scholarly journals Controlled Fractional Order Processes with Distributed Parameters

2021 ◽  
Vol 2068 (1) ◽  
pp. 012001
Author(s):  
Mashrabjon Mamatov ◽  
Xakimjon Alimov
Keyword(s):  
Finite Difference ◽  
Fractional Order ◽  
Dynamic Systems ◽  
Optimal Control Problems ◽  
Numerical Solutions ◽  
Arbitrary Order ◽  
Control Problems ◽  
Control Laws ◽  
Sampling Schemes ◽  
Distributed Parameters

Abstract This work is devoted to the study of the problem of pursuit in systems controlled with distributed parameters of fractional order. Derivatives with respect to spatial variables are ordinary, integer, and even of arbitrary order. Designed and studied sampling schemes. A numerical method is constructed for finding strategies in suitable classes and for constructing the corresponding control laws. Theorems are proved for the possibility of completing the pursuit by the finite difference method, and they can be used to solve finite-difference optimal control problems or numerical solutions of differential games of fractional order. Problems of the type under study are encountered in modeling the processes of economic growth and in problems of stabilizing dynamic systems.

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.

Shifted Chebyshev schemes for solving fractional optimal control problems

2019 ◽  
Vol 25 (15) ◽  
pp. 2143-2150 ◽  
Author(s):  
M Abdelhakem ◽  
H Moussa ◽  
D Baleanu ◽  
M El-Kady
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Chebyshev Polynomials ◽  
Optimal Control Problems ◽  
Optimization Problems ◽  
Control Problems ◽  
Numerical Examples ◽  
Fractional Optimal Control ◽  
Functional Approximation ◽  
Fractional Optimal Control Problems

Two schemes to find approximated solutions of optimal control problems of fractional order (FOCPs) are investigated. Integration and differentiation matrices were used in these schemes. These schemes used Chebyshev polynomials in the shifted case as a functional approximation. The target of the presented schemes is to convert such problems to optimization problems (OPs). Numerical examples are included, showing the strength of the schemes.

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