Singular Characteristics of the HJBI Equation in State Constraint Optimal Control Problems

2001 ◽  
Vol 34 (20) ◽  
pp. 19-21
Author(s):  
Arik Melikyan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
State Constraint ◽  
Control Problems ◽  
Singular Characteristics

scholarly journals A Lagrange multiplier method for semilinear elliptic state constrained optimal control problems

2020 ◽  
Vol 77 (3) ◽  
pp. 831-869
Author(s):  
Veronika Karl ◽  
Ira Neitzel ◽  
Daniel Wachsmuth
Keyword(s):  
Optimal Control ◽  
Weak Convergence ◽  
Original Problem ◽  
Optimal Control Problems ◽  
State Constraint ◽  
Stationary Points ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
Semilinear Elliptic ◽  
Augmented Lagrange Method

Abstract In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the original problem as well as weak convergence of the adjoint states and weak-* convergence of the multipliers associated to the state constraint. Moreover, we show existence of stationary points in arbitrary small neighborhoods of local solutions of the original problem. Additionally, various numerical results are presented.

scholarly journals Pontryagin's maximum principle for optimal control of a non-well-posed parabolic differential equation involving a state constraint

2004 ◽  
Vol 46 (2) ◽  
pp. 171-184
Author(s):  
Mi Jin Lee ◽  
Jong Yeoul Park
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Pontryagin’S Maximum Principle ◽  
State Constraint ◽  
Parabolic Differential Equation ◽  
Control Problems ◽  
Pontryagin's Maximum Principle ◽  
Well Posed

AbstractIn this paper, we study Pontryagin's maximum principle for some optimal control problems governed by a non-well-posed parabolic differential equation. A new penalty functional is applied to derive Pontryagin's maximum principle and an application for this system is given.

scholarly journals Necessary Optimality Conditions for a Class of Control Problems with State Constraint

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 9
Author(s):  
Adam Korytowski ◽  
Maciej Szymkat
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
Necessary Optimality Conditions ◽  
State Constraint ◽  
Control Problems ◽  
Elementary Approach

An elementary approach to a class of optimal control problems with pathwise state constraint is proposed. Based on spike variations of control, it yields simple proofs and constructive necessary conditions, including some new characterizations of optimal control. Two examples are discussed.

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