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Dynamic mode decomposition (DMD) is a leading tool for equation-free analysis of high-dimensional dynamical systems from observations. In this work, we focus on a combination of delay-coordinates embedding and DMD, i.e., delay-coordinates…
In this paper we address the question how the control of delayed measured chaotic systems can be improved. Both unmodified OGY control and difference control can be successfully applied only for a certain range of Lyapunov numbers depending…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
We examine the Detrended Fluctuation Analysis (DFA), which is a well-established method for the detection of long-range correlations in time series. We show that deviations from scaling that appear at small time scales become stronger in…
We propose a hybrid approach to temporal anomaly detection in access data of users to databases --- or more generally, any kind of subject-object co-occurrence data. We consider a high-dimensional setting that also requires fast computation…
This paper studies detectability for switched linear differential-algebraic equations (DAEs) and its application to the synthesis of observers, which generate asymptotically converging state estimates. Equating detectability to asymptotic…
The ability to collect and analyze large amounts of data is a growing problem within the scientific community. The growing gap between data and users calls for innovative tools that address the challenges faced by big data volume, velocity…
In the context of filtering chaotic dynamical systems it is well-known that partial observations, if sufficiently informative, can be used to control the inherent uncertainty due to chaos. The purpose of this paper is to investigate, both…
In this paper we present an approach in which synchronization of chaos is used to address identification problems. In particular, we are able to identify: (i) the discontinuity points of systems described by piecewise dynamical equations…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
Analysis of the systems involving delay is a popular topic among applied scientists. In the present work, we analyze the generalized equation $D^{\alpha} x(t) = g\left(x(t-\tau_1), x(t-\tau_2)\right)$ involving two delays viz. $\tau_1\geq…
Repetitive operations are widely conducted by automatic machines in industry. Periodic disturbances induced by the repetitive operations must be compensated to achieve precise functioning. In this paper, a periodic-disturbance observer…
We introduce the map representation of a time-delayed system in the presence of delay time modulation. Based on this representation, we find the method by which to analyze the stability of that kind of a system. We apply this method to a…
In this note, we propose a novel approach for a class of autonomous dynamical systems that allows, given some observations of the solutions, to identify its parameters and reconstruct the state vector. This approach relies on proving the…
This paper presents a dynamic state observer design for discrete-time linear time-varying systems that robustly achieves equalized recovery despite delayed or missing observations, where the set of all temporal patterns for the missing or…
Systems with time-delayed chaotic dynamics are common in nature, from control theory to aeronautical propulsion. The overarching objective of this paper is to compute the stability properties of a chaotic dynamical system, which is…
Psychological research often focuses on examining group differences in a set of numeric variables for which normality is doubtful. Longitudinal studies enable the investigation of developmental trends. For instance, a recent study…
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…
Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have…
This paper studies the problem of designing sampled-data observers and observer-based, sampled-data, output feedback stabilizers for systems with both discrete and distributed, state and output time-delays. The obtained results can be…