Towards Computing Suboptimal Controls in a Zero-Sum Linear-Quadratic Differential Game: Artificial Parameter Approach

17 pages•Published: December 11, 2024

Abstract

We consider a zero-sum finite horizon linear-quadratic differential game. Suboptimal state-feedback controls of the players in this game are derived. This derivation is based on the approximate solution (with a novel error’s estimate) of the corresponding Riccati matrix differential equation by the method of artificial parameter. The theoretical results are illustrated by the approximate solution of the problem of pursuit-evasion engagement between two flying vehicles.

Keyphrases: finite horizon linear quadratic game, method of auxiliary parameter, pursuit evasion engagement, riccati matrix differential equation, suboptimal state feedback control, zero sum differential game

In: Varvara L Turova, Andrey E Kovtanyuk and Johannes Zimmer (editors). Proceedings of 3rd International Workshop on Mathematical Modeling and Scientific Computing, vol 104, pages 295-311.

Links:	https://easychair.org/publications/paper/hl9C
	https://doi.org/10.29007/tzmt

BibTeX entry

@inproceedings{MMSC2024:Towards_Computing_Suboptimal_Controls,
  author    = {Vladimir Turetsky and Valery Glizer},
  title     = {Towards Computing Suboptimal Controls in a Zero-Sum Linear-Quadratic Differential Game: Artificial Parameter Approach},
  booktitle = {Proceedings of  3rd International Workshop on Mathematical Modeling and Scientific Computing},
  editor    = {Varvara L Turova and Andrey E Kovtanyuk and Johannes Zimmer},
  series    = {EPiC Series in Computing},
  volume    = {104},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/hl9C},
  doi       = {10.29007/tzmt},
  pages     = {295-311},
  year      = {2024}}

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