Optimal Control Theory for Non-Scalar-Valued Performance Criteria.
Abstract
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 Pontryagin's minimum principle as a special case. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1971
- Accession Number
- AD0731213
Entities
People
- Hans P. Geering
Organizations
- Massachusetts Institute of Technology