分数阶欧拉小波技术在多维分布阶最优控制中的应用

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-24 DOI:10.1016/j.cnsns.2025.109316

Akanksha Singh, Ankur Kanaujiya, Jugal Mohapatra

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引用次数: 0

摘要

本文将二维分布阶最优控制问题扩展为多维分布阶最优控制问题，并利用分数阶欧拉小波方法求解。导出了最优性的充分必要条件。该方法需要将最优控制问题转化为使用Riemann-Liouville分布阶运算矩阵和Newton-Cotes并置点的代数方程组。拉格朗日乘子法求解了这些方程，得到了最优值。文中还建立了收敛分析和误差界。通过算例验证了数值方法的精度，并通过实际问题说明了该方法的合理性和有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Fractional-order euler wavelet technique for multidimensional distributed-order optimal control problem

This manuscript extends two-dimensional distributed-order optimal control problems into multidimensional distributed-order optimal control problems and solves them using the fractional-order Euler wavelets approach. The necessary and sufficient conditions for optimality are derived. The method entails transforming the optimal control problem into a system of algebraic equations using Riemann-Liouville distributed-order operational matrices and Newton-Cotes collocation points. The Lagrange multiplier method solves these equations and gets the optimized value. The manuscript also establishes the convergence analysis and error bounds. Several examples are examined to demonstrate the high precision of the numerical method and also show rationality and validity through real-life problems.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.