EconPapers    
Economics at your fingertips  
 

Analysis of nonlinear fractional optimal control systems described by delay Volterra–Fredholm integral equations via a new spectral collocation method

Hamid Reza Marzban and Atiyeh Nezami

Chaos, Solitons & Fractals, 2022, vol. 162, issue C

Abstract: We aim to introduce a new spectral collocation method for investigating and analyzing nonlinear delay control systems governed by the fractional mixed Volterra–Fredholm integral equations (MVFIEs). The generalized fractional Legendre basis (GFLB) is used as a complete orthogonal basis, and the fractional Legendre–Gaussian nodes are introduced and employed as the fractional collocation points. These nodes correspond to the zeros of the fractional-order Legendre function of degree M. The convergence of the generalized orthogonal basis is discussed in detail based on the Sobolev and L2 norms. Additionally, new fractional integral and delay operators are implemented to reduce the primary control system to a static optimization system. Two benchmark fractional control problems, including delay, are considered to demonstrate the powerfulness and superiority of the new methodology. The introduced collocation approach can be successfully performed for solving even those fractional control problems having any irregularities in the control function, including jump discontinuities and bang–bang behavior.

Keywords: Nonlinear delay fractional control; Fractional Volterra–Fredholm; Generalized fractional Legendre functions; Spectral collocation method; Sobolev space; Fractional operators (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077922007044
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922007044

DOI: 10.1016/j.chaos.2022.112499

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().

 
Page updated 2025-03-19
Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922007044