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A Lyapunov analysis of accelerated methods in optimization
J. Mach. Learn. Res., 2021Summary: Accelerated optimization methods, such as Nesterov's accelerated gradient method, play a significant role in optimization. Several accelerated methods are provably optimal under standard oracle models. Such optimality results are obtained using a technique known as ``estimate sequences,'' which yields upper bounds on convergence properties ...
Ashia C. Wilson +2 more
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Lyapunov Optimal Saturated Control for Nonlinear Systems
Journal of Guidance, Control, and Dynamics, 1997A generalized feedback control law design methodology is presented that applies to systems under control saturation constraints. Lyapunov stability theory is used to develop stable saturated control laws that can be augmentedtoanyunsaturatedcontrollawthattransitionscontinuouslyatatouchpointonthesaturationboundary.
Robinett, Rush D. +3 more
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Optimal neural network for solution of Lyapunov equation
Proceedings of ICNN'95 - International Conference on Neural Networks, 2002An efficient scheme, using N(N+1)/2 linear neurons, is suggested for solving the Lyapunov equation of order N. It is found that the proposed scheme is computationally superior, and offers faster convergence in comparision to an existing structured network.
P. K. Meher, S. K. Pradhan
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Optimization Approach to the Estimation and Control of Lyapunov Exponents
Journal of Optimization Theory and Applications, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pardalos, P. M., Yatsenko, V. A.
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A Lyapunov Function for Economic Optimizing Model Predictive Control
IEEE Transactions on Automatic Control, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Diehl, Moritz +2 more
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Lyapunov controllability and global optimal control
1986 25th IEEE Conference on Decision and Control, 1986Certain problems in nonlinear optimal control where we are required to steer the state away from attracting sets are related to global Lyapunov functions for the uncontrolled dynamics. In particular. the optimal cost as a function of terminal point, starting from an attracting set turns out to be a Lyapunov function.
Efthimios Kappos, Shankar Sastry
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APL: Adaptive Preloading of Short Video with Lyapunov Optimization
2020 IEEE International Conference on Visual Communications and Image Processing (VCIP), 2020Short video applications, like TikTok, have attracted many users across the world. It can feed short videos based on users' preferences and allow users to slide the boring content anywhere and anytime. To reduce the loading time and keep playback smoothness, most of the short video apps will preload the recommended short videos in advance.
Haodan Zhang +7 more
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Optimal Lyapunov-based states transfer for superconducting qubits
2016 IEEE International Conference on Information and Automation (ICIA), 2016Quantum control is responsible for many key problems in quantum information processing, such as decoherence suppression, quantum state engineering and quantum gate, etc. In recent years quantum control has become a major topic in the fields of quantum optics and quantum information.
Yinghua Ji, Jianhua Huang, Juju Hu
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Lyapunov Optimal Feedback Control of a Nonlinear Inverted Pendulum
Journal of Dynamic Systems, Measurement, and Control, 1989Lyapunov optimal feedback control is applied to a nonlinear inverted pendulum in which the control torque was constrained to be less than the nonlinear gravity torque in the model. This necessitates a control algorithm which “rocks” the pendulum out of its potential wells, in order to stabilize it at a unique vertical position.
Anderson, M. J., Grantham, Walter J.
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Optimal Lyapunov metrics of expansive homeomorphisms
Izvestiya: Mathematics, 2006We sharpen the following results of Reddy, Sakai and Fried: any expansive homeomorphism of a metrizable compactum admits a Lyapunov metric compatible with the topology, and if we also assume the existence of a local product structure (that is, if the homeomorphism is an A-homeomorphism in the terminology of Alekseev and Yakobson, or possesses ...
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