A Feedback Descent Method for Solving Constrained LQG Control Problems

This paper presents a new method for the numerical solution of LQG optimal control problems subject to constraints. In general, solutions to these problems necessarily satisfy a set of coupled Lyapunov and/or Riccati equations. These equations are solved in an iterative manner based on a quasi-Newton type algorithm. Key features of the method are the simplicity afforded in developing iterative algorithms satisfying the necessary conditions for solution of such problems, and the speed and efficiency of these algorithms. The technique is illustrated for the optimal static output feedback problem and the optimal LQG problem with an H¿ norm bound on a closed-loop transfer function.