Optimization of Disturbance Rejection in Systems with Saturating Actuators

An extension of the LQR LQG methodology to systems with saturating actuators, referred to as SLQR SLQG, is obtained. The development is based on the method of stochastic linearization. Using this method and the Lagrange multiplier technique, a solution to the SLQR SLQG problem is derived. This solution is given by the standard Riccati equations coupled with two transcendental equations, which define the variance of the signal at the input of the saturation and the Lagrange multiplier associated with the quadratic performance index. It is shown that, under the standard stabilizability and detectability conditions, these equations have a unique solution, which can be found by a simple bisection algorithm. When the saturation is removed, these equations reduce to the standard LQR LQG solution.