Title: An optimal control problem associated with Lorentz group SO(3; 1)

Authors: Archana Tiwari; K.C. Pati

Addresses: Department of Mathematics, National Institute of Technology, Rourkela, Odisha, 769008, India ' Department of Mathematics, National Institute of Technology, Rourkela, Odisha, 769008, India

Abstract: Lorentz group is the group of transformations of spatial and time coordinates associated with special theory of relativity. It is both a group and admits a topological description as a smooth manifold. Hence, Lorentz group can act as a configuration manifold of control systems. This opens up the scope to study the controllability and optimal control problems of control systems on Lorentz group. Here, a left invariant, driftless control system is defined on the group. An optimal control problem is formulated with an objective to minimise the cost function and satisfy the given dynamical constraints. Stability of the system around equilibrium points is studied. Two unconventional numerical integrators, Kahan's and Lie-Trotter integrator and conventional Runge-Kutta integrator, are implemented to study the system dynamics and their corresponding trajectories are shown.

Keywords: Lorentz group; control system; optimal control; stability.

DOI: 10.1504/IJMIC.2022.125066

International Journal of Modelling, Identification and Control, 2022 Vol.40 No.3, pp.271 - 278

Received: 13 Aug 2021
Accepted: 14 Oct 2021
Published online: 25 Aug 2022 *

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