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Penalty boundary sequential convex programming algorithm for non-convex optimal control problems.

Zhe Zhang1, Gumin Jin1, Jianxun Li1

  • 1Department of Automation, School of Electronic Information and Electric Engineering, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai, China.

ISA Transactions
|October 25, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces a new penalty boundary sequential convex programming algorithm to solve complex nonlinear optimal control problems. The method handles infeasible starting points and improves convergence for trajectory planning.

Keywords:
Globally convergenceInfeasible initial pointNon-convex optimal controlPenalty boundary sequential convex programmingTrajectory planning

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Area of Science:

  • Optimization
  • Control Theory
  • Robotics

Background:

  • Nonlinear optimal control problems with non-convex elements are challenging.
  • Previous methods require feasible initial solutions for convergence.
  • Infeasible initial points hinder the application of convex programming techniques.

Purpose of the Study:

  • To develop a robust algorithm for nonlinear optimal control problems with non-convexities.
  • To address the issue of infeasible initial solutions in trajectory planning.
  • To improve the convergence and efficiency of solving complex control problems.

Main Methods:

  • Introduced slack variables to manage infeasible initial points.
  • Incorporated a penalty term for slack variables in the cost function.
  • Utilized a novel approximation point on constraint boundaries in each iteration.
  • Proposed a penalty boundary sequential convex programming algorithm.

Main Results:

  • The proposed algorithm demonstrates global convergence to a Karush-Kuhn-Tucker (KKT) point.
  • The method effectively handles non-convex cost functions and state constraints.
  • Simulations involving single UAV and multi-robot trajectory planning validate the algorithm's effectiveness.

Conclusions:

  • The penalty boundary sequential convex programming algorithm offers a robust solution for nonlinear optimal control.
  • The approach overcomes limitations of previous methods by handling infeasible initial points.
  • The algorithm is validated for practical applications in trajectory optimization for autonomous systems.