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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
Asymptotic Stability and Smooth Lyapunov Functions
TL;DR: In this article, it was shown that the existence of a smooth Lyapunov function is a necessary condition for weakly asymptotically stable differential inclusions, which is an extension to the context of Brockett's celebrated covering condition from continuous feedback stabilization theory.
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Brief paper: Distributed nonlinear control algorithms for network consensus
Qing Hui,Wassim M. Haddad +1 more
TL;DR: A thermodynamic framework for addressing consensus problems for nonlinear multiagent dynamical systems with fixed and switching topologies is developed and distributed nonlinear static and dynamic controller architectures for multiagent coordination are presented.
Posted Content
Clarke subgradients of stratifiable functions
TL;DR: In this paper, it was shown that if the graph of a nonsmooth real-extended-valued function is closed and admits a Whitney stratification, then the norm of the gradient of the function at the vertices of the graph is a function of the stratum containing the minimum norm of Clarke subgradients.
Proceedings ArticleDOI
Lyapunov stability theory of nonsmooth systems
D. Shevitz,Brad Paden +1 more
TL;DR: In this paper, the authors developed nonsmooth Lyapunov stability theory and LaSalle invariance principle for a class of Lipschitz continuous LyAPunov functions and absolutely continuous state trajectories, based on Filippov's differential inclusion and Clarke's generalized gradient.
Journal ArticleDOI
Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks
TL;DR: It is shown by theoretic proof that the estimation bound of the settling time given in this paper is less conservative and more accurate compared with the classical results.