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This paper presents a new robust data-driven predictive control scheme for unknown linear time-invariant systems by using input-state-output or input-output data based on whether the state is measurable. To remove the need for the…

Systems and Control · Electrical Eng. & Systems 2024-01-17 Kaijian Hu , Tao Liu

From the beginning of chaos research until today, the unpredictability of chaos has been a central theme. It is widely believed and claimed by philosophers, mathematicians and physicists alike that chaos has a new implication for…

Chaotic Dynamics · Physics 2013-10-08 Charlotte Werndl

We study the implementation of a weak multiple delayed feedback for controlling coherence of chaotic oscillations. The specific system we treat is the Lorenz system with classical set of parameters. There are two reasons behind the interest…

Statistical Mechanics · Physics 2009-12-03 Denis S. Goldobin , Elizaveta V. Shklyaeva

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

Chaotic Dynamics · Physics 2025-10-06 Chenyu Dong , Davide Faranda , Adriano Gualandi , Valerio Lucarini , Gianmarco Mengaldo

This paper explores the theoretical limits of using discrete abstractions for nonlinear control synthesis. More specifically, we consider the problem of deciding continuous-time control with temporal logic specifications. We prove that…

Systems and Control · Computer Science 2019-03-18 Jun Liu

We propose an uncertainty principle for chaos, focusing on two key characteristics: alpha unpredictability and Lorenz sensitivity. This principle outlines a limitation on the relationship between two infinite sequences that underpin these…

Chaotic Dynamics · Physics 2025-05-01 Marat Akhmet

Chaos presents complex dynamics arising from nonlinearity and a sensitivity to initial states. These characteristics suggest a depth of expressivity that underscores their potential for advanced computational applications. However,…

Neural and Evolutionary Computing · Computer Science 2024-06-06 Shuhong Liu , Nozomi Akashi , Qingyao Huang , Yasuo Kuniyoshi , Kohei Nakajima

A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the physical processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have…

Machine Learning · Computer Science 2018-05-09 Jaideep Pathak , Alexander Wikner , Rebeckah Fussell , Sarthak Chandra , Brian Hunt , Michelle Girvan , Edward Ott

This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state…

Machine Learning · Computer Science 2020-05-28 David K. E. Green , Filip Rindler

Understanding the interplay of order and disorder in chaotic systems is a central challenge in modern quantitative science. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work…

Dynamical Systems · Mathematics 2017-07-05 Steven L. Brunton , Bingni W. Brunton , Joshua L. Proctor , Eurika Kaiser , J. Nathan Kutz

In this paper, based on real-time nonlinear receding horizon control methodology, a novel approach is developed for parameter estimation of time invariant and time varying nonlinear dynamical systems in chaotic environments. Here, the…

Optimization and Control · Mathematics 2016-11-21 Fei Sun , Kamran Turkoglu

This work investigates the challenge of ensuring safety guarantees in the presence of uncontrollable agents, whose behaviors are stochastic and depend on both their own and the system's states. We present a neural model predictive control…

Systems and Control · Electrical Eng. & Systems 2026-04-21 Shuqi Wang , Mingyang Feng , Yu Chen , Yue Gao , Xiang Yin

Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data. Here we show that learning from noise-free observations in such systems can be achieved up…

Chaotic Dynamics · Physics 2025-07-15 Christof Schötz , Niklas Boers

The design of reliable indicators to anticipate critical transitions in complex systems is an im portant task in order to detect a coming sudden regime shift and to take action in order to either prevent it or mitigate its consequences. We…

Data Analysis, Statistics and Probability · Physics 2022-12-14 Martin Heßler , Oliver Kamps

The dynamics of the tubular chemical reactor with mass recycle were examined. In such a system, temperature and concentrations may oscillate chaotically. This means that state variable values are then unpredictable. In this paper it has…

Dynamical Systems · Mathematics 2026-02-10 Marek Berezowski

Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by Random Matrix Theory (RMT). We propose and develop a complementary version of this conjecture: quantum…

High Energy Physics - Theory · Physics 2023-12-08 Vijay Balasubramanian , Javier M. Magan , Qingyue Wu

The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to…

Quantum Physics · Physics 2008-02-03 B. Kaulakys

Non-deterministic chaos is a form of low-dimensional dynamics which is characterized by the existence of a countable set of {\em sensitive decision points} (SDP's). Away from these points, the dynamics is well-behaved. Near these points,…

chao-dyn · Physics 2008-02-03 D. D. Dixon

Causal discovery from time series is a fundamental task in machine learning. However, its widespread adoption is hindered by a reliance on untestable causal assumptions and by the lack of robustness-oriented evaluation in existing…

Machine Learning · Computer Science 2026-05-01 Huiyang Yi , Xiaojian Shen , Yonggang Wu , Duxin Chen , He Wang , Wenwu Yu

Although deterministic chaos has been predicted to occur in the triply resonant optical parametric oscillator (TROPO) fifteen years ago, experimental evidence of chaotic behavior in this system has been lacking so far, in marked contrast…

Chaotic Dynamics · Physics 2009-11-10 Axelle Amon , Marc Lefranc