Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2000 / Article

Open Access

Volume 6 |Article ID 269364 | https://doi.org/10.1155/S1024123X00001319

Guojun Shi, Robert E. Skelton, Karolos M. Grigoriadis, "Minimum output variance control for FSN models: Continuous-time case", Mathematical Problems in Engineering, vol. 6, Article ID 269364, 18 pages, 2000. https://doi.org/10.1155/S1024123X00001319

Minimum output variance control for FSN models: Continuous-time case

Received14 Dec 1998

Abstract

In this paper we consider the Finite Signal-to-Noise ratio model for linear stochastic systems. It is assumed that the intensity of noise corrupting a signal is proportional to the variance of the signal. Hence, the signal-to-noise ratio of each sensor and actuator is finite – as opposed to the infinite signal-to-noise ratio assumed in LQG theory. Computational errors in the controller implementation are treated similarly. The objective is to design a state feedback control law such that the closed loop system is mean square asymptotically stable and the output variance is minimized. The main result is a controller which achieves its maximal accuracy with finite control gains – as opposed to the infinite controls required to achieve maximal accuracy in LQG controllers. Necessary and sufficient conditions for optimality are derived. An optimal control law which involves the positive definite solution of a Riccati-like equation is derived. An algorithm for solving the Riccati-like equation is given and its convergence is guaranteed if a solution exists.

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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