Generalized quadratic optimal controllers for linear hereditary systems

A generalization of the quadratic optimal control theory for linear hereditary control systems is presented. The generalization involves admitting delay terms in the cost index so that for example, a quadratic function of the system output can be minimized. Questions of existence of optimal control as well as necessary and sufficient conditions for optimal control are treated. The results have been achieved using a geometric approach based on properties of the set of reachable points.