NDLI: A maximum principle for hybrid optimal control problems

Content Provider	IEEE Xplore Digital Library
Author	Sussmann, H.J.
Copyright Year	1999
Description	Author affiliation: Dept. of Math., Rutgers State Univ., Piscataway, NJ, USA (Sussmann, H.J.)
Abstract	Presents a version of the maximum principle for hybrid optimal control problems under weak regularity conditions. In particular, we only consider autonomous systems, in which the dynamical behavior and the cost are invariant under time translations. The maximum principle is stated as a general assertion involving terms that are not yet precisely defined, and without a detailed specification of technical assumptions. One version of the principle, where the terms are precisely defined and the appropriate technical requirements are completely specified, is stated for problems where all the basic objects-the dynamics, the Lagrangian and the cost functions for the switchings and the end-point constraints-are differentiable along the reference arc. Another version, involving nonsmooth maps, is also stated, and some brief remarks on even more general versions are given. To illustrate the use of the maximum principle, two very simple examples are shown, involving problems that can easily be solved directly. Our results are stronger than the usual versions of the finite-dimensional maximum principle. For example, even the theorem for classical differentials applies to situations where the maps are not of class C/sup 1/, and can fail to be Lipschitz-continuous. The nonsmooth result applies to maps that are neither Lipschitz-continuous nor differentiable in the classical sense. In each case, it would be trivial to construct hybrid examples of a similar nature. On the other hand, the results presented in this paper are much weaker than what can actually be proved by our methods.
Starting Page	425
Ending Page	430
File Size	685406
Page Count	6
File Format	PDF
ISBN	0780352505
ISSN	01912216
DOI	10.1109/CDC.1999.832814
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1999-12-07
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Optimal control Control systems State-space methods Mathematics Electronic mail Lagrangian functions Cost function Hydrogen
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

A maximum principle for optimal control problems with equality and inequality constraints

A strong maximum principle for systems of differential inclusions

A strong version of the maximum principle under weak hypotheses

Necessary conditions for hybrid optimization

A Maximum Principle for Hybrid Optimal Control Problems with Pathwise State Constraints

Transversality conditions and a strong maximum principle for systems of differential inclusions

Reduction of Euler Lagrange problems for constrained variational problems and relation with optimal control problems

Hybrid Computer Solution of Optimal Control Problems by the Maximum Principle

From the brachystochrone to the maximum principle

A maximum principle for hybrid optimal control problems

Similar Documents

A maximum principle for optimal control problems with equality and inequality constraints

A strong maximum principle for systems of differential inclusions

A strong version of the maximum principle under weak hypotheses

Necessary conditions for hybrid optimization

A Maximum Principle for Hybrid Optimal Control Problems with Pathwise State Constraints

Transversality conditions and a strong maximum principle for systems of differential inclusions

Reduction of Euler Lagrange problems for constrained variational problems and relation with optimal control problems

Hybrid Computer Solution of Optimal Control Problems by the Maximum Principle

From the brachystochrone to the maximum principle

A maximum principle for hybrid optimal control problems