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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., Comment: IFAC World Congress (2023)

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.

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 2{\pi}-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.

We present a price-based approach for congestion management in distribution power systems with renewable generations with the final goal of maximizing a social welfare function which includes net revenues of network users as well as the cost of real power losses. Particularly, we design a combined nodal and uniform pricing mechanism for maximization of the social welfare function while maintaining voltage magnitudes in a desired bound and respecting the grid's actual capacity. Storage systems are considered in order to increase/add elasticity to generations and loads. Simulation results are provided for a modified IEEE-37 bus. A scenario is numerically simulated where the excess of generation in the absence of storage and price signals leads to deviations of voltages from a desired bound. Thereafter, it is shown that the application of the price signals is effective to maintain the voltages within the desired bound while the designed social welfare function is maximized., QC 20200325

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., QC 20210331

This paper studies synchronization of a network of hybrid quadratic integrate-and-fire spiking neurons communicating over a complete graph and interconnected by means of bidirectional electrical couplings. Synchronization of the network of identical neurons with a common and constant coupling strength is studied using a Lyapunov-based argument for sufficiently large coupling strength. In addition, a voltage-dependent coupling law is proposed. It is assumed that each neuron is coupled to each of its neighbors by a coupling law which depends on the voltage of its neighboring neuron. For the voltage-dependent case, a sufficient condition for synchronization of two interconnected neurons is presented. Moreover, a comparison between the two mechanisms is given. Simulation results are provided to verify the theoretical analysis., QC 20200702

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 (kappa) 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., QC 20191114

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., Comment: American Control Conference 2020

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., Comment: Accepted in the European Control Conference (ECC) 2019

Distributed formation keeping control is a motion coordination problem which aims at achieving a desired geometrical shape for the positions of a group of agents (e.g. robots). In problems of formation control, an important component is the flow of information among the agents. Although the usual assumption in the literature is the exchange of perfect information among the agents, the latter might be a restrictive requirement due to real-world constraints. To cope with this restriction, quantized information and control have been proposed and studied in the literature. In particular, there has been a growing interest in binary quantizers and controllers owing to the recent developments in cyber-physical systems. This thesis is mainly focused on the problem of distributed position-based formation keeping of a group of continuous-time dynamic agents using binary controllers. The binary information and control models a sensing scenario in which each agent detects whether or not the components of its current distance vector from a neighbor are above or below the prescribed distance and applies a force (in which each component takes a binary value) to reduce or increase the actual distance. In this context, we consider different classes of dynamical agents, including strict output passive systems, unicycles, and nonholonomic wheeled carts. For the control design and analysis, we use tools from discontinuous dynamical systems, passivity, hybrid dynamical systems, graph theory and internal-model-based approach.

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 source 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., QC 20190305

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., Comment: 1- IEEE Conference on Decision and Control (CDC), 2018. 2- The word `source' has been mistakenly used instead of `head' in the paper to be published in the 57th IEEE Conference on Decision and Control, 2018

This paper studies the distributed freeway ramp metering problem, for which the cell transmission model (CTM) is utilized. Considering the jam density and the upper bounds on the queue lengths and the ramp metering, we first provide feasibility conditions with respect to the external demand to ensure the controllability of the freeway. Assuming that the freeway is controllable, we formulate an optimization problem which tradeoffs the maximum average flow speed and the minimum waiting queue for each cell. Although the cells of the CTM are dynamically coupled, we propose a distributed backward algorithm for the optimization problem and prove that the solution to the problem is a Nash equilibrium. Furthermore, if the optimization problem is simplified to only maximization of the average flow speed, we argue that the obtained explicit distributed controller is globally optimal. A numerical example is given to illustrate the effectiveness of the proposed control algorithm., QC 20180306

As one of the extensions of model predictive control (MPC), event-triggered MPC takes advantage of the reduction of control updates. However, approaches to event-triggered MPCs may be subject to frequent event-triggering instants in the presence of large disturbances. Motivated by this, this paper suggests an application of machine learning to this control method in order to learn a compensation model for disturbance attenuation. The suggested method improves both event-triggering policy efficiency and control accuracy compared to previous approaches to event-triggered MPCs. We employ the radial basis function (RBF) kernel based machine learning technique. By the universial approximation property of the RBF, which imposes an upper bound on the training error, we can present the stability analysis of the learningaided control system. The proposed algorithm is evaluated by means of position control of a nonholonomic robot subject to state-dependent disturbances. Simulation results show that the developed method yields not only two times less event triggering instants, but also improved tracking performance., QC 20180305

This paper presents consensus of the orientations and average positions for a group of unicycles using ternary and hybrid controllers. The decentralized controllers designed to reach consensus of the average positions take only values in the set {-1; 0; +1}. In addition, a hybrid controller is introduced to control the orientations. Finite-time practical consensus of the average positions is proven despite the simple ternary control laws together with asymptotic consensus of the orientations. Furthermore, the consensus problem is studied in the presence of matched input disturbances that are locally rejected using an internal-model-based controller. The analysis is performed in a hybrid framework. Simulation results illustrate the effectiveness of the design., QC 20180112

This document presents the data for a single-phase distribution bus (based on IEEE 37 bus) together with the model and data for a PV inverter and active and reactive power loads.

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., Comment: Submitted to The IEEE Control Systems Letters

Distributed formation keeping control is a motion coordination problem which aims at achieving a desired geometrical shape for the positions of a group of agents (e.g. robots). In problems of formation control, an important component is the flow of information among the agents. Although the usual assumption in the literature is the exchange of perfect information among the agents, the latter might be a restrictive requirement due to real-world constraints. To cope with this restriction, quantized information and control have been proposed and studied in the literature. In particular, there has been a growing interest in binary quantizers and controllers owing to the recent developments in cyber-physical systems. This thesis is mainly focused on the problem of distributed position-based formation keeping of a group of continuous-time dynamic agents using binary controllers. The binary information and control models a sensing scenario in which each agent detects whether or not the components of its current distance vector from a neighbor are above or below the prescribed distance and applies a force (in which each component takes a binary value) to reduce or increase the actual distance. In this context, we consider different classes of dynamical agents, including strict output passive systems, unicycles, and nonholonomic wheeled carts. For the control design and analysis, we use tools from discontinuous dynamical systems, passivity, hybrid dynamical systems, graph theory and internal-model-based approach.

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., Comment: 21 pages, 9 figures. Submitted for publication