The Maximum Principle for Optimal Control Problems with State Constraints by R.V. Gamkrelidze: Revisited

Journal of Optimization Theory and Applications ◽

10.1007/s10957-011-9807-5 ◽

2011 ◽

Vol 149 (3) ◽

pp. 474-493 ◽

Author(s):

A. V. Arutyunov ◽

D. Y. Karamzin ◽

F. L. Pereira

Keyword(s):

Optimal Control ◽

Maximum Principle ◽

State Constraints ◽

Optimal Control Problems ◽

Control Problems ◽

The Maximum Principle

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Conditions for the absence of jumps of the solution to the adjoint system of the maximum principle for optimal control problems with state constraints

Proceedings of the Steklov Institute of Mathematics ◽

10.1134/s0081543816020036 ◽

2016 ◽

Vol 292 (S1) ◽

pp. 27-35 ◽

Author(s):

A. V. Arutyunov ◽

D. Yu. Karamzin ◽

F. L. Pereira

Keyword(s):

Optimal Control ◽

Maximum Principle ◽

State Constraints ◽

Optimal Control Problems ◽

Adjoint System ◽

Control Problems ◽

The Maximum Principle

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Investigation of the Degeneracy Phenomenon of the Maximum Principle for Optimal Control Problems with State Constraints

SIAM Journal on Control and Optimization ◽

10.1137/s036301299426996x ◽

1997 ◽

Vol 35 (3) ◽

pp. 930-952 ◽

Author(s):

Aram V. Arutyunov ◽

Sergei M. Aseev

Keyword(s):

Optimal Control ◽

Maximum Principle ◽

State Constraints ◽

Optimal Control Problems ◽

Control Problems ◽

The Maximum Principle

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LIPSCHITZ CONTINUITY OF THE MEASURE LAGRANGE MULTIPLIER FROM THE MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS OF EQUALITY AND INEQUALITY TYPE

Tambov University Reports Series Natural and Technical Sciences ◽

10.20310/1810-0198-2017-22-3-508-516 ◽

2017 ◽

Vol 22 (3) ◽

pp. 508-516

Author(s):

A.V. Gorbacheva ◽

◽

D.Yu. Karamzin ◽

Keyword(s):

Optimal Control ◽

Maximum Principle ◽

Lagrange Multiplier ◽

State Constraints ◽

Optimal Control Problems ◽

Lipschitz Continuity ◽

Control Problems ◽

The Maximum Principle ◽

Inequality Type

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The connection between the maximum principle and the value function for optimal control problems under state constraints

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) ◽

10.1109/cdc.2004.1428798 ◽

2004 ◽

Author(s):

A. Cernea ◽

H. Frankowska

Keyword(s):

Optimal Control ◽

Maximum Principle ◽

State Constraints ◽

Value Function ◽

Optimal Control Problems ◽

Control Problems ◽

The Maximum Principle ◽

The Value Function

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New approximation method in the proof of the Maximum Principle for nonsmooth optimal control problems with state constraints

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2006.03.056 ◽

2007 ◽

Vol 326 (2) ◽

pp. 974-1000 ◽

Author(s):

Ilya A. Shvartsman

Keyword(s):

Optimal Control ◽

Maximum Principle ◽

Approximation Method ◽

State Constraints ◽

Optimal Control Problems ◽

Control Problems ◽

The Maximum Principle ◽

Nonsmooth Optimal Control

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An integral-type constraint qualification to guarantee nondegeneracy of the maximum principle for optimal control problems with state constraints

Systems & Control Letters ◽

10.1016/j.sysconle.2013.05.005 ◽

2013 ◽

Vol 62 (8) ◽

pp. 686-692 ◽

Author(s):

S.O. Lopes ◽

F.A.C.C. Fontes ◽

M.d.R. de Pinho

Keyword(s):

Optimal Control ◽

Maximum Principle ◽

Constraint Qualification ◽

State Constraints ◽

Optimal Control Problems ◽

Control Problems ◽

Integral Type ◽

The Maximum Principle ◽

Type Constraint

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OPtimal Synthesis And Normality Of The Maximum Principle For Optimal Control Problems With Pure State Constraints

2011 9th IEEE International Conference on Control and Automation (ICCA) ◽

10.1109/icca.2011.6137892 ◽

2011 ◽

Author(s):

Helene Frankowska ◽

Marco Mazzola

Keyword(s):

Optimal Control ◽

Maximum Principle ◽

State Constraints ◽

Optimal Control Problems ◽

Optimal Synthesis ◽

Control Problems ◽

The Maximum Principle ◽

Pure State Constraints

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

Proceedings of the 45th IEEE Conference on Decision and Control ◽

10.1109/cdc.2006.377241 ◽

2006 ◽

Author(s):

P. E. Caines ◽

F. H. Clarke ◽

X. Liu ◽

R. B. Vinter

Keyword(s):

Optimal Control ◽

Maximum Principle ◽

State Constraints ◽

Optimal Control Problems ◽

Control Problems ◽

Hybrid Optimal Control

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The Maximum Principle for Optimal Control Problems with Time Delays

SIAM Journal on Control and Optimization ◽

10.1137/16m1085474 ◽

2017 ◽

Vol 55 (5) ◽

pp. 2905-2935 ◽

Author(s):

A. Boccia ◽

R. B. Vinter

Keyword(s):

Optimal Control ◽

Maximum Principle ◽

Time Delays ◽

Optimal Control Problems ◽

Control Problems ◽

The Maximum Principle

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The maximum principle in optimal control problems for an elliptic equation (in Russian)

Zeitschrift für Analysis und ihre Anwendungen ◽

10.4171/zaa/200 ◽

1986 ◽

Vol 5 (4) ◽

pp. 289-306 ◽

Author(s):

Uldis Raitums

Keyword(s):

Optimal Control ◽

Maximum Principle ◽

Elliptic Equation ◽

Optimal Control Problems ◽

Control Problems ◽

The Maximum Principle

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