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Iterative Chebyshev approximation method for optimal control problems.

Di Wu1, Changjun Yu1, Hailing Wang1

  • 1Department of Mathematics, Shanghai University, Shanghai 200444, China.

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|June 26, 2024
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Summary
This summary is machine-generated.

A new numerical method solves nonlinear constrained optimal control problems by linearizing constraints and using Chebyshev polynomials for high-precision approximation. This approach reduces approximation errors compared to existing methods.

Keywords:
Chebyshev polynomialsGlobal convergenceLinearizationNonlinear optimal control problems

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Area of Science:

  • Numerical Analysis
  • Control Theory

Background:

  • Nonlinear constrained optimal control problems (NCOCPs) are complex to solve directly.
  • Conventional collocation methods can introduce errors at non-collocation points.

Purpose of the Study:

  • To develop a novel numerical approach for solving NCOCPs with high precision.
  • To reduce approximation errors inherent in existing methods.

Main Methods:

  • Linearize constraints and dynamic systems to create sub-problems.
  • Employ Chebyshev polynomials to estimate state and control vectors.
  • Estimate coefficient functions using Chebyshev polynomials to eliminate non-collocation errors.

Main Results:

  • The proposed method transforms sub-problems into nonlinear optimization problems with linear equality constraints.
  • Achieved lower approximation error compared to the Chebyshev pseudo-spectral method.
  • Demonstrated efficacy through three example problems.

Conclusions:

  • The novel method offers a high-precision approximation for NCOCPs.
  • Suitable for applications demanding accuracy, like aerospace and precision manufacturing.