A max-plus primal space fundamental solution for a class of differential Riccati equations
A max-plus primal space fundamental solution for a class of differential Riccati equations
复制标题
一类微分Riccati方程的最大加原始空间基本解
DOI：
10.1007/s00498-017-0200-2
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Huan Zhang
中科院分区：
文献类型：
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作者：
P. Dower;Huan Zhang
考虑一类微分Riccati方程（DREs），其中任何解的演化都可以通过$${\mathscr {L}_2}$$L2-增益分析中出现的相应最优控制问题的值函数的传播来识别。通过利用从伴随的动态规划原理继承的半群性质，开发了一个最大-加线性最大-加积分算子的最大-加原空间基本解半群，它封装了所有这样的值函数传播。利用这个半群，我们构造了一类DRE的单参数矩阵基本解半群。它表明，这个半群可以用来计算这些DREs的特解，并以一种简单的方式来表征有限逃逸时间（如果它们存在）。
A class of differential Riccati equations (DREs) is considered for which the evolution of any solution can be identified with the propagation of a value function of a corresponding optimal control problem arising in $${\mathscr {L}_2}$$L2-gain analysis. By exploiting the semigroup properties inherited from the attendant dynamic programming principle, a max-plus primal space fundamental solution semigroup of max-plus linear max-plus integral operators is developed that encapsulates all such value function propagations. Using this semigroup, a one-parameter fundamental solution semigroup of matrices is constructed for the aforementioned class of DREs. It is demonstrated that this semigroup can be used to compute particular solutions of these DREs, and to characterize finite escape times (should they exist) in a simple way.