Euler-Poincaré reduction of externally forced rigid body motion

Rafał Wiśniewski; Piotr Kulczycki

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We classify the left-invariant control affine systems evolving on the orthogonal group $S O (4)$ . The equivalence relation under consideration is detached feedback equivalence. Each possible number of inputs is considered; both the homogeneous and inhomogeneous systems are covered. A complete list of class representatives is identified and controllability of each representative system is determined.

Symmetries of control systems

Alexey Samokhin (1996)

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Simplified multitime maximum principle.

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Lech Górniewicz, Paolo Nistri (1996)

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This paper deals with a class of nonlinear control systems in $R^{n}$ in presence of deterministic uncertainty. The uncertainty is modelled by a multivalued map F with nonempty, closed, convex values. Given a nonempty closed set $K \subset R^{n}$ from a suitable class, which includes the convex sets, we solve the problem of finding a state feedback ū(t,x) in such a way that K is invariant under any system dynamics f. As a system dynamics we consider any continuous selection of the uncertain controlled dynamics...