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A high-speed method for computing reachable sets based on variable-size grid.

Wei Liao1, Ming Tang2, Yu Zhang1

  • 1Advanced Manufacturing School, Nanchang University, Nanchang 330031, China; Jiangxi Key Laboratory of Intelligent Robot, Nanchang University, Nanchang 330031, China.

ISA Transactions
|November 26, 2024
PubMed
Summary
This summary is machine-generated.

This study enhances dynamic programming for reachable set computation using variable-sized grids. The improved method significantly reduces computation time while preserving accuracy for complex systems.

Keywords:
Dynamic programmingFunction approximationGrid sizeReachable set

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Area of Science:

  • Control Theory
  • Computational Mathematics

Background:

  • Dynamic programming is crucial for computing reachable sets in control systems.
  • Existing methods using constant-sized grids face computational challenges and accuracy limitations.

Purpose of the Study:

  • To improve the efficiency and accuracy of dynamic programming-based reachable set computation.
  • To introduce a novel method utilizing variable-sized grids for cost-to-go function approximation.

Main Methods:

  • The proposed method represents reachable sets as sublevel sets of a discount cost-to-go function.
  • A three-step approach is employed: rough computation on a coarse grid, upsampling for a fine grid, and fine-tuning for accurate approximation.
  • This dynamic programming approach leverages interpolation functions for efficient computation.

Main Results:

  • The use of variable-sized grids significantly reduces computational time compared to constant-sized grids.
  • The method maintains or improves the accuracy of reachable set computation.
  • Theoretical correctness is proven, and effectiveness is demonstrated through examples.

Conclusions:

  • The variable-sized grid approach offers a more efficient and accurate alternative for reachable set computation.
  • This method advances dynamic programming applications in control theory and related fields.
  • The findings have implications for real-time control system design and analysis.