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We present a distributed nonlinear control law for synchronization of identical agents on one-parameter Lie subgroups. If the agents are initialized sufficiently close to one another, then synchronization is achieved exponentially fast. The proof does not use Jacobian linearization, instead the local nature of our result stems from our use of exponential coordinates on a matrix Lie group.
We study a local feedback equivalence problem for a nonlinear control-affine system with two nested, controlled invariant, embedded submanifolds in its state space. The main result of this paper gives necessary and sufficient conditions for (i) the dynamics of the system transversal to the larger submanifold to be linear and controllable and (ii) the system dynamics, restricted to the larger submanifold,...
This paper concerns the design of path following controllers for mechanical systems. Our method is to find a coordinate and feedback transformation that puts the mechanical system in a convenient form for path following control design. In this form, linear and controllable subsystems govern motions toward and along the path. We choose a particular “virtual output” to perform input-output feedback...
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