Modified fractional homotopy method for solving nonlinear optimal control problems

Qing, Wenjie; Pan, Binfeng

doi:10.1007/s11071-023-09191-2

Nonlinear Dyn

2024

DOI: 10.1007/s11071-023-09191-2

|View full text |Cite

Modified fractional homotopy method for solving nonlinear optimal control problems

Wenjie Qing,

Binfeng Pan

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Fractional logarithmic Chebyshev cardinal functions: Application for Caputo–Hadamard fractional optimal control problems

Karami,

Heydari,

Baleanu

2024

Journal of Vibration and Control

View full text Add to dashboard Cite

This study investigates a specific type of fractional optimization problems, subject to a dynamical system including the Caputo–Hadamard fractional differentiation. In this way, a novel class of basis functions known as the fractional logarithmic Chebyshev cardinal functions is introduced. An operational matrix regarding the Hadamard fractional integral of these fractional functions is derived and employed to develop an efficient numerical method for the provided problem. The established algorithm converts the solution of the primary fractional optimization problem into the solution of an algebraic system of equations by representing the state and control variables via the introduced fractional functions. Two test problems are considered to confirm the effectiveness of the suggested method. The derived outcomes of solving these examples highlight the satisfactory accuracy and efficiency of the designed method.

show abstract

Fractional logarithmic Chebyshev cardinal functions: Application for Caputo–Hadamard fractional optimal control problems

Karami,

Heydari,

Baleanu

2024

Journal of Vibration and Control

View full text Add to dashboard Cite

show abstract

Heat-Equation-Based Smoothing Homotopy Method for Nonlinear Optimal Control Problems

Pan,

Ran,

Qing

et al. 2024

Journal of Guidance, Control, and Dynamics

View full text Add to dashboard Cite

This paper presents a new heat-equation-based smoothing homotopy method for solving nonlinear optimal control problems with the indirect method. The surrogates, derived from the heat equation solution, are first incorporated into the necessary conditions as replacement of the terminal state and costate variables. The homotopy process is then applied to the heat conduction time: a longer time results in a more uniform temperature distribution and greater stability against initial temperature variations, thereby making the corresponding homotopy problem much easier to solve; zero time implies no heat conduction and reverts to the original problem. Furthermore, capitalizing on the heat equation’s boundedness characteristic, an efficient approach for determining the hypersensitive parameters is proposed, thus obviating the necessity of manual tuning. Challenging numerical examples are provided to demonstrate the superior performance of the proposed method, indicating that its convergence and efficiency are significantly enhanced compared to the original smoothing homotopy methods.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Modified fractional homotopy method for solving nonlinear optimal control problems

Cited by 2 publications

References 48 publications

Fractional logarithmic Chebyshev cardinal functions: Application for Caputo–Hadamard fractional optimal control problems

Fractional logarithmic Chebyshev cardinal functions: Application for Caputo–Hadamard fractional optimal control problems

Heat-Equation-Based Smoothing Homotopy Method for Nonlinear Optimal Control Problems

Contact Info

Product

Resources

About