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Optimization and nonsmooth analysis
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TLDR
The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.Abstract:
1. Introduction and Preview 2. Generalized Gradients 3. Differential Inclusions 4. The Calculus of Variations 5. Optimal Control 6. Mathematical Programming 7. Topics in Analysis.read more
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Journal ArticleDOI
A calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulators
Brad Paden,S. Shankar Sastry +1 more
TL;DR: A calculus for computing Filippov's differential inclusion is developed which simplifies the analysis of dynamical systems described by differential equations with a discontinuous right-hand side and the rigorous stability analysis of variable structure systems is routine.
Journal ArticleDOI
Input-output stability properties of networked control systems
Dragan Nesic,Andrew R. Teel +1 more
TL;DR: The results provide a unifying framework for generating new scheduling protocols that preserve L/sub p/ stability properties of the system if a design parameter is chosen sufficiently small.
Journal ArticleDOI
Rigid-Body Dynamics with Friction and Impact
TL;DR: This paper presents rigorous results about rigid-body dynamics with Coulomb friction and impulses, which have come from several sources: "sweeping processes" and the measure differential inclusions of Moreau in the 1970s and 1980s, the variational inequality approaches of Duvaut and J.-L.
Input-Output Stability Properties of Networked Control Systems D. Neÿ ´, Senior Member, IEEE, and A. R. Teel, Fellow, IEEE
TL;DR: In this paper, the authors provide a unifying framework for generating new scheduling protocols that preserve stability properties of the system if a design parameter is chosen suffi- ciently small.
Proceedings ArticleDOI
Gossip algorithms: design, analysis and applications
TL;DR: This work analyzes the averaging problem under the gossip constraint for arbitrary network, and finds that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly stochastic matrix characterizing the algorithm.