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 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.

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.

A weak maximum principle for optimal control problems with mixed constraints under a constant rank condition

2020 ◽  
Vol 37 (3) ◽  
pp. 1021-1047
Author(s):  
Roberto Andreani ◽  
Valeriano Antunes de Oliveira ◽  
Jamielli Tomaz Pereira ◽  
Geraldo Nunes Silva
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Necessary Optimality Conditions ◽  
Inequality Constraints ◽  
Equality Constraints ◽  
Control Problems ◽  
Constant Rank ◽  
Rank Condition ◽  
Weak Maximum Principle

Abstract Necessary optimality conditions for optimal control problems with mixed state-control equality constraints are obtained. The necessary conditions are given in the form of a weak maximum principle and are obtained under (i) a new regularity condition for problems with mixed linear equality constraints and (ii) a constant rank type condition for the general non-linear case. Some instances of problems with equality and inequality constraints are also covered. Illustrative examples are presented.

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