Hardy-Schatten Norms of Systems, Output Energy Cumulants and Linear Quadro-Quartic Gaussian Control
Hardy-Schatten Norms of Systems, Output Energy Cumulants and Linear Quadro-Quartic Gaussian Control
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系统的 Hardy-Schatten 范数、输出能量累积量和线性四次-四次高斯控制
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
I. Petersen
中科院分区：
文献类型：
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作者：
I. Vladimirov;I. Petersen
本文研究状态空间中的线性随机控制系统。在有界时间间隔上系统输出的平方范数的积分被解释为能量。输出能量在无限时域极限的累积量与系统在传递函数的哈代空间中的Schatten范数和风险敏感性能指标有关。我们采用了一种新的性能标准，旨在最大限度地减少每单位时间的系统的输出能量的平均值和方差的组合。由此产生的线性四次高斯控制问题涉及闭环系统的H2和H4范数。我们得到的最优控制器方程和轮廓同伦方法，减少了问题的解决方案的数值积分的微分方程初始化的标准线性二次高斯控制器。
This paper is concerned with linear stochastic control systems in state space. The integral of the squared norm of the system output over a bounded time interval is interpreted as energy. The cumulants of the output energy in the infinite-horizon limit are related to Schatten norms of the system in the Hardy space of transfer functions and the risk-sensitive performance index. We employ a novel performance criterion which seeks to minimize a combination of the average value and the variance of the output energy of the system per unit time. The resulting linear quadro-quartic Gaussian control problem involves the H2 and H4-norms of the closed-loop system. We obtain equations for the optimal controller and outline a homotopy method which reduces the solution of the problem to the numerical integration of a differential equation initialized by the standard linear quadratic Gaussian controller.