Suboptimal linear regulators with incomplete state feedback

A method of designing linear regulators with incomplete state feedback has been suggested by Rekasius [1]. Ramar and Ramaswami [2] have pointed out the difficulties encountered in applying this method. This correspondence presents, briefly, an alternative approach to this problem in two cases of a) unknown initial state and b) known initial state statistics, viz., mean and covariance matrix. Solution for the control law utilizing only the available states is obtained by minimizing an upper bound on the ratio of the suboptimal to optimal cost in case a). In case b) the expected value of the suboptimal cost is minimized. It is assumed that the available states are sufficient to make the feedback system stable. The solution is in the form of necessary conditions and results in a set of simultaneous polynomial equations, but the solution to the optimal control problem is not required.