Optimal Control Theory for Non-Scalar-Valued Performance Criteria.

The report is concerned with the theory of optimal control for non-scalar-valued performance criteria. In the space, where the performance criterion attains its value, the relations better than, worse than, not better than, and not worse than are defined by a partial order relation. The notion of optimality splits up into superiority and non-inferiority, because worse than is not the complement of better than, in general. A superior solution is better than every other solution. A noninferior solution is not worse than any other solution. In the control literature, noninferior solutions have been investigated particularly for vector-valued performance criteria. This research concentrates on superior solutions for non-scalar-valued performance criteria attaining their values in abstract partially ordered spaces. The main result is the infimum principle in Chapter 4, which constitutes necessary conditions for a control to be a superior solution to an optimal control problem. The infimum principle contains Pontryagins minimum principle as a special case. Author