Minimax Control of Linear Stochastic Systems with Noise Uncertainty

The linear-quadratic-Gaussian regulator problem is considered for multivariable linear stochastic systems with uncertain second-order statistical properties. 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 is discussed. To illustrate the analytical results, the specific example of regulating a double-integrator plant is treated in detail.