Minimax Control of Linear Stochastic Systems with Noise Uncertainty

The problem of linear-quadratic-Gaussian control of multivariable linear stochastic systems with uncertain second-order statistical properties is considered. Uncertainty is modeled by allowing process and observation noise spectral density matrices to vary' arbitrarily within given classes, and a minimax control formulation is applied to the quadratic objective functional. General theorems proving the existence and characterization of saddle-point solutions to this problem are presented, and the relationship of these results to earlier results on minimax state estimation are discussed. To illustrate the analytical results, the specific example of regulating a double-integrator plant is treated in detail.