A Homotopy Algorithm for Maximum Entropy Design

Abstract

Maximum entropy design is a generalization of LQG that was developed to enable the synthesis of robust control laws for flexible structures. The method was developed by Hyland and motivated by insights gained from Statistical Energy Analysis. Maximum entropy design has been used successfully in control design for ground-based structural testbeds and certain benchmark problems. The maximum entropy design equations consist of two Riccati equations coupled to two Lyapunov equations. When the uncertainty is zero the equations decouple and the Riccati equations become the standard LQG regulator and estimator equations. A previous homotopy algorithm to solve the coupled equations relies on an iterative scheme that exhibits slow convergence properties as the uncertainty level is increased. This paper develops a new homotopy algorithm that does not suffer from this defect and in fact has quadratic convergence rates along the homotopy curve.