两篇关于“相对论遇到控制论”的 note：

[1] Relativistic Control: Feedback Control of Relativistic Dynamics

https://arxiv.org/abs/1912.03367

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 further discussions on, e.g., controllability, state feedback and output feedback, as well as PID control, in the relativistic setting.

[2] Relativistic Rocket Control (Relativistic Space-Travel Flight Control): Feedback Control of Relativistic Dynamics Propelled by Ejecting Mass

https://arxiv.org/abs/2101.00957

In this short note, we investigate the feedback control of relativistic dynamics propelled by mass ejection, modeling, e.g., the relativistic rocket control or the relativistic (space-travel) flight control. As an extreme case, we also examine the control of relativistic photon rockets which are propelled by ejecting photons.

简要总结：

Briefly speaking, [1] is on the feedback control of relativistic dynamics propelled by an external force, whereas the mass of the dynamical system does not vary over time. Meanwhile, [2] is on the feedback control of relativistic dynamics propelled by ejecting mass.

另外可参考 Relativistic Flight Mechanics and Space Travel 一书：

http://blog.sciencenet.cn/blog-286797-1265919.html