Performance study of LQG, MCV, and risk-sensitive control methods for satellite structure control

Abstract

This paper will review the full-state-feedback LQG, minimal cost variance (MCV), and risk-sensitive (RS) control for infinite time horizon case. In deriving the solutions of LQG, MCV, and RS control, Hamilton-Jacobi-Bellman equations are obtained using dynamic programming method. Unlike LQG and RS controllers, a pair of coupled algebraic Riccati-type equations arises in the solutions of MCV control. Average behavior of optimally controlled system is one possible performance indicator. The steady-state covariance matrices of the state and the control action are determined for finite an infinite time horizon. Furthermore, the equation for average values of the cost function is derived. A simple, single input, single output, one state example is discussed. The LQG, MCV, and RS controllers for this simple example are determined. Performance and stability characteristics of the three controllers are investigated. The performance of LQG, MCV, and RS controllers are investigated using a satellite structure control application. The objective of satellite structure control is to control the orientation of a satellite precisely and quickly. Results show that we can improve on LQG performance with both MCV and RS control.