Optimal problem of cost function for the linear neutral systems (Q5945173)

The authors study optimal control problem for systems with delays described by linear neutral equations in a Hilbert space with a quadratic cost function. Applying Lions' approach [\textit{J.-L. Lions}: ``Optimal control systems governed by partial differential equations'' (1971; Zbl 0203.09001)] they derive necessary and sufficient conditions for the unique optimal control for systems under considerations in the form of Pontryagin's maximum principle. Applications of the obtained results are demonstrated on three examples: Bolza problem, terminal value control problem and minimum energy problem.