HOMOTOPY ALGORITHM FOR MAXIMUM-ENTROPY DESIGN

Maximum entropy design is a generalization of the LQG method that was developed to enable the synthesis of robust control laws for flexible structures. The method was developed by Hyland and motivated by insigh ts 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 eq uations consist of two Riccati equations coupled to two Lyapunov equat ions. When the uncertainty is zero, the equations decouple and the Ric cati equations become the standard LQG regulator and estimator equatio ns. A previous homotopy algorithm to solve the coupled equations relie s 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 can have quadratic convergence rates along the homotopy curve. Algorithms of th is type should also prove effective in the solution of other sets of c oupled Riccati and Lyapunov equations appearing in robust control theo ry.