Optimal Control of Delayed Differential-Algebraic Inclusions

This paper concerns constrained dynamic optimization problems governed by delayed differentialalgebraic systems. Dynamic constraints in such systems, which are particularly important for engineering applications, are described by interconnected delay-differential inclusions and algebraic equations. We pursue a two-hold goal: to study variational stability of such control systems with respect to discrete approximations and to derive necessary optimality conditions for both delayed differential-algebraic systems and their finite-difference counterparts using modern tools of variational analysis and generalized differentiation. We are not familiar with any results in these directions for differential-algebraic inclusions even in the delay-free case. In the first part of the paper we establish the value convergence of discrete approximations as well as the strong convergence of optimal arcs in the classical Sobolev space W 1 •2 • Then using discrete approximations a vehicle, we derive necessary optimality conditions for delayed differential-algebraic inclusions in both Euler-Lagrange and Hamiltonian forms via basic generalized differential constructions of variational analysis.