Relativistic Control: Feedback Control of Relativistic Dynamics

TL;DR

This paper explores the design of feedback control laws for relativistic dynamics, accounting for the nonlinear effects introduced by high velocities close to the speed of light, and extends classical control methods to this relativistic regime.

Contribution

It introduces a novel approach to control relativistic systems using feedback linearization, adapting classical control techniques to nonlinear relativistic dynamics.

Findings

Developed a state-space representation for relativistic dynamics.

Proposed a feedback linearization method tailored for relativistic systems.

Discussed controllability and control strategies like PID in the relativistic context.

Abstract

Strictly speaking, Newton's second law of motion is only an approximation of the so-called relativistic dynamics, i.e., Einstein's modification of the second law based on his theory of special relativity. Although the approximation is almost exact when the velocity of the dynamical system is far less than the speed of light, the difference will become larger and larger (and will eventually go to infinity) as the velocity approaches the speed of light. Correspondingly, feedback control of such dynamics should also take this modification into consideration (though it will render the system nonlinear), especially when the velocity is relatively large. Towards this end, we start this note by studying the state-space representation of the relativistic dynamics. We then investigate on how to employ the feedback linearization approach for such relativistic dynamics, based upon which an additional linear controller may then be designed. As such, the feedback linearization together with the linear controller compose the overall relativistic feedback control law. We also provide discussions on, e.g., controllability, state feedback and output feedback, as well as PID control, in the relativistic setting.