A conservation law expresses the physical property that some quantity of a physical system's model is invariant under a transformation (e.g. time translation for the energy conservation law) [21]. On the other hand, a conservation law is derived from a mathematical property, called a variational symmetry [14]. The conservation laws of some system of partial differential equations are widely used in science and engineering. In control theory, port-representations [10], [1] are originally based on a conservative system, a Hamiltonian system. One of them, a field port-Lagrangian system [6], [8] can describe a conservation law. We studied a boundary observer for detecting the variational symmetry breaking by the field port-Lagrangian representation [7].
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