A Gradient Flow Approach to Computing LQ Optimal Output Feedback Gains

This paper considers the linear quadratic problem with static output feedback. It is shown that an optimal solution can be successfully computed by finding the limiting solution of an ordinary differential equation which is given in terms of the gradient flow associated with the cost function. Several properties are obtained concerning 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 by an example.