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1. Identification of Self-Excited Systems Using Discrete-Time, Time-Delayed Lur’e Models

   Paredes, Juan; Bernstein, Dennis S. (May 2021, Proceedings of the American Control Conference)

   null (Ed.)

   This paper considers system identification for systems whose output is asymptotically periodic under constant inputs. The model used for system identification is a discretetime Lur’e model consisting of asymptotically stable linear dynamics, a time delay, a washout filter, and a static nonlinear feedback mapping. For sufficiently large scaling of the loop transfer function, these components cause divergence under small signal levels and decay under large signal amplitudes, thus producing an asymptotically oscillatory output. A leastsquares technique is used to estimate the coefficients of the linear model as well as the parameters of a piecewise-linear approximation of the feedback mapping. 

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2. Global forecasts in reservoir computers

   https://doi.org/10.1063/5.0181694  

   Harding, S; Leishman, Q; Lunceford, W; Passey, D J; Pool, T; Webb, B (February 2024, Chaos: An Interdisciplinary Journal of Nonlinear Science)

   A reservoir computer is a machine learning model that can be used to predict the future state(s) of time-dependent processes, e.g., dynamical systems. In practice, data in the form of an input-signal are fed into the reservoir. The trained reservoir is then used to predict the future state of this signal. We develop a new method for not only predicting the future dynamics of the input-signal but also the future dynamics starting at an arbitrary initial condition of a system. The systems we consider are the Lorenz, Rossler, and Thomas systems restricted to their attractors. This method, which creates a global forecast, still uses only a single input-signal to train the reservoir but breaks the signal into many smaller windowed signals. We examine how well this windowed method is able to forecast the dynamics of a system starting at an arbitrary point on a system’s attractor and compare this to the standard method without windows. We find that the standard method has almost no ability to forecast anything but the original input-signal while the windowed method can capture the dynamics starting at most points on an attractor with significant accuracy. 

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3. Sparse signal recovery from modulo observations

   https://doi.org/10.1186/s13634-021-00722-w  

   Shah, Viraj; Hegde, Chinmay (December 2021, EURASIP Journal on Advances in Signal Processing)

   Abstract We consider the problem of reconstructing a signal from under-determined modulo observations (or measurements). This observation model is inspired by a relatively new imaging mechanism called modulo imaging, which can be used to extend the dynamic range of imaging systems; variations of this model have also been studied under the category of phase unwrapping. Signal reconstruction in the under-determined regime with modulo observations is a challenging ill-posed problem, and existing reconstruction methods cannot be used directly. In this paper, we propose a novel approach to solving the signal recovery problem under sparsity constraints for the special case to modulo folding limited to two periods. We show that given a sufficient number of measurements, our algorithm perfectly recovers the underlying signal. We also provide experiments validating our approach on toy signal and image data and demonstrate its promising performance. 

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4. Data‐enabled extremum seeking: A cooperative concurrent learning‐based approach

   https://doi.org/10.1002/acs.3189  

   Poveda, Jorge I.; Benosman, Mouhacine; Vamvoudakis, Kyriakos G. (October 2020, International Journal of Adaptive Control and Signal Processing)

   Summary This paper introduces a new class of feedback‐based data‐driven extremum seeking algorithms for the solution of model‐free optimization problems in smooth continuous‐time dynamical systems. The novelty of the algorithms lies on the incorporation of memory to store recorded data that enables the use of information‐rich datasets during the optimization process, and allows to dispense with the time‐varying dither excitation signal needed by standard extremum seeking algorithms that rely on a persistence of excitation (PE) condition. The model‐free optimization dynamics are developed for single‐agent systems, as well as for multi‐agent systems with communication graphs that allow agents to share their state information while preserving the privacy of their individual data. In both cases, sufficient richness conditions on the recorded data, as well as suitable optimization dynamics modeled by ordinary differential equations are characterized in order to guarantee convergence to a neighborhood of the solution of the extremum seeking problems. The performance of the algorithms is illustrated via different numerical examples in the context of source‐seeking problems in multivehicle systems. 

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5. Enhancing Optical Network Emulation (ONE) with Fast Gaussian Noise Modeling of Nonlinear Interference

   https://doi.org/10.1109/ICTON67126.2025.11125290  

   Latha, Aparaajitha Gomathinayakam; Ridwanur_Rahim, Muhammad; Hui, Ron; Tacca, Marco; Fumagalli, Andrea (July 2025, IEEE)

   The Optical Network Emulation (ONE) engine is a real-time, multi-container software platform designed to model and emulate open optical transport networks with realistic fidelity. This paper introduces an enhanced version of the ONE engine that integrates a distributed implementation of a Gaussian Noise (GN) model for estimating nonlinear interference (NLI) in wavelength division multiplexing (WDM) systems. The inclusion of the GN model enables more realistic emulation of nonlinear signal degradation across diverse link configurations and operating conditions. The enhanced ONE package is then used to document the model’s impact on system performance under varying transmission conditions, including signal launched power and increased spectral loading. With this upgrade, the ONE engine expands its utility for research, development, and education, providing a scalable and flexible environment for testing physical-layer impairments and control strategies in software-defined optical networks. 

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