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We investigate single-input mechanical control systems where the Lagrangian is the kinetic energy associated with a Riemannian metric. It is demonstrated that such a system is locally configuration controllable only if the dimension of the configuration manifold is one.
Open problems in controllability and stabilisability of analytic systems are discussed. In particular, questions like, “Can controllability and/or stabilisability be tested by solving algebraic equations?” and, “What is the relationship between controllability from a state and stabilisability to the same state?” are discussed. A main idea is a rethinking of how one might examine stabilisability by...
In this letter we present a decomposition for control systems whose drift vector field is the geodesic spray associated with an affine connection. With the geometric insight attained with this decomposition, we are able to easily prove some special results for this class of control systems. Examples illustrate the theory.
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