线性系统稳定性与最优性的关系(Ⅱ)
The Relationship between the Stability and the Optimality of Linear Systems (Ⅱ)
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摘要: 我们在[1]中提出并讨论了与R.E.Kalman的最优控制反问题不同的另一类线性最优控制的反问题:任给一渐近稳定的定常线性系统和一个非负二次型性能指标,问是否可以从该稳定系统中分解出一个状态反馈,使得这个状态反馈就是给定指标下的最优控制。本文将上述问题加以推广,对线性离散系统和线性时变系统得出了相应的结论,进而得出[1]中提出的渐近稳定系统和最优系统之间的对应关系是一切线性系统的内在特征。Abstract: Different from the inverse problem put forward by R.E.Kalman, another kind of inverse problem of linear optimal control is proposed and discussed in [1] as follows:Given an asymptotically stable linear constant system and a nonnegative quadratic performance index, when can a state-feedback be separated from the stable system so that this state-feedback control law is optimal for the given index? In this paper this problem is extended. Similar conclusions are obtained for linear discrete systems and linear time-variable systems. According to these conclusions we can say that the correspondence between the asymptotically stable system and the optimal feedback system is the inherent character of all kinds of linear systems.
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[1] 陈小林、黄琳,线性系统稳定性与最优性的关系——线性最优控制反问题的另一种提法,应用数学与力学,6,2 (1985). [2] Kalman, R, E,When is linear control system optimal, Trans, ASME, Ser,D; Basic Eng.,86 (1964). [3] Kailath, T.,Linear System, Prentice-Hall (1980). [4] 黄琳,《系统与控制理论中的线性代数》,科学出版社,北京(1984). [5] Anderson, B, D, O, and 7. B, Moore, Linear Optimal.Control, Prexntice-Hall Press(1970). -
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