Galerkin approximation of optimal control problems for parabolic systems with distributed parameters

1979 ◽  
Vol 19 (4) ◽  
pp. 53-70 ◽  
Author(s):  
A.K. Kerimov
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Galerkin Approximation ◽  
Parabolic Systems ◽  
Control Problems ◽  
Distributed Parameters ◽  
Systems With Distributed Parameters

scholarly journals METHODS FOR PROBLEMS OF VECTOR GENERALIZED OPTIMAL CONTROL OF SYSTEMS WITH DISTRIBUTED PARAMETERS

2020 ◽  
pp. 71-98
Author(s):  
O. S. Kharkov ◽  
Ya. I. Vedel ◽  
V. V. Semenov
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
Necessary Optimality Conditions ◽  
Quality Criterion ◽  
Control Problems ◽  
Convergence Of Algorithms ◽  
Distributed Parameters ◽  
Admissible Controls ◽  
Systems With Distributed Parameters

The paper develops the theory of existence and necessary optimality conditions for optimal control problems with a vector quality criterion for systems with distributed parameters and generalized impacts. The concept of $(K, e, \epsilon)$-approximate efficiency is investigated. Necessary conditions for $(K, e, \epsilon)$-approximate efficiency of admissible controls in the form of variational inclusions are proved. Methods for solving problems of vector optimization of linear distributed systems with generalized control are proposed. Convergence of algorithms with errors is proved.

scholarly journals FIRST-ORDER METHODS FOR GENERALIZED OPTIMAL CONTROL PROBLEMS FOR SYSTEMS WITH DISTRIBUTED PARAMETERS

2020 ◽  
pp. 18-44
Author(s):  
S. V. Denisov ◽  
V. V. Semenov
Keyword(s):  
Optimal Control Problems ◽  
A Priori Estimates ◽  
A Priori ◽  
Control Problems ◽  
First Order ◽  
Admissible Sets ◽  
Distributed Parameters ◽  
Priori Estimates ◽  
Systems With Distributed Parameters ◽  
First Order Methods

The problems of optimization of linear distributed systems with generalized control and first-order methods for their solution are considered. The main focus is on proving the convergence of methods. It is assumed that the operator describing the model satisfies a priori estimates in negative norms. For control problems with convex and preconvex admissible sets, the convergence of several first-order algorithms with errors in iterative subproblems is proved.

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