieved. This means that the output tracking error converges to a prescribed, arbitrarily small region within a prescribed time interval, while the convergence time is not influenced by the initial state. Simulation results on the numerical example and the single-link robot manipulator system demonstrate the merits of the proposed control scheme.