Makowski, Karol; Neustadt, Lucien W. Optimal control problems with mixed control-phase variable equality and inequality constraints. (English) Zbl 0241.49007 SIAM J. Control 12, 184-228 (1974). In this paper, necessary conditions are obtained for optimal control problems containing equality constraints defined in terms of functions of the control and phase variables. The control system is assumed to be characterized by an ordinary differential equation, and more conventional constraints, including phase inequality constraints, are also assumed to be present. Because the first-mentioned equality constraint must be satisfied for all t (the independent variable of the differential equation) belonging to an arbitrary (prescribed) measurable set, this problem gives rise to infinite-dimensional equality constraints. To obtain the necessary conditions, which are in the form of a maximum principle, an implicit function type theorem in Banach spaces is derived. This review text is based on a scanned copy of the printed version. It was converted to LaTeX using MathPix and a specifically developed LLM to assign the text parts to the metadata. It may contain errors, misassignments, or gaps; in particular, the reviewer signature has not yet been extracted reliably in general. If you notice any errors, please report them directly to our editorial team via the Contact Form. Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 22 Documents MSC: 49K15 Optimality conditions for problems involving ordinary differential equations × Cite Format Result Cite Review PDF Full Text: DOI