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Generalized Lagrange–Jacobi–Gauss–Radau collocation method for solving a nonlinear optimal control problem with the classical diffusion equation

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Abstract

In this paper, a well-known nonlinear optimal control problem (OCP) arisen in a variety of biological, chemical, and physical applications is considered. The quadratic form of the nonlinear cost function is endowed with the state and control functions. In this problem, the dynamic constraint of the system is given by a classical diffusion equation. This article is concerned with a generalization of Lagrange functions. Besides, a generalized Lagrange–Jacobi–Gauss–Radau (GLJGR) collocation method is introduced and applied to solve the aforementioned OCP. Based on initial and boundary conditions, the time and space variables, t and x, are clustered with Jacobi–Gauss–Radau points. Then, to solve the OCP, Lagrange multipliers are used and the optimal control problem is reduced to a parameter optimization problem. Numerical results demonstrate its accuracy, efficiency, and versatility of the presented method.

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Authors and Affiliations

  1. Department of Computer Sciences, Amirkabir University of Technology, Tehran, Iran

    Sobhan Latifi

  2. Department of Computer Sciences, Shahid Beheshti University, G.C. Tehran, Iran

    Kourosh Parand

  3. Department of Cognitive Modeling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, G.C. Tehran, Iran

    Kourosh Parand

  4. Department of Mathematics and Computer Science, Islamic Azad University, Bardaskan Branch, Bardaskan, Iran

    Mehdi Delkhosh

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  1. Sobhan Latifi
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  2. Kourosh Parand
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  3. Mehdi Delkhosh
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Correspondence to Mehdi Delkhosh.

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Latifi, S., Parand, K. & Delkhosh, M. Generalized Lagrange–Jacobi–Gauss–Radau collocation method for solving a nonlinear optimal control problem with the classical diffusion equation. Eur. Phys. J. Plus 135, 834 (2020). https://doi.org/10.1140/epjp/s13360-020-00847-1

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