Hardy-Schatten Norms of Systems, Output Energy Cumulants and Linear Quadro-Quartic Gaussian Control
arXiv:1208.3815
Abstract
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.
arXiv comment14 pages, 3 figures, published in the Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems, 5-9 July 2010, Budapest, Hungary, pp. 2383-2390