Linear-Quadratic-Gaussian Control with Time-Varying Disturbance Forecast

Linear-quadratic-Gaussian (LQG) control is a classical optimal control problem where the disturbance in the system dynamics is traditionally treated as random noise. Motivated by the possibility of forecasting future disturbance in some relevant works for linear-quadratic regulator (LQR) systems where the disturbance distribution is arbitrary, we introduce a time-varying disturbance forecast model in the LQG problem. Our model characterizes the Gaussianity of the disturbances and thus enables us to give theoretical results including optimal average cost even though the forecast error can be unbounded. Numerical examples are provided to illustrate the theoretical results.