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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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Distributed Coordinated Tracking With Reduced Interaction via a Variable Structure Approach
Yongcan Cao,Wei Ren +1 more
TL;DR: A distributed coordinated tracking problem is solved via a variable structure approach when there exists a dynamic virtual leader who is a neighbor of only a subset of a group of followers, all followers have only local interaction, and only partial measurements of the states of the virtual leader and the followers are available.
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Finite-time and fixed-time stabilization
TL;DR: New nonlinear control laws are designed for robust stabilization of a chain of integrators using Implicit Lyapunov Functions for finite-time and fixed-time stability analysis of nonlinear systems.
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Lagrange multipliers and optimality
TL;DR: Lagrange multipliers are now being seen as arising from a general rule for the subdifferentiation of a nonsmooth objective function which allows black-and-white constraints to be replaced by penalty expressions.
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Lyapunov conditions for input-to-state stability of impulsive systems
TL;DR: A set of Lyapunov-based sufficient conditions for establishing input-to-state stability (ISS) and integral-ISS for impulsive systems, i.e., dynamical systems that evolve according to ordinary differential equations most of the time, but occasionally exhibit discontinuities.
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The computation of visible-surface representations
TL;DR: A well-posed variational formulation results from the use of a controlled-continuity surface model, and Finite-element shape primitives yield a local discretization of the variational principle, which is an efficient algorithm for visible-surface reconstruction.