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摘要: 讨论奇异系统的不定号LQ问题 (二次型指标中的权矩阵含有负特征值的最优控制问题). 首先指出问题的可解性, 并给出了问题等价转化为奇异系统的奇异LQ问题的充要条件. 然后基于等价的奇异系统奇异LQ问题, 给出问题存在唯一最优控制—轨线对的充分条件. 最后用一个算例说明结论的正确性.Abstract: The indefinite LQ problem (i.e., the weighting matrix in the quadratic cost has some negative eigenvalues) for singular systems is discussed. First, it is pointed out that the problem is solvable, and the sufficient and necessary condition that the problem can be transformed into singular LQ problem for singular systems is given. Then, based on the equivalent singular LQ problem, the sufficient condition that the problem has a unique optimal control-trajectory pair is given. Finally, an example is given to show the validity of the proposed conclusion.
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Key words:
- Indefinite LQ problem /
- optimal control /
- singular system
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