scholarly journals Remarks on some existence theorems for optimal control

1969 ◽  
Vol 3 (5) ◽  
pp. 296-305 ◽  
Author(s):  
L. Cesari ◽  
J. R. La Palm ◽  
T. Nishiura
Keyword(s):  
Optimal Control ◽  
Existence Theorems

Lagrange principle and its regularization as a theoretical basis of stable solving optimal control and inverse problems

2021 ◽  
pp. 151-171
Author(s):  
Mikhail I. Sumin
Keyword(s):  
Optimal Control ◽  
Inverse Problems ◽  
Theoretical Basis ◽  
Optimization Problems ◽  
Existence Theorems ◽  
General Structure ◽  
Approximate Solutions ◽  
Lagrange Principle ◽  
Ill Posed ◽  
Final Observation

The paper is devoted to the regularization of the classical optimality conditions (COC) — the Lagrange principle and the Pontryagin maximum principle in a convex optimal control problem for a parabolic equation with an operator (pointwise state) equality-constraint at the final time. The problem contains distributed, initial and boundary controls, and the set of its admissible controls is not assumed to be bounded. In the case of a specific form of the quadratic quality functional, it is natural to interpret the problem as the inverse problem of the final observation to find the perturbing effect that caused this observation. The main purpose of regularized COCs is stable generation of minimizing approximate solutions (MAS) in the sense of J. Warga. Regularized COCs are: 1) formulated as existence theorems of the MASs in the original problem with a simultaneous constructive representation of specific MASs; 2) expressed in terms of regular classical Lagrange and Hamilton–Pontryagin functions; 3) are sequential generalizations of the COCs and retain the general structure of the latter; 4) “overcome” the ill-posedness of the COCs, are regularizing algorithms for solving optimization problems, and form the theoretical basis for the stable solving modern meaningful ill-posed optimization and inverse problems.

scholarly journals Existence theorems for optimal control of quasilinear parabolic partial differential equations

1979 ◽  
Vol 21 (1) ◽  
pp. 90-101 ◽  
Author(s):  
S. Nababan ◽  
E. S. Noussair
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence Theorems ◽  
Parabolic Partial Differential Equations ◽  
Optimal Controls ◽  
Integral Functionals ◽  
Partial Differential ◽  
Lower Semi ◽  
Quasilinear Parabolic

AbstractThe question on existence of optimal controls for a system governed by quasilinear parabolic partial differential equations which is linear in the control variables is considered. It is shown that whenever the controls converge in the weak * topology of L∞, the corresponding solutions converge uniformly. Using this result and results on lower semi-continuity of integral functionals, existence theorems for optimal controls are proved.

Sign in / Sign up

Export Citation Format

Share Document