Hyperbolic Tangent Smoothing

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A smoothing technique that approximates discontinuous bang-off-bang control inputs using a hyperbolic tangent function. In fuel-optimal control, the engine throttle theoretically switches discontinuously between 0 and 1, causing numerical difficulties. HTS introduces a smoothing parameter rho and replaces the step discontinuity with a continuous tanh function, making the Hamiltonian BVP solvable. As rho approaches zero, the smoothed solution converges to the original discontinuous optimal control.

Application Value

This term has significant practical applications in cislunar mission planning and execution.

  • Hidden-Genes Genetic Algorithm, HGGA
  • Variable-Size Design Space, VSDS
  • Station-Keeping
  • Target Point Method

References

  • Singh et al., 2021
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Contributors: ouyangjiahong, Ou Yang Jiahong