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首页> 外文期刊>International Journal of Innovative Computing Information and Control >LINEAR QUADRATIC OPTIMAL CONTROL BASED ON DYNAMIC COMPENSATION
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LINEAR QUADRATIC OPTIMAL CONTROL BASED ON DYNAMIC COMPENSATION

机译：基于动态补偿的线性二次最优控制

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摘要

The linear-quadratic (LQ) optimal problem based on dynamic compensation is considered for a general quadratic performance index in this paper. First, it is shown that there exists a dynamic compensator with a proper dynamic order such that the closed-loop system is asymptotically stable and its associated Lyapunov equation has a symmetric positive-definite solution. Then, the quadratic performance index is derived to be a simple expression related to the symmetric positive-definite solution and the initial value of the closed-loop system. In order to solve the optimal control problem for the system, the proposed Lyapunov equation is transformed into a Bilinear Matrix Inequality (BMI) and a corresponding path-following algorithm to minimize the quadratic performance index is proposed in which an optimal dynamic compensator can be obtained. Finally, several numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed approach.
机译：本文针对一般的二次性能指标，考虑了基于动态补偿的线性二次（LQ）最优问题。首先，表明存在一个具有适当动态阶数的动态补偿器，以使闭环系统渐近稳定，并且其相关的Lyapunov方程具有对称的正定解。然后，将二次性能指标导出为与对称正定解和闭环系统的初始值有关的简单表达式。为了解决系统的最优控制问题，将提出的李雅普诺夫方程转化为双线性矩阵不等式（BMI），并提出了相应的路径跟踪算法以最小化二次性能指标，从而获得了最优的动态补偿器。 。最后，提供了几个数值示例来证明所提方法的有效性和可行性。

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