Optimal control of causal differential–algebraic systems ✩

Existence theory of Filippov–Roxin type as well as a maximum principle for optimal control problem governed by nonlinear differential–algebraic equations of index 1, or 2, or 3 are formulated and proved. The index-3 case is illustrated on mechanical descriptor systems arising in robotics.  2002 Elsevier Science (USA). All rights reserved.