Suboptimal Learning Control for Nonlinear Systems with Both Parametric and Nonparametric Uncertainties
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摘要: 针对不确定非线性系统, 提出准最优学习控制方法, 解决参数与非参数不确定特性同时存在情形下的轨迹跟踪问题. 给出迭代学习与重复学习两种控制策略, 根据Sontag公式解决标称系统的优化控制, 并以鲁棒学习手段处理参数与非参数不确定特性. 提出断续函数连续化方案, 以避免传统Sontag公式在实现时可能存在的颤振问题. 分析证明经过足够多次迭代或足够多个周期的重复运行后, 闭环系统可实现系统状态以预设精度跟踪参考信号. 仿真结果表明所设计学习系统在收敛速度 方面快于非优化设计.Abstract: In this paper, two suboptimal learning control methods, an iterative one and a repetitive one, are proposed for a class of nonlinear systems with both time-varying parametric and nonparametric uncertainties. Sontag formula is used for the control design of a nominal system, while the robust learning mechanism is adopted to deal with both parametric and nonparametric uncertainties. A continuous controller design is carried out in order to avoid the chattering phenomenon that may arise due to the use of Sontag formula. It is shown that the closed-loop system state follows the desired trajectory with the pre-specified accuracy, as iteration or repetition increases. Numerical results demonstrate the effectiveness of the suboptimal learning control scheme.
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