Enhancing the Legendre-Gauss-Radau pseudospectral method with sigmoid-based control parameterization for solving bang-bang optimal control problems

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Samadi Fereshteh

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Journal Paper

Paper Information

Journal: Computational Methods for Differential Equations Year:2025 | Volume:13 | Issue:3 Page(s): 802-814

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Information Journal Paper

Title

Enhancing the Legendre-Gauss-Radau pseudospectral method with sigmoid-based control parameterization for solving bang-bang optimal control problems

Author(s)

Samadi Fereshteh | Issue Writer Certificate

Keywords

Bang-bang optimal control problems

Legendre-Gauss-Radau pseudospectral methods

Sigmoid function

Abstract

In Bang-bang optimal control problems, the control function is inherently piecewise constant. This feature creates substantial difficulties for the standard Legendre-Gauss-Radau pseudospectral method, which relies on polynomial approximation for the control function. This study introduces a simplified approach that seamlessly integrates sigmoid-based control parameterization with the traditional Legendre-Gauss-Radau pseudospectral method. This integration enables precise approximation of discontinuous control profiles while maintaining the polynomial approximation for state variables. The proposed method significantly minimizes the number of decision variables in the optimization problem while precisely determining both the number and locations of switching points. This leads to notable enhancements in computational efficiency and solution accuracy. Numerical experiments conducted on two benchmark problems, a bridge crane system and a robotic arm control problem, demonstrate the exceptional precision and efficiency of the proposed method. Despite its simplicity, the method delivers results that are on par with those produced by more advanced and intricate techniques.

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