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
TLDR
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.Abstract:
This paper develops a calculus for computing Filippov's differential inclusion which simplifies the analysis of dynamical systems described by differential equations with a discontinuous right-hand side. In particular, when a slightly generalized Lyapunov theory is used, the rigorous stability analysis of variable structure systems is routine. As an example, a variable structure control law for rigid-link robot manipulators is described and its stability is proved.read more
Citations
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Journal ArticleDOI
Variable structure control: a survey
John Y. Hung,W. Gao,J.C. Hung +2 more
TL;DR: A tutorial account of variable structure control with sliding mode is presented, introducing in a concise manner the fundamental theory, main results, and practical applications of this powerful control system design approach.
Journal ArticleDOI
Variable structure control of nonlinear multivariable systems: a tutorial
TL;DR: In this paper, the design of variable-structure control (VSC) systems for a class of multivariable, nonlinear, time-varying systems is presented.
Journal ArticleDOI
Flocking in Fixed and Switching Networks
TL;DR: In this article, the stability properties of a group of mobile agents that align their velocity vectors, and stabilize their inter-agent distances, using decentralized, nearest-neighbor interaction rules, exchanging information over networks that change arbitrarily (no dwell time between consecutive switches).
Journal ArticleDOI
Discontinuous dynamical systems
TL;DR: In this paper, the authors present an introductory tutorial on discontinuous dynamical systems, and present non-smooth stability tools to characterize the asymptotic behavior of solutions.
Journal ArticleDOI
Lyapunov stability theory of nonsmooth systems
D. Shevitz,Brad Paden +1 more
TL;DR: This paper develops nonsmooth Lyapunov stability theory and LaSalle's invariance principle and Computable tests based on Filipov's differential inclusion and Clarke's generalized gradient are derived in analyzing the stability of equilibria of differential equations with discontinuous right-hand side.
References
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Optimization and nonsmooth analysis
TL;DR: 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.
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Differential Equations with Discontinuous Righthand Sides
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.
Journal ArticleDOI
Variable structure systems with sliding modes
TL;DR: Design and analysis forVariable structure systems are surveyed in this paper and it is shown that advantageous properties result from changing structures according to this switching logic.
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Sliding Modes and their Application in Variable Structure Systems
TL;DR: An electric dynamically operated storage element comprises two energy stores and circuitry is provided for applying periodically repeating phase clock pulses simultaneously to the energy stores through the charging circuits.