FRACTIONAL OPTIMAL CONTROL PROBLEMS ON A STAR GRAPH: OPTIMALITY SYSTEM AND NUMERICAL SOLUTION

Mehandiratta V, Mehra M, Leugering G (2021)

Publication Type: Journal article

Publication year: 2021

Journal

Mathematical Control and Related Fields American Institute of Mathematical Sciences (AIMS)

Book Volume: 11

Pages Range: 189-209

Journal Issue: 1

DOI: 10.3934/mcrf.2020033

Abstract

In this paper, we study optimal control problems for nonlinear fractional order boundary value problems on a star graph, where the fractional derivative is described in the Caputo sense. The adjoint state and the optimality system are derived for fractional optimal control problem (FOCP) by using the Lagrange multiplier method. Then, the existence and uniqueness of solution of the adjoint equation is proved by means of the Banach contraction principle. We also present a numerical method to find the approximate solution of the resulting optimality system. In the proposed method, the L2 scheme and the GrUnwald-Letnikov formula is used for the approximation of the Caputo fractional derivative and the right Riemann-Liouville fractional derivative, respectively, which converts the optimality system into a system of linear algebraic equations. Two examples are provided to demonstrate the feasibility of the numerical method.

Authors with CRIS profile

Günter Leugering Lehrstuhl für Angewandte Mathematik

Involved external institutions

Indian Institute of Technology (IIT), Delhi IN India (IN)

How to cite

APA:

Mehandiratta, V., Mehra, M., & Leugering, G. (2021). FRACTIONAL OPTIMAL CONTROL PROBLEMS ON A STAR GRAPH: OPTIMALITY SYSTEM AND NUMERICAL SOLUTION. Mathematical Control and Related Fields, 11(1), 189-209. https://dx.doi.org/10.3934/mcrf.2020033

MLA:

Mehandiratta, Vaibhav, Mani Mehra, and Günter Leugering. "FRACTIONAL OPTIMAL CONTROL PROBLEMS ON A STAR GRAPH: OPTIMALITY SYSTEM AND NUMERICAL SOLUTION." Mathematical Control and Related Fields 11.1 (2021): 189-209.

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