Kaart S, Schouten J C, van den Bleek C M
Department of Chemical Process Technology, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 May;59(5 Pt A):5303-12. doi: 10.1103/physreve.59.5303.
Linear feedback control, specifically model predictive control (MPC), was used successfully to synchronize an experimental chaotic pendulum both on unstable periodic and aperiodic orbits. MPC enables tuning of the controller to give an optimal controller performance. That is, both the fluctuations around the target trajectory and the necessary control actions are minimized using a least-squares solution of the linearized problem. It is thus shown that linear control methods can be applied to experimental chaotic systems, as long as an adequate model is available that can be linearized along the desired trajectory. This model is used as an observer, i.e., it is synchronized with the experimental pendulum to estimate the state of the experimental pendulum. In contrast with other chaos control procedures like the map-based Ott, Grebogi, and York method [Phys. Rev. Lett. 64, 1196 (1990)], the continuous type feedback control proposed by Pyragas [Phys. Lett. A 170, 421 (1992)], or the feedback control method recently proposed by Brown and Rulkov [Chaos 7 (3), 395 (1997)], the procedure outlined in this paper automatically results in a choice for the feedback gains that gives optimum performance, i.e., minimum fluctuations around the desired trajectory using minimum control actions.
线性反馈控制，特别是模型预测控制（MPC），已成功用于使实验混沌摆同步到不稳定周期轨道和非周期轨道。MPC能够对控制器进行调整，以实现最优的控制器性能。也就是说，利用线性化问题的最小二乘解，目标轨迹周围的波动以及必要的控制动作都能被最小化。由此表明，只要有一个足够的、能沿期望轨迹线性化的模型，线性控制方法就可以应用于实验混沌系统。该模型用作观测器，即它与实验摆同步，以估计实验摆的状态。与其他混沌控制方法，如基于映射的奥特、格雷博吉和约克方法[《物理评论快报》64, 1196 (1990)]、皮拉加斯提出的连续型反馈控制[《物理快报A》170, 421 (1992)]或布朗和鲁尔科夫最近提出的反馈控制方法[《混沌》7(3), 395 (1997)]不同，本文概述的方法会自动得出能给出最优性能的反馈增益选择，即使用最小控制动作使期望轨迹周围的波动最小。
