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simmediumaerialmetric · varies
On Controller Design for Systems on Manifolds in Euclidean Space
Description
A new method is developed to design controllers in Euclidean space for systems defined on manifolds. The idea is to embed the state-space manifold $M$ of a given control system into some Euclidean space $\mathbb R^n$, extend the system from $M$ to the ambient space $\mathbb R^n$, and modify it outside $M$ to add transversal stability to $M$ in the final dynamics in $\mathbb R^n$. Controllers are designed for the final system in the ambient space $\mathbb R^n$. Then, their restriction to $M$ prod