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A symplectic pseudospectral method for nonlinear optimal control problems with inequality constraints.

Xinwei Wang1, Haijun Peng1, Sheng Zhang1

  • 1Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial, Equipment, Dalian University of Technology, Dalian, Liaoning 116024, China.

ISA Transactions
|March 21, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces a novel symplectic pseudospectral method to solve complex nonlinear optimal control problems with inequality constraints. The method efficiently transforms and solves these problems, demonstrating high accuracy and efficiency.

Keywords:
inequality constraintslinear complementary problemnonlinear optimal controlparametric variational principlequasilinearization

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Area of Science:

  • Computational mathematics
  • Optimal control theory

Background:

  • Nonlinear optimal control problems (NOCPs) with inequality constraints are challenging to solve.
  • Existing methods often struggle with accuracy and efficiency for complex constraints.

Purpose of the Study:

  • To develop a novel symplectic pseudospectral method for solving NOCPs with inequality constraints.
  • To enhance the accuracy and efficiency of solving these complex control problems.

Main Methods:

  • Quasilinearization technique to convert NOCPs into a series of linear-quadratic optimal control problems.
  • Symplectic pseudospectral method utilizing a dual variational principle.
  • Transformation of inequality constraints into equality constraints using parametric variables.
  • Interpolation of variables at Legendre-Gauss-Lobatto points.
  • Conversion to a standard linear complementary problem for easy solution.

Main Results:

  • The proposed method successfully solves nonlinear optimal control problems with inequality constraints.
  • Numerical examples confirm the method's high accuracy.
  • The method demonstrates significant efficiency in solving these problems.

Conclusions:

  • The developed symplectic pseudospectral method offers an accurate and efficient approach for NOCPs with inequality constraints.
  • The integration of quasilinearization and dual variational principles is effective.
  • This method provides a valuable tool for researchers and engineers in optimal control.