Paper Info
Title
Pontryagin Maximum Principle for Finite Dimensional Nonlinear Optimal Control Problems on Time Scales.
Abstract
In this paper we derive a strong version of the Pontryagin maximum principle for general nonlinear optimal control problems on time scales in finite dimension. The final time can be fixed or not, and in the case of general boundary conditions we derive the corresponding transversality conditions. Our proof is based on Ekeland's variational principle. Our statement and comments clearly show the distinction between right-dense points and right-scattered points. At right-dense points a maximization condition of the Hamiltonian is derived, similarly to the continuous-time case. At right-scattered points a weaker condition is derived, in terms of so-called stable Omega-dense directions. We do not make any specific restrictive assumption on the dynamics or on the set Omega of control constraints. Our statement encompasses the classical continuous-time and discrete-time versions of the Pontryagin maximum principle, and holds on any general time scale, that is, any closed subset of R.
Year
DOI
Venue
2013
10.1137/130912219
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Keywords
Field
DocType
Pontryagin maximum principle,optimal control,time scale,transversality conditions,Ekeland's variational principle,needle-like variations,right-scattered point,right-dense point
Nonlinear optimal control,Boundary value problem,Mathematical optimization,Optimal control,Hamiltonian (quantum mechanics),Mathematical analysis,Variational principle,Transversality,Hamiltonian (control theory),Mathematics,Maximization
Journal
Volume
Issue
ISSN
51
5
0363-0129
Citations 
PageRank 
References 
0
0.34
6
Authors
2
Name
Order
Citations
PageRank
Loïc Bourdin142.29
Emmanuel Trélat218324.42