Controllability, observability, and optimality in hereditary systems of neutral type

Control systems governed by linear functional differential equations of neutral type are considered. Attention is given to some problems of controllability, observability, and optimization for such systems under constraints. Necessary and sufficient optimality conditions are obtained for nonautonomous neutral systems with convex cost functionals. Then a variational approach to controllability and observability of linear hereditary systems is developed. Using this approach, the author proves a duality principle between some concepts of controllability for neutral systems under constraints and ideal observability of dual systems governed by the Volterra integro-functional equations. This duality principle shows that, in the case of continuous initial states, the controllability studied is dual to the physically visual concept of observability connected with the one-valued evaluation (prediction) of the system motion in the future on the basis of current values of output data