Related papers: Controlling Transient Chaos in the Lorenz System w…
Transient chaos is a characteristic behavior in nonlinear dynamics where trajectories in a certain region of phase space behave chaotically for a while, before escaping to an external attractor. In some situations the escapes are highly…
The study of chaos has long relied on computationally intensive methods to quantify unpredictability and design control strategies. Recent advances in machine learning, from convolutional neural networks to transformer architectures,…
Partial control is a technique used in systems with transient chaos. The aim of this control method is to avoid the escape of the orbits from a region Q of the phase space where the transient chaotic dynamics takes place. This technique is…
In dealing with nonlinear systems, it is common to use numerical solutions. Unlike the careful behavior towards the numerical results in chaotic regions, the validity of numerical results in regions of transient chaos might not always be…
Transient stability and critical clearing time (CCT) are important concepts in power system protection and control. This paper explores and compares various learning-based methods for predicting CCT under uncertainties arising from…
In this work we deal with the H\'enon and the Lozi map for a choice of parameters where they show transient chaos. Orbits close to the chaotic saddle behave chaotically for a while to eventually escape to an external attractor.…
We present here a new approach of the partial control method, which is a useful control technique applied to transient chaotic dynamics affected by a bounded noise. Usually we want to avoid the escape of these chaotic transients outside a…
We introduce transfer learning for nonlinear dynamics, which enables efficient predictions of chaotic dynamics by utilizing a small amount of data. For the Lorenz chaos, by optimizing the transfer rate, we accomplish more accurate inference…
In this work, inspired in the symbolic dynamic of chaotic systems and using machine learning techniques, a control strategy for complex systems is designed. Unlike the usual methodologies based on modeling, where the control signal is…
Power systems, including synchronous generator systems, are typical systems that strive for stable operation. In this article, we numerically study the fault transient process of a synchronous generator system based on the first benchmark…
Online identification of post-contingency transient stability is essential in power system control, as it facilitates the grid operator to decide and coordinate system failure correction control actions. Utilizing machine learning methods…
Chaotic behavior in dynamical systems poses a significant challenge in trajectory control, traditionally relying on computationally intensive physical models. We present a machine learning-based algorithm to compute the minimum control…
Using the predictor-corrector scheme, the fractional order diffusionless Lorenz system is investigated numerically. The effective chaotic range of the fractional order diffusionless system for variation of the single control parameter is…
Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…
We propose a neural network model with transient chaos, or a transiently chaotic neural network (TCNN) as an approximation method for combinatorial optimization problem, by introducing transiently chaotic dynamics into neural networks.…
We demonstrate that chaos can be controlled using a multiplicative exponential feedback control. All three types of unstable orbits - unstable fixed points, limit cycles and chaotic trajectories can be stabilized using this control. The…
The spatiotemporal chaos in the Frenkel-Kontorova (FK) model is studied. A model-free reinforcement learning algorithm is proposed to the design of a controller. There is no need for explicit knowledge on system, target states and unstable…
In this paper, a nonlinear system aiming at reducing the signal transmission rate in a networked control system is constructed by adding nonlinear constraints to a linear feedback control system. Its stability is investigated in detail. It…
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…
This chapter offers a principled approach to the prediction of chaotic systems from data. First, we introduce some concepts from dynamical systems' theory and chaos theory. Second, we introduce machine learning approaches for…