522 results on '"Sepulchre P"'
Search Results
2. Excitable crawling
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Arbelaiz, Juncal, Franci, Alessio, Leonard, Naomi Ehrich, Sepulchre, Rodolphe, and Bamieh, Bassam
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Electrical Engineering and Systems Science - Systems and Control ,Computer Science - Robotics - Abstract
We propose and analyze the suitability of a spiking controller to engineer the locomotion of a soft robotic crawler. Inspired by the FitzHugh-Nagumo model of neural excitability, we design a bistable controller with an electrical flipflop circuit representation capable of generating spikes on-demand when coupled to the passive crawler mechanics. A proprioceptive sensory signal from the crawler mechanics turns bistability of the controller into a rhythmic spiking. The output voltage, in turn, activates the crawler's actuators to generate movement through peristaltic waves. We show through geometric analysis that this control strategy achieves endogenous crawling. The electro-mechanical sensorimotor interconnection provides embodied negative feedback regulation, facilitating locomotion. Dimensional analysis provides insights on the characteristic scales in the crawler's mechanical and electrical dynamics, and how they determine the crawling gait. Adaptive control of the electrical scales to optimally match the mechanical scales can be envisioned to achieve further efficiency, as in homeostatic regulation of neuronal circuits. Our approach can scale up to multiple sensorimotor loops inspired by biological central pattern generators., Comment: 5 pages, MTNS 2024 extended abstract
- Published
- 2024
3. A Large-Scale Simulation Method for Neuromorphic Circuits
- Author
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Shahhosseini, Amir, Chaffey, Thomas, and Sepulchre, Rodolphe
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Electrical Engineering and Systems Science - Systems and Control - Abstract
Splitting algorithms are well-established in convex optimization and are designed to solve large-scale problems. Using such algorithms to simulate the behavior of nonlinear circuit networks provides scalable methods for the simulation and design of neuromorphic systems. For circuits made of linear capacitors and inductors with nonlinear resistive elements, we propose a splitting that breaks the network into its LTI lossless component and its static resistive component. This splitting has both physical and algorithmic advantages and allows for separate calculations in the time domain and in the frequency domain. To demonstrate the scalability of this approach, a network made from one hundred neurons modeled by the well-known FitzHugh-Nagumo circuit with all-to-all diffusive coupling is simulated., Comment: Submitted to CDC 2024
- Published
- 2024
4. A birdcage resonant antenna for helicon wave generation in TORPEX
- Author
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Vincent, Simon, Guittienne, Philippe, Quigley, Patrick, Sepulchre, Cyrille, Jacquier, Rémy, Bertizzolo, Robert, Baquero-Ruiz, Marcelo, Howling, Alan A., and Furno, Ivo
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Physics - Plasma Physics - Abstract
A birdcage resonant helicon antenna is designed, mounted and tested in the toroidal device TORPEX. The birdcage resonant antenna is an alternative to the usual Boswell or half-helical antenna designs commonly used for $\sim$ 10 cm diameter helicon sources in low temperature plasma devices. The main advantage of the birdcage antenna lies in its resonant nature, which makes it easily operational even at large scales, an appealing feature for the TORPEX device whose poloidal cross section is 40 cm in diameter. With this antenna helicon waves are shown to be launched and sustained throughout the whole torus of TORPEX. The helicon waves can be launched at low power on a pre-existing magnetron-generated plasma with little effect on the density profiles. The birdcage antenna can also be used alone to produce plasma, which removes the constraint of a narrow range of applied magnetic fields required by the magnetron, opening the way to a new range of studies on TORPEX with the external magnetic field as a control parameter.
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- 2024
5. Neuromorphic Control of a Pendulum
- Author
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Schmetterling, Raphael, Forni, Fulvio, Franci, Alessio, and Sepulchre, Rodolphe
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Electrical Engineering and Systems Science - Systems and Control - Abstract
We illustrate the potential of neuromorphic control on the simple mechanical model of a pendulum, with both event-based actuation and sensing. The controller and the pendulum are regarded as event-based systems that occasionally interact to coordinate their respective rhythms. Control occurs through a proper timing of the interacting events. We illustrate the mixed nature of the control design: the design of a rhythmic automaton, able to generate the right sequence of events, and the design of a feedback regulator, able to tune the timing of events., Comment: 6 pages, 10 figures. Accepted by IEEE Control Systems Letters
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- 2024
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6. Kernel Modelling of Fading Memory Systems
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Huo, Yongkang, Chaffey, Thomas, and Sepulchre, Rodolphe
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Electrical Engineering and Systems Science - Systems and Control ,Mathematics - Optimization and Control - Abstract
The paper introduces a kernel-based framework to model and identify time-invariant systems with the fading memory property. The key departure from the previous literature is to bypass the state-space representation of the model. Instead, a kernel representation is used to directly model the memory functional that maps past inputs to the present output. We explore the versatility of this approach to encode important system properties in the hyperparameters of the kernel. The approach is illustrated on the Hodgkin and Huxley model of neuronal excitability.
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- 2024
7. Relaxation systems and cyclic monotonicity
- Author
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Chaffey, Thomas, van Waarde, Henk J., and Sepulchre, Rodolphe
- Subjects
Mathematics - Optimization and Control - Abstract
It is shown that an LTI system is a relaxation system if and only if its Hankel operator is cyclic monotone. Cyclic monotonicity of the Hankel operator implies the existence of a storage function whose gradient is the Hankel operator. This storage is a function of past inputs alone, is independent of the state space realization, and admits a generalization to nonlinear circuit elements., Comment: Accepted to the 2023 IEEE Conference on Decision and Control
- Published
- 2023
8. Robust online estimation of biophysical neural circuits
- Author
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Schmetterling, Raphael, Burghi, Thiago B., and Sepulchre, Rodolphe
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Electrical Engineering and Systems Science - Systems and Control ,Quantitative Biology - Neurons and Cognition - Abstract
The control of neuronal networks, whether biological or neuromorphic, relies on tools for estimating parameters in the presence of model uncertainty. In this work, we explore the robustness of adaptive observers for neuronal estimation. Inspired by biology, we show that decentralization and redundancy help recover the performance of a centralized recursive mean square algorithm in the presence of uncertainty and mismatch on the internal dynamics of the model., Comment: 6 pages, 5 figures, accepted at the 62nd IEEE Conference on Decision and Control
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- 2023
9. Differential geometry with extreme eigenvalues in the positive semidefinite cone
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Mostajeran, Cyrus, Da Costa, Nathaël, Van Goffrier, Graham, and Sepulchre, Rodolphe
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Mathematics - Differential Geometry ,Statistics - Computation ,Statistics - Machine Learning - Abstract
Differential geometric approaches to the analysis and processing of data in the form of symmetric positive definite (SPD) matrices have had notable successful applications to numerous fields including computer vision, medical imaging, and machine learning. The dominant geometric paradigm for such applications has consisted of a few Riemannian geometries associated with spectral computations that are costly at high scale and in high dimensions. We present a route to a scalable geometric framework for the analysis and processing of SPD-valued data based on the efficient computation of extreme generalized eigenvalues through the Hilbert and Thompson geometries of the semidefinite cone. We explore a particular geodesic space structure based on Thompson geometry in detail and establish several properties associated with this structure. Furthermore, we define a novel iterative mean of SPD matrices based on this geometry and prove its existence and uniqueness for a given finite collection of points. Finally, we state and prove a number of desirable properties that are satisfied by this mean.
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- 2023
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10. Constitutional mismatch repair deficiency mimicking Lynch syndrome is associated with hypomorphic mismatch repair gene variants
- Author
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Gallon, Richard, Brekelmans, Carlijn, Martin, Marie, Bours, Vincent, Schamschula, Esther, Amberger, Albert, Muleris, Martine, Colas, Chrystelle, Dekervel, Jeroen, De Hertogh, Gert, Coupier, Jérôme, Colleye, Orphal, Sepulchre, Edith, Burn, John, Brems, Hilde, Legius, Eric, and Wimmer, Katharina
- Published
- 2024
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11. Constitutional mismatch repair deficiency mimicking Lynch syndrome is associated with hypomorphic mismatch repair gene variants
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Richard Gallon, Carlijn Brekelmans, Marie Martin, Vincent Bours, Esther Schamschula, Albert Amberger, Martine Muleris, Chrystelle Colas, Jeroen Dekervel, Gert De Hertogh, Jérôme Coupier, Orphal Colleye, Edith Sepulchre, John Burn, Hilde Brems, Eric Legius, and Katharina Wimmer
- Subjects
Neoplasms. Tumors. Oncology. Including cancer and carcinogens ,RC254-282 - Abstract
Abstract Lynch syndrome (LS) and constitutional mismatch repair deficiency (CMMRD) are distinct cancer syndromes caused, respectively, by mono- and bi-allelic germline mismatch repair (MMR) variants. LS predisposes to mainly gastrointestinal and genitourinary cancers in adulthood. CMMRD predisposes to brain, haematological, and LS-spectrum cancers from childhood. Two suspected LS patients with first cancer diagnosis aged 27 or 38 years were found to be homozygous for an MMR (likely) pathogenic variant, MSH6 c.3226C>T (p.(Arg1076Cys)), or variant of uncertain significance (VUS), MLH1 c.306G>A (p.(Glu102=)). MLH1 c.306G>A was shown to cause leaky exon 3 skipping. The apparent genotype-phenotype conflict was resolved by detection of constitutional microsatellite instability in both patients, a hallmark feature of CMMRD. A hypomorphic effect of these and other variants found in additional late onset CMMRD cases, identified by literature review, likely explains a LS-like phenotype. CMMRD testing in carriers of compound heterozygous or homozygous MMR VUS may find similar cases and novel hypomorphic variants. Individualised management of mono- and bi-allelic carriers of hypomorphic MMR variants is needed until we better characterise the associated phenotypes.
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- 2024
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12. Open-loop contraction design
- Author
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Lee, Jin Gyu, Burghi, Thiago B., and Sepulchre, Rodolphe
- Subjects
Electrical Engineering and Systems Science - Systems and Control - Abstract
Given a non-contracting trajectory of a nonlinear system, we consider the question of designing an input perturbation that makes the perturbed trajectory contracting. This paper stresses the analogy of this question with the classical question of feedback stabilization. In particular, it is shown that the existence of an output variable that ensures contraction of the inverse system facilitates the design of a contracting input perturbation. We illustrate the relevance of this question in parameter estimation., Comment: 7 pages, 6 figures
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- 2022
13. Loop Shaping with Scaled Relative Graphs
- Author
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Chaffey, Thomas, Forni, Fulvio, and Sepulchre, Rodolphe
- Subjects
Electrical Engineering and Systems Science - Systems and Control ,93D25, 93C10, 93C80, 47H05 - Abstract
The Scaled Relative Graph (SRG) is a generalization of the Nyquist diagram that may be plotted for nonlinear operators, and allows nonlinear robustness margins to be defined graphically. This abstract explores techniques for shaping the SRG of an operator in order to maximize these robustness margins., Comment: To be presented at MTNS 2022
- Published
- 2022
14. On the incremental form of dissipativity
- Author
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Sepulchre, Rodolphe, Chaffey, Thomas, and Forni, Fulvio
- Subjects
Electrical Engineering and Systems Science - Systems and Control ,Mathematics - Optimization and Control ,93D25 - Abstract
Following the seminal work of Zames, the input-output theory of the 70s acknowledged that incremental properties (e.g. incremental gain) are the relevant quantities to study in nonlinear feedback system analysis. Yet, non-incremental analysis has dominated the use of dissipativity theory in nonlinear control from the 80s. Results connecting dissipativity theory and incremental analysis are scattered and progress has been limited. This abstract investigates whether this theoretical gap is of fundamental nature and considers new avenues to circumvent it., Comment: To be presented at MTNS 2022
- Published
- 2022
15. Splitting algorithms and circuit analysis
- Author
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Chaffey, Thomas, Das, Amritam, and Sepulchre, Rodolphe
- Subjects
Mathematics - Optimization and Control ,Electrical Engineering and Systems Science - Systems and Control ,93C10, 47H05, 47N70 - Abstract
The splitting algorithms of monotone operator theory find zeros of sums of relations. This corresponds to solving series or parallel one-port electrical circuits, or the negative feedback interconnection of two subsystems. One-port circuits with series and parallel interconnections, or block diagrams with multiple forward and return paths, give rise to current-voltage relations consisting of nested sums and inverses. In this extended abstract, we present new splitting algorithms specially suited to these structures, for interconnections of monotone and anti-monotone relations., Comment: To be presented at MTNS 2022
- Published
- 2022
16. Rapid and robust synchronization via weak synaptic coupling Extended arXiv version
- Author
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Lee, Jin Gyu and Sepulchre, Rodolphe
- Subjects
Electrical Engineering and Systems Science - Systems and Control - Abstract
This paper examines how weak synaptic coupling can achieve rapid synchronization in heterogeneous networks. The assumptions aim at capturing the key mathematical properties that make this possible for biophysical networks. In particular, the combination of nodal excitability and synaptic coupling are shown to be essential to the phenomenon., Comment: 20 pages, 3 figures
- Published
- 2022
17. Affine-Invariant Midrange Statistics
- Author
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Mostajeran, Cyrus, Grussler, Christian, and Sepulchre, Rodolphe
- Subjects
Mathematics - Optimization and Control ,Statistics - Computation - Abstract
We formulate and discuss the affine-invariant matrix midrange problem on the cone of $n\times n$ positive definite Hermitian matrices $\mathbb{P}(n)$, which is based on the Thompson metric. A particular computationally efficient midpoint of this metric is investigated as a highly scalable candidate for an average of two positive definite matrices within this context, before studying the $N$-point problem in the vector and matrix settings., Comment: arXiv admin note: substantial text overlap with arXiv:1907.04188
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- 2022
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18. Adaptive Conductance Control
- Author
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Schmetterling, Raphael, Burghi, Thiago, and Sepulchre, Rodolphe
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Electrical Engineering and Systems Science - Systems and Control ,Quantitative Biology - Neurons and Cognition - Abstract
Neuromodulation is central to the adaptation and robustness of animal nervous systems. This paper explores the classical paradigm of indirect adaptive control to design neuromodulatory controllers in conductance-based neuronal models. The adaptive control of maximal conductance parameters is shown to provide a methodology aligned with the central concepts of neuromodulation in physiology and of impedance control in robotics., Comment: 32 pages, 8 figures, submitted to IFAC Annual Reviews in Control
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- 2022
- Full Text
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19. Distributed online estimation of biophysical neural networks
- Author
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Burghi, Thiago B., O'Leary, Timothy, and Sepulchre, Rodolphe
- Subjects
Electrical Engineering and Systems Science - Systems and Control ,Quantitative Biology - Neurons and Cognition - Abstract
In this work, we propose a distributed adaptive observer for a class of nonlinear networked systems inspired by biophysical neural network models. Neural systems learn by adjusting intrinsic and synaptic weights in a distributed fashion, with neuronal membrane voltages carrying information from neighbouring neurons in the network. We show that this learning principle can be used to design an adaptive observer based on a decentralized learning rule that greatly reduces the number of observer states required for exponential convergence of parameter estimates. This novel design is relevant for biological, biomedical and neuromorphic applications., Comment: Submitted to Conference on Decision and Control (CDC) 2022
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- 2022
20. Reliability of Event Timing in Silicon Neurons
- Author
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Kirby, Tai Miyazaki, Ribar, Luka, and Sepulchre, Rodolphe
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Quantitative Biology - Neurons and Cognition ,Computer Science - Neural and Evolutionary Computing ,Electrical Engineering and Systems Science - Systems and Control - Abstract
Analog, low-voltage electronics show great promise in producing silicon neurons (SiNs) with unprecedented levels of energy efficiency. Yet, their inherently high susceptibility to process, voltage and temperature (PVT) variations, and noise has long been recognised as a major bottleneck in developing effective neuromorphic solutions. Inspired by spike transmission studies in biophysical, neocortical neurons, we demonstrate that the inherent noise and variability can coexist with reliable spike transmission in analog SiNs, similarly to biological neurons. We illustrate this property on a recent neuromorphic model of a bursting neuron by showcasing three different relevant types of reliable event transmission: single spike transmission, burst transmission, and the on-off control of a half-centre oscillator (HCO) network.
- Published
- 2021
21. Spiking Control Systems
- Author
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Sepulchre, Rodolphe
- Subjects
Electrical Engineering and Systems Science - Systems and Control - Abstract
Spikes and rhythms organize control and communication in the animal world, in contrast to the bits and clocks of digital technology. As continuous-time signals that can be counted, spikes have a mixed nature. This paper reviews ongoing efforts to develop a control theory of spiking systems. The central thesis is that the mixed nature of spiking results from a mixed feedback principle, and that a control theory of mixed feedback can be grounded in the operator theoretic concept of maximal monotonicity. As a nonlinear generalization of passivity, maximal monotonicity acknowledges at once the physics of electrical circuits, the algorithmic tractability of convex optimization, and the feedback control theory of incremental passivity. We discuss the relevance of a theory of spiking control systems in the emerging age of event-based technology.
- Published
- 2021
22. Training Lipschitz continuous operators using reproducing kernels
- Author
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van Waarde, Henk J. and Sepulchre, Rodolphe
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Mathematics - Optimization and Control - Abstract
This paper proposes that Lipschitz continuity is a natural outcome of regularized least squares in kernel-based learning. Lipschitz continuity is an important proxy for robustness of input-output operators. It is also instrumental for guaranteeing closed-loop stability of kernel-based controlllers through small incremental gain arguments. We introduce a new class of nonexpansive kernels that are shown to induce Hilbert spaces consisting of only Lipschitz continuous operators. The Lipschitz constant of estimated operators within such Hilbert spaces can be tuned by suitable selection of a regularization parameter. As is typical for kernel-based models, input-output operators are estimated from data by solving tractable systems of linear equations. The approach thus constitutes a promising alternative to Lipschitz-bounded neural networks, that have recently been investigated but are computationally expensive to train., Comment: arXiv admin note: substantial text overlap with arXiv:2110.11735
- Published
- 2021
23. Monotone one-port circuits
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Chaffey, Thomas and Sepulchre, Rodolphe
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Electrical Engineering and Systems Science - Systems and Control ,Mathematics - Optimization and Control ,93C10, 47H05, 47N70 - Abstract
Maximal monotonicity is explored as a generalization of the linear theory of passivity, aiming at an algorithmic input/output analysis of physical models. The theory is developed for maximal monotone one-port circuits, formed by the series and parallel interconnection of basic elements. These circuits generalize passive LTI transfer functions. Periodic input signals are shown to be mapped to periodic output signals, and these input-output behaviors can be efficiently computed using a maximal monotone splitting algorithm, which decomposes the computation according to the circuit topology. A new splitting algorithm is presented, which applies to any monotone one-port circuit defined as a port interconnection of monotone elements.
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- 2021
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24. Adaptive observers for biophysical neuronal circuits
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Burghi, Thiago B. and Sepulchre, Rodolphe
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Electrical Engineering and Systems Science - Systems and Control ,Quantitative Biology - Neurons and Cognition - Abstract
This paper presents adaptive observers for online state and parameter estimation of a class of nonlinear systems motivated by biophysical models of neuronal circuits. We first present a linear-in-the-parameters design that solves a classical recursive least squares problem. Then, building on this simple design, we present an augmented adaptive observer for models with a nonlinearly parameterized internal dynamics, the parameters of which we interpret as structured uncertainty. We present a convergence and robustness analysis based on contraction theory, and illustrate the potential of the approach in neurophysiological applications by means of numerical simulations., Comment: 16 pages. The Julia code used in this paper can be found in https://github.com/thiagoburghi/online-learning
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- 2021
- Full Text
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25. Kernel-based models for system analysis
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van Waarde, Henk J. and Sepulchre, Rodolphe
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Mathematics - Optimization and Control ,Mathematics - Dynamical Systems - Abstract
This paper introduces a computational framework to identify nonlinear input-output operators that fit a set of system trajectories while satisfying incremental integral quadratic constraints. The data fitting algorithm is thus regularized by suitable input-output properties required for system analysis and control design. This biased identification problem is shown to admit the tractable solution of a regularized least squares problem when formulated in a suitable reproducing kernel Hilbert space. The kernel-based framework is a departure from the prevailing state-space framework. It is motivated by fundamental limitations of nonlinear state-space models at combining the fitting requirements of data-based modeling with the input-output requirements of system analysis and physical modeling., Comment: 16 pages
- Published
- 2021
26. Graphical Nonlinear System Analysis
- Author
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Chaffey, Thomas, Forni, Fulvio, and Sepulchre, Rodolphe
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Electrical Engineering and Systems Science - Systems and Control ,Mathematics - Optimization and Control ,93C10, 93C80, 47H05 - Abstract
We use the recently introduced concept of a Scaled Relative Graph (SRG) to develop a graphical analysis of input-output properties of feedback systems. The SRG of a nonlinear operator generalizes the Nyquist diagram of an LTI system. In the spirit of classical control theory, important robustness indicators of nonlinear feedback systems are measured as distances between SRGs., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible
- Published
- 2021
- Full Text
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27. A nested bistable module within a negative feedback loop ensures different types of oscillations in signaling systems
- Author
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Marrone, Juan Ignacio, Sepulchre, Jacques-Alexandre, and Ventura, Alejandra C.
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- 2023
- Full Text
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28. Oscillations in Mixed-Feedback Systems
- Author
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Das, Amritam, Chaffey, Thomas, and Sepulchre, Rodolphe
- Subjects
Electrical Engineering and Systems Science - Systems and Control - Abstract
A new method is presented for the analysis of limit cycle oscillations in mixed-feedback systems. The calculation of the limit cycle is reformulated as the zero finding of a mixed-monotone relation, that is, of the difference of two maximally monotone relations. The problem can then be solved efficiently by borrowing existing algorithms that minimize the difference of two convex functions. The potential of the method is illustrated on the classical Van der Pol oscillator.
- Published
- 2021
29. Scaled relative graphs for system analysis
- Author
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Chaffey, Thomas, Forni, Fulvio, and Sepulchre, Rodolphe
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Electrical Engineering and Systems Science - Systems and Control ,Mathematics - Optimization and Control ,93C10, 93C80, 47H05 - Abstract
Scaled relative graphs were recently introduced to analyze the convergence of optimization algorithms using two dimensional Euclidean geometry. In this paper, we connect scaled relative graphs to the classical theory of input/output systems. It is shown that the Nyquist diagram of an LTI system on $L_2$ is the convex hull of its scaled relative graph under a particular change of coordinates. The SRG may be used to visualize approximations of static nonlinearities such as the describing function and quadratic constraints, allowing system properties to be verified or disproved. Interconnections of systems correspond to graphical manipulations of their SRGs. This is used to provide a simple, graphical proof of the classical incremental passivity theorem., Comment: Accepted to the 2021 IEEE Conference on Decision and Control
- Published
- 2021
30. Target formation on the circle by monotone system design
- Author
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Mostajeran, Cyrus, Lee, Jin Gyu, Van Goffrier, Graham, and Sepulchre, Rodolphe
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Mathematics - Optimization and Control ,Mathematics - Dynamical Systems - Abstract
Positivity and Perron-Frobenius theory provide an elegant framework for the convergence analysis of linear consensus algorithms. Here we consider a generalization of these ideas to the analysis of nonlinear consensus algorithms on the circle and establish tools for the design of consensus protocols that monotonically converge to target formations on the circle.
- Published
- 2021
31. Digenic Inheritance of Mutations in Homologous Recombination Genes in Cancer Patients
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Maria Valeria Freire, Marie Martin, Karin Segers, Edith Sepulchre, Natacha Leroi, Jérôme Coupier, Hassan Rezaei Kalantari, Pascal Wolter, Joëlle Collignon, Marc Polus, Olivier Plomteux, Claire Josse, and Vincent Bours
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digenic inheritance ,double heterozygosity ,familial cancer ,BRCA1 ,BRCA2 ,ATM ,Medicine - Abstract
Background/Objectives: BRCA1, BRCA2, ATM, and CHEK2 are known cancer predisposition genes (CPGs), but tumor risk in patients with simultaneous pathogenic variants (PVs) in CPGs remains largely unknown. In this study, we describe six patients from five families with multiple cancers who coinherited a combination of PVs in these genes. Methods: PVs were identified using NGS DNA sequencing and were confirmed by Sanger. Results: Families 1, 2, and 3 presented PVs in BRCA2 and ATM, family 4 in BRCA2 and BRCA1, and family 5 in BRCA2 and CHEK2. PVs were identified using NGS DNA sequencing and were confirmed by Sanger. The first family included patients with kidney, prostate, and breast cancer, in addition to pancreatic adenocarcinomas. In the second family, a female had breast cancer, while a male from the third family had prostate, gastric, and pancreatic cancer. The fourth family included a male with pancreatic cancer, and the fifth family a female with breast cancer. Conclusions: The early age of diagnosis and the development of multiple cancers in the reported patients indicate a very high risk of cancer in double-heterozygous patients associated with PVs in HR-related CPGs. Therefore, in families with patients who differ from other family members in terms of phenotype, age of diagnosis, or type of cancer, the cascade testing needs to include the study of other CPGs.
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- 2024
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32. Monotone RLC Circuits
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Chaffey, Thomas and Sepulchre, Rodolphe
- Subjects
Electrical Engineering and Systems Science - Systems and Control ,Mathematics - Optimization and Control ,93C10, 47H05, 47N70 - Abstract
The circuit-theoretic origins of maximal monotonicity are revisited using modern optimization algorithms for maximal monotone operators. We present an algorithm for computing the periodic behavior of an interconnection of maximal monotone systems using a fixed point iteration. The fixed point iteration may be split according to the interconnection structure of the system. In this preliminary work, the approach is demonstrated on port interconnections of maximal monotone resistors and LTI capacitors and inductors., Comment: Accepted for presentation at the 2021 European Control Conference
- Published
- 2020
33. System identification of biophysical neuronal models
- Author
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Burghi, Thiago B., Schoukens, Maarten, and Sepulchre, Rodolphe
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Quantitative Biology - Neurons and Cognition ,Computer Science - Machine Learning ,Electrical Engineering and Systems Science - Systems and Control - Abstract
After sixty years of quantitative biophysical modeling of neurons, the identification of neuronal dynamics from input-output data remains a challenging problem, primarily due to the inherently nonlinear nature of excitable behaviors. By reformulating the problem in terms of the identification of an operator with fading memory, we explore a simple approach based on a parametrization given by a series interconnection of Generalized Orthonormal Basis Functions (GOBFs) and static Artificial Neural Networks. We show that GOBFs are particularly well-suited to tackle the identification problem, and provide a heuristic for selecting GOBF poles which addresses the ultra-sensitivity of neuronal behaviors. The method is illustrated on the identification of a bursting model from the crab stomatogastric ganglion., Comment: Slightly extended pre-print of the paper to be presented at the 59th Conference on Decision and Control, held remotely between December 14-18, 2020
- Published
- 2020
- Full Text
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34. Neuromorphic Control
- Author
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Ribar, Luka and Sepulchre, Rodolphe
- Subjects
Electrical Engineering and Systems Science - Systems and Control ,Computer Science - Neural and Evolutionary Computing ,Quantitative Biology - Neurons and Cognition - Abstract
Neuromorphic engineering is a rapidly developing field that aims to take inspiration from the biological organization of neural systems to develop novel technology for computing, sensing, and actuating. The unique properties of such systems call for new signal processing and control paradigms. The article introduces the mixed feedback organization of excitable neuronal systems, consisting of interlocked positive and negative feedback loops acting in distinct timescales. The principles of biological neuromodulation suggest a methodology for designing and controlling mixed-feedback systems neuromorphically. The proposed design consists of a parallel interconnection of elementary circuit elements that mirrors the organization of biological neurons and utilizes the hardware components of neuromorphic electronic circuits. The interconnection structure endows the neuromorphic systems with a simple control methodology that reframes the neuronal control as an input-output shaping problem. The potential of neuronal control is illustrated on elementary network examples that suggest the scalability of the mixed-feedback principles.
- Published
- 2020
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35. Balanced truncation of $k$-positive systems
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Grussler, Christian, Damm, Tobias, and Sepulchre, Rodolphe
- Subjects
Mathematics - Optimization and Control ,47A58, 93A15, 93A30 - Abstract
This paper considers balanced truncation of discrete-time Hankel $k$-positive systems, characterized by Hankel matrices whose minors up to order $k$ are nonnegative. Our main result shows that if the truncated system has order $k$ or less, then it is Hankel totally positive ($\infty$-positive), meaning that it is a sum of first order lags. This result can be understood as a bridge between two known results: the property that the first-order truncation of a positive system is positive ($k=1$), and the property that balanced truncation preserves state-space symmetry. It provides a broad class of systems where balanced truncation is guaranteed to result in a minimal internally positive system.
- Published
- 2020
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36. From biophysical to integrate-and-fire modelling
- Author
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Van Pottelbergh, Tomas, Drion, Guillaume, and Sepulchre, Rodolphe
- Subjects
Quantitative Biology - Neurons and Cognition - Abstract
This paper proposes a methodology to extract a low-dimensional integrate-and-fire model from an arbitrarily detailed single-compartment biophysical model. The method aims at relating the modulation of maximal conductance parameters in the biophysical model to the modulation of parameters in the proposed integrate-and-fire model. The approach is illustrated on two well-documented examples of cellular neuromodulation: the transition between Type I and Type II excitability and the transition between spiking and bursting., Comment: This is the authors' final version. The article has been accepted for publication in Neural Computation
- Published
- 2020
37. Variation diminishing linear time-invariant systems
- Author
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Grussler, Christian and Sepulchre, Rodolphe
- Subjects
Mathematics - Optimization and Control ,Mathematics - Statistics Theory ,93C05, 93C28 - Abstract
This paper studies the variation diminishing property of $k$-positive linear time-invariant (LTI) systems, which map inputs with $k-1$ sign changes to outputs with at most the same variation. We characterize this property for the Toeplitz and Hankel operators of finite-dimensional systems. Our main result is that these operators have a dominant approximation in the form of series or parallel interconnections of $k$ first order positive systems. This is shown by expressing the $k$-positivity of a LTI system as the external positivity (that is, $1$-positivity) of $k$ compound LTI systems. Our characterization generalizes well known properties of externally positive systems ($k=1$) and totally positive systems ($k=\infty$; also known as relaxation systems).
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- 2020
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38. Inductive Geometric Matrix Midranges
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Van Goffrier, Graham W., Mostajeran, Cyrus, and Sepulchre, Rodolphe
- Subjects
Computer Science - Machine Learning ,Mathematics - Optimization and Control ,Statistics - Machine Learning - Abstract
Covariance data as represented by symmetric positive definite (SPD) matrices are ubiquitous throughout technical study as efficient descriptors of interdependent systems. Euclidean analysis of SPD matrices, while computationally fast, can lead to skewed and even unphysical interpretations of data. Riemannian methods preserve the geometric structure of SPD data at the cost of expensive eigenvalue computations. In this paper, we propose a geometric method for unsupervised clustering of SPD data based on the Thompson metric. This technique relies upon a novel "inductive midrange" centroid computation for SPD data, whose properties are examined and numerically confirmed. We demonstrate the incorporation of the Thompson metric and inductive midrange into X-means and K-means++ clustering algorithms.
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- 2020
- Full Text
- View/download PDF
39. Model reduction by balanced truncation of dominant Lure systems
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Padoan, Alberto, Forni, Fulvio, and Sepulchre, Rodolphe
- Subjects
Electrical Engineering and Systems Science - Systems and Control ,Mathematics - Optimization and Control - Abstract
The paper presents a model reduction framework geared towards the analysis and design of systems that switch and oscillate. While such phenomena are ubiquitous in nature and engineering, model reduction methods are not well developed for non-equilibrium behaviors. The proposed framework addresses this need by exploiting recent advances on dominance theory. Classical balanced truncation for linear time-invariant systems is used to develop a dominance-preserving model reduction method for Lure systems, i.e. systems that can be decomposed as the feedback interconnection of a linear system and a static nonlinearity. The method is illustrated by approximating the oscillatory behavior of a discretized heat flow control system., Comment: 6 pages, 6 figures, submitted to the IFAC World Congress 2020
- Published
- 2020
40. Differential dissipativity analysis of reaction-diffusion systems
- Author
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Miranda-Villatoro, Felix and Sepulchre, Rodolphe
- Subjects
Electrical Engineering and Systems Science - Systems and Control ,Mathematics - Analysis of PDEs ,35K57, 93C10, 35A24, 35B40 - Abstract
This note shows how classical tools from linear control theory can be leveraged to provide a global analysis of nonlinear reaction-diffusion models. The approach is differential in nature. It proceeds from classical tools of contraction analysis and recent extensions to differential dissipativity., Comment: 8 pages, 5 figures, Submitted to Systems and Control Letters
- Published
- 2020
41. Feedback for nonlinear system identification
- Author
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Burghi, Thiago B., Schoukens, Maarten, and Sepulchre, Rodolphe
- Subjects
Electrical Engineering and Systems Science - Systems and Control - Abstract
Motivated by neuronal models from neuroscience, we consider the system identification of simple feedback structures whose behaviors include nonlinear phenomena such as excitability, limit-cycles and chaos. We show that output feedback is sufficient to solve the identification problem in a two-step procedure. First, the nonlinear static characteristic of the system is extracted, and second, using a feedback linearizing law, a mildly nonlinear system with an approximately-finite memory is identified. In an ideal setting, the second step boils down to the identification of a LTI system. To illustrate the method in a realistic setting, we present numerical simulations of the identification of two classical systems that fit the assumed model structure., Comment: 18th European Control Conference (ECC), Napoli, Italy, June 25-28 2019
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- 2020
- Full Text
- View/download PDF
42. Feedback Identification of conductance-based models
- Author
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Burghi, Thiago B., Schoukens, Maarten, and Sepulchre, Rodolphe
- Subjects
Electrical Engineering and Systems Science - Systems and Control ,Quantitative Biology - Neurons and Cognition - Abstract
This paper applies the classical prediction error method (PEM) to the estimation of nonlinear discrete-time models of neuronal systems subject to input-additive noise. While the nonlinear system exhibits excitability, bifurcations, and limit-cycle oscillations, we prove consistency of the parameter estimation procedure under output feedback. Hence, this paper provides a rigorous framework for the application of conventional nonlinear system identification methods to discrete-time stochastic neuronal systems. The main result exploits the elementary property that conductance-based models of neurons have an exponentially contracting inverse dynamics. This property is implied by the voltage-clamp experiment, which has been the fundamental modeling experiment of neurons ever since the pioneering work of Hodgkin and Huxley.
- Published
- 2020
- Full Text
- View/download PDF
43. A nested bistable module within a negative feedback loop ensures different types of oscillations in signaling systems
- Author
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Juan Ignacio Marrone, Jacques-Alexandre Sepulchre, and Alejandra C. Ventura
- Subjects
Medicine ,Science - Abstract
Abstract In this article, we consider a double phosphorylation cycle, a ubiquitous signaling component, having the ability to display bistability, a behavior strongly related to the existence of positive feedback loops. If this component is connected to other signaling elements, it very likely undergoes some sort of protein–protein interaction. In several cases, these interactions result in a non-explicit negative feedback effect, leading to interlinked positive and negative feedbacks. This combination was studied in the literature as a way to generate relaxation-type oscillations. Here, we show that the two feedbacks together ensure two types of oscillations, the relaxation-type ones and a smoother type of oscillations functioning in a very narrow range of frequencies, in such a way that outside that range, the amplitude of the oscillations is severely compromised. Even more, we show that the two feedbacks are essential for both oscillatory types to emerge, and it is their hierarchy what determines the type of oscillation at work. We used bifurcation analyses and amplitude vs. frequency curves to characterize and classify the oscillations. We also applied the same ideas to another simple model, with the goal of generalizing what we learned from signaling models. The results obtained display the wealth of oscillatory dynamics that exists in a system with a bistable module nested within a negative feedback loop, showing how to transition between different types of oscillations and other dynamical behaviors such as excitability. Our work provides a framework for the study of other oscillatory systems based on bistable modules, from simple two-component models to more complex examples like the MAPK cascade and experimental cases like cell cycle oscillators.
- Published
- 2023
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44. The role of paleogeography in Asian monsoon evolution: a review and new insights from climate modelling
- Author
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Tardif, D., Sarr, A.-C., Fluteau, F., Licht, A., Kaya, M., Ladant, J.-B., Meijer, N., Donnadieu, Y., Dupont-Nivet, G., Bolton, C.T., Le Hir, G., Pillot, Q., Poblete, F., Sepulchre, P., Toumoulin, A., and Banfield, W.
- Published
- 2023
- Full Text
- View/download PDF
45. Leukemic conversion involving RAS mutations of type 1 CALR-mutated primary myelofibrosis in a patient treated for HCV cirrhosis: a case report
- Author
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Petruta Gurban, Cristina Mambet, Anca Botezatu, Laura G. Necula, Ana I. Neagu, Lilia Matei, Ioana M. Pitica, Saviana Nedeianu, Mihaela Chivu-Economescu, Coralia Bleotu, Marius Ataman, Gabriela Mocanu, Carmen Saguna, Anca G. Pavel, Danae Stambouli, Elise Sepulchre, Gabriela Anton, Carmen C. Diaconu, and Stefan N. Constantinescu
- Subjects
primary myelofibrosis (PMF) ,hepatitis C virus (HCV) cirrhosis ,type 1 calreticulin (CALR) ,targeted next-generation sequencing (NGS) ,NRAS ,acquired uniparental disomy (aUPD) ,Neoplasms. Tumors. Oncology. Including cancer and carcinogens ,RC254-282 - Abstract
Somatic frameshift mutations in exon 9 of calreticulin (CALR) gene are recognized as disease drivers in primary myelofibrosis (PMF), one of the three classical Philadelphia-negative myeloproliferative neoplasms (MPNs). Type 1/type 1-like CALR mutations particularly confer a favorable prognostic and survival advantage in PMF patients. We report an unusual case of PMF incidentally diagnosed in a 68-year-old woman known with hepatitis C virus (HCV) cirrhosis who developed a progressive painful splenomegaly, without anomalies in blood cell counts. While harboring a type 1 CALR mutation, the patient underwent a leukemic transformation in less than 1 year from diagnosis, with a lethal outcome. Analysis of paired DNA samples from chronic and leukemic phases by a targeted next-generation sequencing (NGS) panel and single-nucleotide polymorphism (SNP) microarray revealed that the leukemic clone developed from the CALR-mutated clone through the acquisition of genetic events in the RAS signaling pathway: an increased variant allele frequency of the germline NRAS Y64D mutation present in the chronic phase (via an acquired uniparental disomy of chromosome 1) and gaining NRAS G12D in the blast phase. SNP microarray analysis showed five clinically significant copy number losses at regions 7q22.1, 8q11.1-q11.21, 10p12.1-p11.22, 11p14.1-p11.2, and Xp11.4, revealing a complex karyotype already in the chronic phase. We discuss how additional mutations, detected by NGS, as well as HCV infection and antiviral therapy, might have negatively impacted this type 1 CALR-mutated PMF. We suggest that larger studies are required to determine if more careful monitoring would be needed in MPN patients also carrying HCV and receiving anti-HCV treatment.
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- 2023
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46. Pseudo-nullclines enable the analysis and prediction of signaling model dynamics
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Juan Ignacio Marrone, Jacques-Alexandre Sepulchre, and Alejandra C. Ventura
- Subjects
pseudo-nullclines ,oscillations ,bistability ,MAPK ,signaling ,bifurcations ,Biology (General) ,QH301-705.5 - Abstract
A powerful method to qualitatively analyze a 2D system is the use of nullclines, curves which separate regions of the plane where the sign of the time derivatives is constant, with their intersections corresponding to steady states. As a quick way to sketch the phase portrait of the system, they can be sufficient to understand the qualitative dynamics at play without integrating the differential equations. While it cannot be extended straightforwardly for dimensions higher than 2, sometimes the phase portrait can still be projected onto a 2-dimensional subspace, with some curves becoming pseudo-nullclines. In this work, we study cell signaling models of dimension higher than 2 with behaviors such as oscillations and bistability. Pseudo-nullclines are defined and used to qualitatively analyze the dynamics involved. Our method applies when a system can be decomposed into 2 modules, mutually coupled through 2 scalar variables. At the same time, it helps track bifurcations in a quick and efficient manner, key for understanding the different behaviors. Our results are both consistent with the expected dynamics, and also lead to new responses like excitability. Further work could test the method for other regions of parameter space and determine how to extend it to three-module systems.
- Published
- 2023
- Full Text
- View/download PDF
47. The $\mathcal{H}_{\infty,p}$ norm as the differential $\mathcal{L}_{2,p}$ gain of a $p$-dominant system
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Padoan, Alberto, Forni, Fulvio, and Sepulchre, Rodolphe
- Subjects
Mathematics - Optimization and Control ,Electrical Engineering and Systems Science - Systems and Control - Abstract
The differential $\mathcal{L}_{2,p}$ gain of a linear, time-invariant, $p$-dominant system is shown to coincide with the $\mathcal{H}_{\infty,p}$ norm of its transfer function $G$, defined as the essential supremum of the absolute value of $G$ over a vertical strip in the complex plane such that $p$ poles of $G$ lie to right of the strip. The close analogy between the $\mathcal{H}_{\infty,p}$ norm and the classical $\mathcal{H}_{\infty}$ norm suggests that robust dominance of linear systems can be studied along the same lines as robust stability. This property can be exploited in the analysis and design of nonlinear uncertain systems that can be decomposed as the feedback interconnection of a linear, time-invariant system with bounded gain uncertainties or nonlinearities., Comment: 6 pages, 3 figures, 58th IEEE Conf. Decision and Control
- Published
- 2019
48. Dissipativity analysis of negative resistance circuits
- Author
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Miranda-Villatoro, Felix A., Forni, Fulvio, and Sepulchre, Rodolphe
- Subjects
Electrical Engineering and Systems Science - Systems and Control ,Mathematics - Dynamical Systems ,Mathematics - Optimization and Control ,34C15, 34C25, 34C26, 34C55, 34C41, 34D45, 93C10 - Abstract
This paper deals with the analysis of nonlinear circuits that interconnect passive elements (capacitors, inductors, and resistors) with nonlinear resistors exhibiting a range of $\it{negative}$ resistance. Such active elements are necessary to design circuits that switch and oscillate. We generalize the classical passivity theory of circuit analysis to account for such non-equilibrium behaviors. The approach closely mimics the classical methodology of (incremental) dissipativity theory, but with dissipation inequalities that combine $\it{signed}$ storage functions and $\it{signed}$ supply rates to account for the mixture of passive and active elements.
- Published
- 2019
49. Geometric Matrix Midranges
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Mostajeran, Cyrus, Grussler, Christian, and Sepulchre, Rodolphe
- Subjects
Mathematics - Optimization and Control - Abstract
We define geometric matrix midranges for positive definite Hermitian matrices and study the midrange problem from a number of perspectives. Special attention is given to the midrange of two positive definite matrices before considering the extension of the problem to $N > 2$ matrices. We compare matrix midrange statistics with the scalar and vector midrange problem and note the special significance of the matrix problem from a computational standpoint. We also study various aspects of geometric matrix midrange statistics from the viewpoint of linear algebra, differential geometry and convex optimization.
- Published
- 2019
50. Dominance margins for feedback systems
- Author
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Padoan, Alberto, Forni, Fulvio, and Sepulchre, Rodolphe
- Subjects
Computer Science - Systems and Control ,Mathematics - Optimization and Control - Abstract
The paper introduces notions of robustness margins geared towards the analysis and design of systems that switch and oscillate. While such phenomena are ubiquitous in nature and in engineering, a theory of robustness for behaviors away from equilibria is lacking. The proposed framework addresses this need in the framework of p-dominance theory, which aims at generalizing stability theory for the analysis of systems with low-dimensional attractors. Dominance margins are introduced as natural generalisations of stability margins in the context of p-dominance analysis. In analogy with stability margins, dominance margins are shown to admit simple interpretations in terms of familiar frequency domain tools and to provide quantitative measures of robustness for multistable and oscillatory behaviors in Lure systems. The theory is illustrated by means of an elementary mechanical example., Comment: 11th IFAC Symposium on Nonlinear Control Systems
- Published
- 2019
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