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

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 infi nite;signal-ro-noise ratio assumed in LQG theory. Computational errors in t he controller implementation are treated similarly. The objective is to des ign a state feedback control law such that the closed loop system is mean s quare asymptotically stable and the output variance is minimized. The main result is a controller which achieves its maximal accuracy with finite cont rol gains - as opposed to the infinite controls required to achieve maximal accuracy in LQG controllers. Necessary and sufficient conditions for optim ality are derived. An optimal control law which involves the positive defin ite solution of a Riccati-like equation is derived. An algorithm for solvin g the Riccati-like equation is given and its convergence is guaranteed if a solution exists.