A fast sampling method for estimating the domain of attraction
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In this paper, a sampling approach is proposed to estimate the domain of attraction (DoA) of nonlinear systems in real time, which is validated to approximate the DoAs of stable equilibria.Abstract:
Most stabilizing controllers designed for nonlinear systems are valid only within a specific region of the state space, called the domain of attraction (DoA). Computation of the DoA is usually costly and time-consuming. This paper proposes a computationally effective sampling approach to estimate the DoAs of nonlinear systems in real time. This method is validated to approximate the DoAs of stable equilibria in several nonlinear systems. In addition, it is implemented for the passivity-based learning controller designed for a second-order dynamical system. Simulation and experimental results show that, in all cases studied, the proposed sampling technique quickly estimates the DoAs, corroborating its suitability for real-time applications.read more
Citations
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The size of the sync basin revisited.
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Automated-Sampling-Based Stability Verification and DOA Estimation for Nonlinear Systems
TL;DR: A sampling-based method for stability verification of piecewise continuous nonlinear systems via Lyapunov functions that extends the validity of LyAPunov's inequality to an infinite, bounded set of states by automatically exploiting local continuity properties.
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Estimation of the regions of attraction for autonomous nonlinear systems
Guoqiang Yuan,Yinghui Li +1 more
TL;DR: The methodology proposed in this paper can compute the region of attraction to achieve any desired accuracy in a dimensionally independent and efficient way.
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The Size of the Sync Basin Revisited
TL;DR: The equal-frequency Kuramoto model on a cycle is considered and it is found that the basin volumes scale as (1-4q/n)n, contrasting with the Gaussian behavior postulated in the study by Wiley et al.
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Robot Contact Language for Manipulation Planning
TL;DR: A contact-based language for robotic manipulation and planning, based on the contact between a collection of objects, robots, and surfaces, is proposed, which considers making and breaking contact as the bridge between high-level planning and low-level controllers.
References
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Pattern Recognition and Machine Learning
TL;DR: Probability Distributions, linear models for Regression, Linear Models for Classification, Neural Networks, Graphical Models, Mixture Models and EM, Sampling Methods, Continuous Latent Variables, Sequential Data are studied.
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Pattern Recognition and Machine Learning
TL;DR: This book covers a broad range of topics for regular factorial designs and presents all of the material in very mathematical fashion and will surely become an invaluable resource for researchers and graduate students doing research in the design of factorial experiments.
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Computation of piecewise quadratic Lyapunov functions for hybrid systems
Mikael Johansson,Anders Rantzer +1 more
TL;DR: The search for a piecewise quadratic Lyapunov function is formulated as a convex optimization problem in terms of linear matrix inequalities and the relation to frequency domain methods such as the circle and Popov criteria is explained.
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Computation of Piecewise Quadratic Lyapunov Functions for Hybrid Systems
Mikael Johansson,Anders Rantzer +1 more
TL;DR: In this paper, the search for a piecewise quadratic Lyapunov function is formulated as a convex optimization problem in terms of linear matrix inequalities, and the relation to frequency domain methods such as the circle and Popov criteria is explained.
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On the estimation of asymptotic stability regions: State of the art and new proposals
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