Mathematical Problems in Engineering
Volume 6 (2000), Issue 2-3, Pages 171-188

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

Guojun Shi,1 Robert E. Skelton,2 and Karolos M. Grigoriadis3

1GM Powertrain, General Motors Corporation, 3300 GM Road, MC 483-331-500, Milford 48380, MI, USA
2AMES Department-0411, 9500 Gilman Dr, University of California at San Diego, La Jolla 92093-0411, CA, USA
3Department of Mechanical Engineering, 4800 Calhoun Road, University of Houston, Houston 77204-4792, TX, USA

Received 14 December 1998

Copyright © 2000 Guojun Shi et al. 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.


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.