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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.
Aiming at the control of continuous-time chaotic (hyperchaotic) systems, a fast and linear generalized predictive control algorithm based on the extended state observer is proposed. The linear extended state observer is used to estimate and compensate the nonlinear dynamics of the chaotic (hyperchaotic) system Learning and existence of uncertainty, the original object is approximately converted into an integrator form, and then the generalized predictive control is designed for single integrator, which solves the problem of large computational load of predictive control. The step coefficient matrix can be directly analytic solution, The prediction of the future output can be calculated directly from the output sampling values at the last two moments, avoiding the use of self-calibration algorithm and solving the Diophantine equation online. The linear algorithm can be directly applied to the control system design of nonlinear objects. The algorithm is applied to the control of a typical Lorenz chaotic system. The results of the mathematical simulation verify the validity.