The Experts below are selected from a list of 62853 Experts worldwide ranked by ideXlab platform
Miroslav Krstic - One of the best experts on this subject based on the ideXlab platform.
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delay robustness of Linear Predictor feedback without restriction on delay rate
2013Co-Authors: Iasson Karafyllis, Miroslav KrsticAbstract:Robustness is established for the Predictor feedback for Linear time-invariant systems with respect to possibly time-varying perturbations of the input delay, with a constant nominal delay. The prior results have addressed qualitatively constant delay perturbations (robustness of stability in L^2 norm of actuator state) and delay perturbations with restricted rate of change (robustness of stability in H^1 norm of actuator state). The present work provides simple formulas that allow direct and accurate computation of the least upper bound of the magnitude of the delay perturbation for which the exponential stability in supremum norm on the actuator state is preserved. While the prior work has employed Lyapunov-Krasovskii functionals constructed via backstepping, the present work employs a particular form of small-gain analysis. Two cases are considered: the case of measurable (possibly discontinuous) time-varying perturbations and the case of constant perturbations.
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delay robustness of Linear Predictor feedback without restriction on delay rate
2012Co-Authors: Iasson Karafyllis, Miroslav KrsticAbstract:Robustness is established for the Predictor feedback for Linear time-invariant systems with respect to possibly time-varying perturbations of the input delay, with a constant nominal delay. Prior results have addressed qualitatively constant delay perturbations (robustness of stability in L2 norm of actuator state) and delay perturbations with restricted rate of change (robustness of stability in H1 norm of actuator state). The present work provides simple formulae that allow direct and accurate computation of the least upper bound of the magnitude of the delay perturbation for which exponential stability in supremum norm on the actuator state is preserved. While prior work has employed Lyapunov-Krasovskii functionals constructed via backstepping, the present work employs a particular form of small-gain analysis. Two cases are considered: the case of measurable (possibly discontinuous) perturbations and the case of constant perturbations.
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lyapunov stability of Linear Predictor feedback for distributed input delays
2010Co-Authors: Nikolaos Bekiarisliberis, Miroslav KrsticAbstract:For multi-input, Linear time-invariant systems with distributed input delays, Artstein's reduction method provides a Predictor-based controller. In this paper, we construct a Lyapunov functional for the resulting closed-loop system and establish exponential stability. The key element in our work is the introduction of an infinite-dimensional forwarding-backstepping transformation of the infinite-dimensional actuator states. We illustrate the construction of the Lyapunov functional with a detailed example of a single-input system, in which the input is entering through two individual channels with different delays. Finally, we develop an observer equivalent to the Predictor feedback design, for the case of distributed sensor delays and prove exponential convergence of the estimation error.
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Lyapunov Stability of Linear Predictor Feedback for Time-Varying Input Delay
2010Co-Authors: Miroslav KrsticAbstract:For Linear time-invariant systems with a time-varying input delay, an explicit formula for Predictor feedback was presented by Nihtila in 1991. In this note we construct a time-varying Lyapunov functional for the closed-loop system and establish exponential stability. The key challenge is the selection of a state for a transport partial differential equation, which has a non-constant propagation speed, and which is the basis of the stability analysis. We illustrate the design and its conditions with several examples. We also develop an observer equivalent of the Predictor feedback design, for the case of time-varying sensor delay.
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lyapunov stability of Linear Predictor feedback for time varying input delay
2009Co-Authors: Miroslav KrsticAbstract:For LTI systems with a time-varying input delay, an explicit formula for Predictor feedback was presented by Nihtila in 1991. In this note we construct a time-varying Lyapunov functional for the closed-loop system and establish exponential stability. The key challenge is the selection of a state for a transport PDE, which has a non-constant propagation speed, and which is the basis of the stability analysis. We illustrate the design and its conditions with several examples. We also develop an observer equivalent of the Predictor feedback design, for the case of time-varying sensor delay.
Robert Shorten - One of the best experts on this subject based on the ideXlab platform.
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an lmi condition for the robustness of constant delay Linear Predictor feedback with respect to uncertain time varying input delays
2019Co-Authors: Hugo Lhachemi, Christophe Prieur, Robert ShortenAbstract:Abstract This paper discusses the robustness of the constant-delay Predictor feedback in the case of an uncertain time-varying input delay. Specifically, we study the stability of the closed-loop system when the Predictor feedback is designed based on the knowledge of the nominal value of the time-varying delay. By resorting to an adequate Lyapunov–Krasovskii functional, we derive an LMI-based sufficient condition ensuring the exponential stability of the closed-loop system for small enough variations of the time-varying delay around its nominal value. These results are extended to the feedback stabilization of a class of diagonal infinite-dimensional boundary control systems in the presence of a time-varying delay in the boundary control input.
Ping Peng - One of the best experts on this subject based on the ideXlab platform.
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all admissible Linear Predictors in the finite populations with respect to inequality constraints under a balanced loss function
2015Co-Authors: Ping Peng, Guikai Hu, Jian LiangAbstract:Under a balanced loss function, we investigate the admissible Linear Predictors of finite population regression coefficient in the inequality constrained superpopulation models with and without the assumption that the underlying distribution is normal. In Model I (non-normal case) with parameter space T1, the relation between admissible homogeneous Linear Predictors and admissible inhomogeneous Linear Predictors is characterized. Moreover, for Model I with parameter space T0, necessary and sufficient conditions for an inhomogeneous Linear prediction to be admissible in the class of inhomogeneous Linear Predictors are given. In Model II (normal case) with parameter space T0, necessary conditions for an inhomogeneous Linear Predictor to be admissible in the class of all Predictors are derived.
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Linear admissible prediction of finite population regression coefficient under a balanced loss function
2014Co-Authors: H U Guikai, Ping PengAbstract:In this paper, under a balanced loss function we investigate admissible prediction of finite population regression coefficient in superpopulation models with and without the assumption that the underlying distribution is normal, respectively. By using the statistical decision theory, necessary and sufficient conditions for a homogeneous Linear Predictor to be admissible in the class of homogeneous Linear Predictors are obtained in the non-normal case, we also obtain a sufficient and necessary condition for a homogeneous Linear Predictor to be admissible in the class of all Predictors in the normal case, which generalize some relative results under quadratic loss to balanced loss function.
Nathan Srebro - One of the best experts on this subject based on the ideXlab platform.
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Implicit Bias of Gradient Descent on Linear Convolutional Networks
2018Co-Authors: Suriya Gunasekar, Daniel Soudry, Nathan SrebroAbstract:We show that gradient descent on full-width Linear convolutional networks of depth $L$ converges to a Linear Predictor related to the $\ell_{2/L}$ bridge penalty in the frequency domain. This is in contrast to Linearly fully connected networks, where gradient descent converges to the hard margin Linear support vector machine solution, regardless of depth.
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implicit bias of gradient descent on Linear convolutional networks
2018Co-Authors: Suriya Gunasekar, Jason D. Lee, Daniel Soudry, Nathan SrebroAbstract:We show that gradient descent on full-width Linear convolutional networks of depth $L$ converges to a Linear Predictor related to the $\ell_{2/L}$ bridge penalty in the frequency domain. This is in contrast to Linearly fully connected networks, where gradient descent converges to the hard margin Linear SVM solution, regardless of depth.
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trading accuracy for sparsity in optimization problems with sparsity constraints
2010Co-Authors: Shai Shalevshwartz, Nathan Srebro, Tong ZhangAbstract:We study the problem of minimizing the expected loss of a Linear Predictor while constraining its sparsity, i.e., bounding the number of features used by the Predictor. While the resulting optimization problem is generally NP-hard, several approximation algorithms are considered. We analyze the performance of these algorithms, focusing on the characterization of the trade-off between accuracy and sparsity of the learned Predictor in different scenarios.
Anton Ponomarev - One of the best experts on this subject based on the ideXlab platform.
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reduction based robustness analysis of Linear Predictor feedback for distributed input delays
2016Co-Authors: Anton PonomarevAbstract:Lyapunov–Krasovskii approach is applied to parameter-robustness and delay-robustness analysis of the feedback suggested by Manitius and Olbrot for a Linear time-invariant system with distributed input delay. A functional is designed based on Artstein's system reduction technique. It depends on the norms of the reduction-transformed plant state and original actuator state. The functional is used to prove that the feedback is stabilizing when there is a slight mismatch in the system matrices and delay values between the plant and controller.
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reduction based robustness analysis of Linear Predictor feedback for distributed input delays
2015Co-Authors: Anton PonomarevAbstract:Lyapunov-Krasovskii approach is applied to parameter- and delay-robustness analysis of the feedback suggested by Manitius and Olbrot for a Linear time-invariant system with distributed input delay. A functional is designed based on Artstein's system reduction technique. It depends on the norms of the reduction-transformed plant state and original actuator state. The functional is used to prove that the feedback is stabilizing when there is a slight mismatch in the system matrices and delay values between the plant and controller.
