Schauder's fixed point theorem and Pontryagin maximum principle
Copyright policy )Schauder's fixed point theorem and Pontryagin maximum principle
We prove the Pontryagin maximum principle for a general optimal control problem. The main ingredient of the proof is the abstract lemma on an inverse function, which is proved via the Schauder fixed-point theorem. Under this approach, the proof of the Pontryagin maximum principle is quite short and transparent.
- Lomonosov Moscow State University Russian Federation
- Moscow Institute of Physics and Technology Russian Federation
- V. A. Trapeznikov Institute of Control Sciences Russian Federation
- Moscow Power Engineering Institute Russian Federation
Fixed-point theorems, Existence theories for optimal control problems involving ordinary differential equations, Schauder's fixed-point theorem, optimal control problem, Pontryagin maximum principle, Optimality conditions for problems in abstract spaces, inverse function, Optimality conditions for problems involving ordinary differential equations
Fixed-point theorems, Existence theories for optimal control problems involving ordinary differential equations, Schauder's fixed-point theorem, optimal control problem, Pontryagin maximum principle, Optimality conditions for problems in abstract spaces, inverse function, Optimality conditions for problems involving ordinary differential equations
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!