Necessary Conditions for Optimal Control Problems Involving Nonlinear Differential Algebraic Equations

Pinho, Maria do Rosário de; Vinter, R. B.

doi:10.1006/jmaa.1997.5523

Cited by 61 publications

(54 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As hipóteses (H2)-(H4) são fundamentais na utilização do Teorema da Função Implícita Uniforme [3]. A hipótese (H4)é uma versão uniforme da qualificação de restrições independência linear da otimização não-linear em dimensão finita.…”

Section: Preliminaresunclassified

“…Com este resultado, a utilização de um Teorema da Função Implícita Uniforme [3] e uma qualificação de restrições tipo independência linear, condições necessárias de primeira e segunda ordens foram desenvolvidas para o problema com restrições de igualdade (RI).…”

Section: Conclusõesunclassified

“…Neste trabalho, propomos o uso de uma qualificação de restrição tipo Independência Linear e de um Teorema da Função Implícita Uniforme [3], para obtenção de condições necessárias de primeira e segunda ordens para o problema (PTC).…”

Section: Introductionunclassified

See 2 more Smart Citations

Condições Necessárias para Problemas de Otimização com Tempo Contínuo sob Regularidade Tipo Independência Linear

Monte¹,

Oliveira²

2018

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

View full text Add to dashboard Cite

show abstract

Section: Preliminaresunclassified

Section: Conclusõesunclassified

See 1 more Smart Citation

Condições Necessárias para Problemas de Otimização com Tempo Contínuo sob Regularidade Tipo Independência Linear

Monte¹,

Oliveira²

2018

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…There are many applications of such dynamic models (called DAEs, i.e., differential-algebraic equations) especially in process systems engineering, robotics, mechanical systems with holonomic and nonholonomic constraints, etc. ; see [1,2,14,15] and the references therein. Observe, however, that the dynamic relations (1.2) and (1.3) and the assumptions made are generally different from those conventional in the control theory for DAEs, especially for deriving necessary optimality conditions.…”

Section: X(t) X(t − ∆) Z(t)ż(t) T) Dt (11)mentioning

confidence: 99%

“…Observe, however, that the dynamic relations (1.2) and (1.3) and the assumptions made are generally different from those conventional in the control theory for DAEs, especially for deriving necessary optimality conditions. The most advanced results in this direction for the so-called index one DAEs are obtained in [14], where it was particularly discovered that optimal processes in such systems do not satisfy the (strong) Maximum Principle in the absence of a convexity hypothesis on the velocity sets.…”

Section: X(t) X(t − ∆) Z(t)ż(t) T) Dt (11)mentioning

confidence: 99%

Optimal control of delay systems with differential and algebraic dynamic constraints

Mordukhovich¹,

Wang

2005

ESAIM: COCV

View full text Add to dashboard Cite

Abstract. This paper concerns constrained dynamic optimization problems governed by delay control systems whose dynamic constraints are described by both delay-differential inclusions and linear algebraic equations. This is a new class of optimal control systems that, on one hand, may be treated as a specific type of variational problems for neutral functional-differential inclusions while, on the other hand, is related to a special class of differential-algebraic systems with a general delay-differential inclusion and a linear constraint link between "slow" and "fast" variables. We pursue a twofold goal: to study variational stability for this class of control systems with respect to discrete approximations and to derive necessary optimality conditions for both delayed differential-algebraic systems under consideration and their finite-difference counterparts using modern tools of variational analysis and generalized differentiation. The authors are not familiar with any results in these directions for such systems even in the delay-free case. In the first part of the paper we establish the value convergence of discrete approximations as well as the strong convergence of optimal arcs in the classical Sobolev space W 1,2 . Then using discrete approximations as a vehicle, we derive necessary optimality conditions for the initial continuous-time systems in both Euler-Lagrange and Hamiltonian forms via basic generalized differential constructions of variational analysis.Mathematics Subject Classification. 49J53, 49K24, 49K25, 49M25, 90C31, 93C30.

show abstract

The Calculus of Variations: A Historical Perspective

Schättler¹,

Ledzewicz²

2012

Interdisciplinary Applied Mathematics

View full text Add to dashboard Cite

Necessary Conditions for Optimal Control Problems Involving Nonlinear Differential Algebraic Equations

Cited by 61 publications

References 4 publications

Condições Necessárias para Problemas de Otimização com Tempo Contínuo sob Regularidade Tipo Independência Linear

Condições Necessárias para Problemas de Otimização com Tempo Contínuo sob Regularidade Tipo Independência Linear

Optimal control of delay systems with differential and algebraic dynamic constraints

The Calculus of Variations: A Historical Perspective

Contact Info

Product

Resources

About