Linear Quadratic Regulator Weighting Matrices for Output Covariance Assignment in Nonlinear Systems

Abstract

A time-varying output covariance assignment problem in the presence of a stochastic disturbance is solved using finite-horizon optimal control formulation. It is shown that an assignment of time-varying output error covariance is possible in the presence of model error by utilizing a time-varying linear quadratic regulator controller with a class of output and control weighting sequences. This paper develops a systematic algorithm to calculate the sequence of such time-varying output weights that are further shown to be the Lagrange multipliers associated with the covariance constraints. A short horizon attitude control problem with stringent covariance constraints and a more nonlinear example concerning a low-thrust interplanetary maneuver are solved to demonstrate the utility of the proposed approach. Numerical results offer a degree of optimism about the broad applicability of the time-varying covariance assignment approach to solve guidance and control problems associated with nonlinear dynamic systems.