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基于快速全线性预测控制的混沌系统控制与同步?
Control and synchronization in chaotic systems based on fast linear predictive control
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摘要: 针对连续时间混沌(超混沌)系统的控制问题，提出了一种基于扩张状态观测器的快速全线性广义预测控制算法。利用线性扩张状态观测器估计和补偿混沌(超混沌)系统的非线性动力学和存在的不确定性，将原始对象近似转化为积分器形式，随后针对单积分器设计广义预测控制，解决了预测控制计算量大的问题。阶跃系数矩阵可以直接得到解析解，而对于未来输出的预测则可以根据最近两个时刻的输出采样值直接计算得到，避免了使用自校正算法和在线求解丢番图方程。该线性算法可以直接应用于非线性对象的控制系统设计。将该算法应用于典型Lorenz混沌系统的控制中，数学仿真结果验证了有效性。Abstract: A kind of fast linear generalized predictive control (GPC) algorithm is proposed based on the extended state observer for chaotic (hyperchaotic) systems. The linear extended state observer is employed to estimate and compensate the nonlinear dynamics and the existing uncertainties of the chaotic (hyperchaotic) systems so that an integrator can be obtained to serve as the model for GPC design. Using this scheme, the computational complexity can be substantially reduced. A step coe?cient matrix can be derived analytically and a future output prediction can be explicitly calculated by only using the last two samples of the output. Therefore, the self-tuning algorithms and the Diophantine equation can be completely avoided. The proposed method can be used to control nonlinear targets in a straightforward manner. Simulation results show the effectiveness of this linear algorithm.
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