Linear optimal control of systems with state and control variable delays (Q794982)

The approach of \textit{R. B. Vinter} and \textit{R. H. Kwong} [SIAM J. Control Optimization 19, 139-153 (1981; Zbl 0465.93043)] to quadratic control problems for autonomous linear systems with delays in states and controls is generalized. Since general delays, in particular point delays, in the controls are admitted, the associated control operator in a state space formulation is unbounded. The paper discusses the appropriate state space setting and linear quadratic control problems over finite and infinite horizons. Invariant embedding methods due to J. L. Lions are adopted in order to derive operator Riccati equations.