Optimal control of a servo derived from nonquadratic performance criteria

Optimal control theory is applied to a serve problem described by linear plant dynamics and a nonquadratic performance index. The performance index consists of the sum of positive semidefinite homogeneous multinomial forms of the error between plant states and a given input. It is shown that by adding conveniently chosen higher multinomial forms to the performance index, the optimal control law can be obtained in closed-form as a nonlinear function of the error between the controllable states and the input vector.