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Matin Jafarian

Publications and source records attributed to Matin Jafarian.

11 recordsLinked to original sources
arXiv2025

Accurate linear modeling of EEG-based cortical activity during a passive motor task with input: a sub-space identification approach

This paper studies linear mathematical modeling of brain's cortical dynamics using electroencephalography (EEG) data in an experiment with continuous exogenous input. The EEG data were recorded while participants were seated with their wrist strapped to a haptic manipulator. The manipulator imposed a continuous multisine angular perturbation to the wrist as the exogenous input to the brain. We show that subspace identification, in particular the PO-MOESP algorithm, leads to a linear time-invariant state-space model that accurately represents the measurements, in a latent space, assuming that the EEG data are the models' output. The model is verified and validated using data from seven participants. Moreover, we construct linear maps to relate the latent space dynamics to the neural source space. We show that findings by our model align with those identified in previous studies.

q-bio.NC↗
arXiv2025

Uncertainty Partitioning with Probabilistic Feasibility and Performance Guarantees for Chance-Constrained Optimization

We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists of partitioning the uncertainty domain in a user-defined number of sets, enabling more flexibility in the trade-off between conservatism and computational complexity. We provide sufficient conditions to ensure that our approximated problem is feasible for the original stochastic program, in terms of chance constraint satisfaction. In addition, we perform a rigorous performance analysis, by quantifying the distance between the optimal values of the original and the approximated problem. We show that our approach is tractable for optimization problems that include model predictive control of piecewise affine systems, and we demonstrate the benefits of our approach, in terms of the trade-off between conservatism and computational complexity, on a numerical example.

math.OC↗
arXiv2023

Utility of the Koopman operator in output regulation of disturbed nonlinear systems

This paper studies the problem of output regulation for a class of nonlinear systems experiencing matched input disturbances. It is assumed that the disturbance signal is generated by an external autonomous dynamical system. First, we show that for a class of nonlinear systems admitting a finite-dimensional Koopman representation, the problem is equivalent to a bilinear output regulation. We then prove that a linear dynamic output feedback controller, inspired by the linear output regulation framework, locally solves the original nonlinear problem. Numerical results validate our analysis.

eess.SY↗
arXiv2023

Astrocytic gliotransmission as a pathway for stable stimulation of post-synaptic spiking: Implications for working memory

The brain consists not only of neurons but also of non-neuronal cells, including astrocytes. Recent discoveries in neuroscience suggest that astrocytes directly regulate neuronal activity by releasing gliotransmitters such as glutamate. In this paper, we consider a biologically plausible mathematical model of a tripartite neuron-astrocyte network. We study the stability of the nonlinear astrocyte dynamics, as well as its role in regulating the firing rate of the post-synaptic neuron. We show that astrocytes enable storing neuronal information temporarily. Motivated by recent findings on the role of astrocytes in explaining mechanisms of working memory, we numerically verify the utility of our analysis in showing the possibility of two competing theories of persistent and sparse neuronal activity of working memory.

eess.SY↗
arXiv2023

Stochastic Stability of Discrete-time Phase-coupled Oscillators over Uncertain and Random Networks

This article studies stochastic relative phase stability, i.e., stochastic phase-cohesiveness, of discrete-time phase-coupled oscillators. Stochastic phase-cohesiveness in two types of networks is studied. First, we consider oscillators coupled with 2π-periodic odd functions over underlying undirected graphs subject to both multiplicative and additive stochastic uncertainties. We prove stochastic phase-cohesiveness of the network with respect to two specific, namely in-phase and anti-phase, sets by deriving sufficient coupling conditions. We show the dependency of these conditions on the size of the mean values of additive and multiplicative uncertainties, as well as the sign of the mean values of multiplicative uncertainties. Furthermore, we discuss the results under a relaxation of the odd property of the coupling function. Second, we study an uncertain network in which the multiplicative uncertainties are governed by the Bernoulli process representing the well-known Erdos-Renyi network. We assume constant exogenous frequencies and derive sufficient conditions for achieving both stochastic phase-cohesive and phase-locked solutions, i.e., stochastic phase-cohesiveness with respect to the origin. For the latter case, where identical exogenous frequencies are assumed, we prove that any positive probability of connectivity leads to phase-locking. Thorough analyses are provided, and insights obtained from stochastic analysis are discussed, along with numerical simulations to validate the analytical results.

eess.SY↗
arXiv2020

Analysis of free recall dynamics of an abstract working memory model

This paper analyzes the free recall dynamics of a working memory model. Free recalling is the reactivation of a stored pattern in the memory in the absence of the pattern. Our free recall model is based on an abstract model of a modular neural network composed on $N$ modules, hypercolumns, each of which is a bundle of minicolumns. This paper considers a network of $N$ modules, each consisting of two minicolumns, over a complete graph topology. We analyze the free recall dynamics assuming a constant, and homogeneous coupling between the network modules. We obtain a sufficient condition for synchronization of network's minicolumns whose activities are positively correlated. Furthermore, for the synchronized network, the bifurcation analysis of one module is presented. This analysis gives a necessary condition for having a stable limit cycle as the attractor of each module. The latter implies recalling a stored pattern. Numerical results are provided to verify the theoretical analysis.

eess.SY↗
arXiv2019

Stochastic phase-cohesiveness of discrete-time Kuramoto oscillators in a frequency-dependent tree network

This paper presents the notion of stochastic phase-cohesiveness based on the concept of recurrent Markov chains and studies the conditions under which a discrete-time stochastic Kuramoto model is phase-cohesive. It is assumed that the exogenous frequencies of the oscillators are combined with random variables representing uncertainties. A bidirectional tree network is considered such that each oscillator is coupled to its neighbors with a coupling law which depends on its own noisy exogenous frequency. In addition, an undirected tree network is studied. For both cases, a sufficient condition for the common coupling strength and a necessary condition for the sampling-period are derived such that the stochastic phase-cohesiveness is achieved. The analysis is performed within the stochastic systems framework and validated by means of numerical simulations.

eess.SY↗
arXiv2018

Synchronization of Kuramoto oscillators in a bidirectional frequency-dependent tree network

This paper studies the synchronization of a finite number of Kuramoto oscillators in a frequency-dependent bidirectional tree network. We assume that the coupling strength of each link in each direction is equal to the product of a common coefficient and the exogenous frequency of its corresponding head oscillator. We derive a sufficient condition for the common coupling strength in order to guarantee frequency synchronization in tree networks. Moreover, we discuss the dependency of the obtained bound on both the graph structure and the way that exogenous frequencies are distributed. Further, we present an application of the obtained result by means of an event-triggered algorithm for achieving frequency synchronization in a star network assuming that the common coupling coefficient is given.

eess.SY↗
arXiv2018

The interconnection of quadratic droop voltage controllers is a Lotka-Volterra system: implications for stability analysis

This paper studies the stability of voltage dynamics for a power network in which nodal voltages are controlled by means of quadratic droop controllers with nonlinear AC reactive power as inputs. We show that the voltage dynamics is a Lotka-Volterra system, which is a class of nonlinear positive systems. We study the stability of the closed-loop system by proving a uniform ultimate boundedness result and investigating conditions under which the network is cooperative. We then restrict to study the stability of voltage dynamics under a decoupling assumption (i.e., zero relative angles). We analyze the existence and uniqueness of the equilibrium in the interior of the positive orthant for the system and prove an asymptotic stability result.

eess.SY↗
arXiv2013

Formation control with binary information

In this paper, we study the problem of formation keeping of a network of strictly passive systems when very coarse information is exchanged. We assume that neighboring agents only know whether their relative position is larger or smaller than the prescribed one. This assumption results in very simple control laws that direct the agents closer or away from each other and take values in finite sets. We show that the task of formation keeping while tracking a desired trajectory and rejecting matched disturbances is still achievable under the very coarse information scenario. In contrast with other results of practical convergence with coarse or quantized information, here the control task is achieved exactly.

eess.SY↗