SLQR/SLQG: an LQR/LQG theory for 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, solutions to the SLQR and SLQG problems are derived. These solutions are given by Riccati and Lyapunov equations coupled with two transcendental equations. It is shown that, under standard stabilizability and detectability conditions, these equations have a unique solution, which can be found by a simple bisection algorithm. When the level of saturation tends to infinity, these equations reduce to their standard LQR/LQG counterparts.