Minimum Relative Entropy State Transitions in Linear Stochastic Systems: the Continuous Time Case
Abstract
This paper is concerned with a dissipativity theory for dynamical systems governed by linear Ito stochastic differential equations driven by random noise with an uncertain drift. The deviation of the noise from a standard Wiener process in the nominal model is quantified by relative entropy. We discuss a dissipation inequality for the noise relative entropy supply. The problem of minimizing the supply required to drive the system between given Gaussian state distributions over a specified time horizon is considered. This problem, known in the literature as the Schroedinger bridge, was treated previously in the context of reciprocal processes. A closed-form smooth solution is obtained for a Hamilton-Jacobi equation for the minimum required relative entropy supply by using nonlinear algebraic techniques.
Cite
@article{arxiv.1208.3981,
title = {Minimum Relative Entropy State Transitions in Linear Stochastic Systems: the Continuous Time Case},
author = {Igor G. Vladimirov and Ian R. Petersen},
journal= {arXiv preprint arXiv:1208.3981},
year = {2012}
}
Comments
15 pages, 1 figure, published in the Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems, 5-9 July 2010, Budapest, Hungary, pp. 51-58