Study of the constrained LQG problem using homotopy

Optimal linear quadratic Gaussian (LQG) compensators with constrained structures are a sensible way to generate good multivariable feedback systems meeting strict implementation requirements. The optimality conditions obtained for the constrained LQG compensator are a set of highly coupled matrix equations that cannot be solved algebraically except when the compensator is centralized and full order. An alternative to the use of general optimization methods for solving the problem is to use homotopy. The benefit of the method is that it uses the solution to a simplified problem as a starting point and the final solution is then obtained by solving a simple differential equation. The author investigates the convergence properties and the limitation of such an approach and sheds some light on the nature and the number of solutions to the constrained LQG problem