Relativistic Control: Feedback Control of Relativistic Dynamics
This work addresses control challenges in high-velocity systems, such as aerospace or particle physics, but is incremental as it applies existing control methods to relativistic dynamics.
The paper tackles the problem of feedback control for relativistic dynamics, which becomes nonlinear as velocities approach the speed of light, by developing a feedback linearization approach combined with a linear controller to design an overall relativistic feedback control law.
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.