On Application of Descriptor-Variable Theory to the Investigation of Optimal Control Problems of Linear Time-Delay Systems

Linear time-invariant time-delay control systems are approximated by time-invariant descriptor-variable systems. The approximating descriptor-variable systems do not contain any time-delay but they are controlled by a linear combination of the input vector and some of its derivatives. Necessary conditions are derived for existence of optimal controls; a "minimum energy" optimal control problem is investigated in some detail.