Quasilinear quadratic Gaussian control for systems with saturating actuators and sensors

Abstract

An extension of the linear quadratic Gaussian control method to systems with saturating actuators and sensors is obtained. The development is based on the method of stochastic linearization, whereby the actuator and sensor saturation characteristics are replaced by their equivalent gains. Using the stochastically linearized system, a quasilinear quadratic Gaussian optimal control problem is formulated and a solution to the problem is derived by employing the Lagrange multiplier method. The solution obtained is given in terms of standard Riccati and Lyapunov equations coupled with four transcendental equations that characterize the variance of the signals at the saturation inputs and the Lagrange multipliers associated with the constrained minimization problem. Under standard stabilizability and detectability conditions, an iterative algorithm is developed to find the solution of these equations. It is shown that proposed method is a proper extension of the linear quadratic Gaussian control in the sense that these equations reduce to their standard linear quadratic Gaussian counterparts when the saturation is removed. Additional analysis results are also developed for quasilinear systems. The developed synthesis method is illustrated by an example