A Control-Theoretic Approach to the Derivations of Electromagnetic Field Equations

摘要

In this paper, the particle's dynamics in an electromagnetic field and Maxwell's equations are derived based on the optimal control theory. There is no doubt that the Maxwell's electromagnetic equations are basic in the modern information and communication technologies. They are given by a set of four partial differential equations (see (18) below) that, together with the Lorentz force law, describe how electric and magnetic fields are generated by charges and currents. Although it is said that Maxwell's equations (which were first formulated by him in 1873) are the mathematical distillation of decades of experimental observations of the electric and magnetic effects of charges and currents, they can be derived from the classical mechanics via the principle of least action (or the calculus of variations) by applying it to the action integral expressed by using electromagnetic tensors. For instance, see the famous textbook by Landau and Lifshitz.