Non-Linear-Quadratic Optimal Control Problem for a Unicycle: Maximin Solution

Gleb Merkulov, Vladimir Turetsky, Tal Shima

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A finite-horizon optimal control problem for a nonlinear unicycle with constant linear velocity is considered. The cost functional consists of the squared norm of a final position and the integral penalty term for the control effort, i.e., both the miss distance and the control are soft-constrained. A finite horizon formulation arises, for instance, in coordinated guidance attack against a stationary target, in which all interceptors have to arrive at the target at the same time. The soft constraint on terminal position allows for tradeoff between the miss distance and control effort. Semi-analytical solution is derived by representing the squared norm as a maximum of a quadratic form and by changing the order of maximization and minimization. The inner minimization problem becomes a problem of calculus of variations, which Euler-Lagrange equation writes as a nonlinear pendulum equation. Based on the solution of this equation, a numerical scheme for constructing the suboptimal control is developed. As a by-product of the approach, the posterior control bounds are obtained.

Original languageEnglish
Title of host publication2024 UKACC 14th International Conference on Control, CONTROL 2024
Pages287-292
Number of pages6
ISBN (Electronic)9798350374261
DOIs
StatePublished - 2024
Event14th UKACC International Conference on Control, CONTROL 2024 - Winchester, United Kingdom
Duration: 10 Apr 202412 Apr 2024

Publication series

Name2024 UKACC 14th International Conference on Control, CONTROL 2024

Conference

Conference14th UKACC International Conference on Control, CONTROL 2024
Country/TerritoryUnited Kingdom
CityWinchester
Period10/04/2412/04/24

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Energy Engineering and Power Technology
  • Control and Systems Engineering
  • Renewable Energy, Sustainability and the Environment

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