A GRADIENT FLOW APPROACH TO COMPUTING LQ OPTIMAL OUTPUT-FEEDBACK GAINS

This short communication considers the linear quadratic problem with s tatic output feedback. It is shown that an optimal solution can be suc cessfully computed by finding the limiting solution of an ordinary dif ferential equation which is given in terms of the gradient flow associ ated with the cost function. Several properties are obtained concernin g the gradient flow. For example, it is shown that the flow contains a subsequence convergent to a locally optimal output feedback gain. In the special case of state feedback the flow is guaranteed to converge to the optimal gain. The effectiveness of the method is demonstrated b y an example.