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In the traditional maneuvering problem, the objective has been to solve a geometric task and a dynamic task, where the former is to converge to and follow a 1-dimensional manifold, a path, in the output space of the system, and the latter is to satisfy a desired dynamic behavior along the path. In this paper the objective is to generalize this problem statement, by rather stabilizing more general...
We investigate stability of a class of singularly perturbed systems whose slow system is a set-valued average defined via an appropriate averaging procedure of the solutions of the continuous-time boundary layer system. An approximate hybrid system consisting of this average, the projection of the jump map in the direction of the slow states and flow and jump sets from the original dynamics is shown...
Singular perturbation results for a class of hybrid systems are presented. It is assumed that the fast states are restricted to a compact set and that the continuous-time boundary layer dynamics generate a well defined average vector field for the slow dynamics. This average is used to define an appropriate reduced hybrid dynamical system. Assuming forward pre-completeness for the reduced hybrid system...
The unit quaternion is a pervasive representation of rigid-body attitude used for the design and analysis of feedback control laws. Quaternion-based feedback control laws that are inconsistent (i.e. do not have a unique value for a given attitude) require an additional mechanism that lifts a continuous attitude trajectory to the unit quaternion space. Lifting mechanisms that are memoryless, for example,...
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