An optimal control problem associated with Lorentz group SO(3; 1)
by Archana Tiwari; K.C. Pati
International Journal of Modelling, Identification and Control (IJMIC), Vol. 40, No. 3, 2022

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.

Online publication date: Thu, 25-Aug-2022

The full text of this article is only available to individual subscribers or to users at subscribing institutions.

 
Existing subscribers:
Go to Inderscience Online Journals to access the Full Text of this article.

Pay per view:
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.

Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Modelling, Identification and Control (IJMIC):
Login with your Inderscience username and password:

Username:        Password:          Forgotten your password?

Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.

If you still need assistance, please email subs@inderscience.com