arXiv subjects

Afroza Shirin

Publications and source records attributed to Afroza Shirin.

13 recordsLinked to original sources

arXiv2022

Towards Stable Interstellar Flight: Levitation of a Laser-Propelled Sailcraft*

Exploring and traveling to distant stars has long fascinated humanity but has been limited due to the vast distances. The Breakthrough Starshot Program aims at eliminating this limitation by traveling to Alpha Centauri, which is 4.37 light-years away. Thus, it is only possible if a vehicle travels at a substantial fraction of the speed of light. The Breakthrough Starshot Program initiatives to develop a proof-of-concept that is accelerating a sail to relativistic speeds using a laser beam aimed at the sail. At this high speed, while a stable beam riding is one of the crucial concerns of this concept, the dynamic stability analysis of a sail is hardly present in the previous literature. Furthermore, it is important to investigate the dynamic stability in the experiment before driving the sail to relativistic speeds. As a proof of concept, we study the dynamic stability of the sail levitated at a certain height by a laser beam. The sail's dynamics are modeled as a rigid body whose shape is parameterized by a sweep function. We estimate the region of attraction (ROA) for dynamic stability analysis using Lyapunov theory and Sum-of-square (SOS) programming. The ROA confirms how much a levitated sail can tolerate the transverse and angular perturbations. We also conclude on some of the important parameters of the sail that affects the dynamic stability. Simulation results validate our theoretical analysis.

eess.SY↗

arXiv2022

Reservoir Computers with Random and Optimized Time-Shifts

We investigate the effects of application of random time-shifts to the readouts of a reservoir computer in terms of both accuracy (training error) and performance (testing error.) For different choices of the reservoir parameters and different `tasks', we observe a substantial improvement in both accuracy and performance. We then develop a simple but effective technique to optimize the choice of the time-shifts, which we successfully test in numerical experiments.

eess.SY↗

arXiv2021

Data-driven Optimized Control of the COVID-19 Epidemics

Optimizing the impact on the economy of control strategies aiming at containing the spread of COVID-19 is a critical challenge. We use daily new case counts of COVID-19 patients reported by local health administrations from different Metropolitan Statistical Areas (MSAs) within the US to parametrize a model that well describes the propagation of the disease in each area. We then introduce a time-varying control input that represents the level of social distancing imposed on the population of a given area and solve an optimal control problem with the goal of minimizing the impact of social distancing on the economy in the presence of relevant constraints, such as a desired level of suppression for the epidemics at a terminal time. We find that with the exception of the initial time and of the final time, the optimal control input is well approximated by a constant, specific to each area, which contrasts with the implemented system of reopening `in phases'. For all the areas considered, this optimal level corresponds to stricter social distancing than the level estimated from data. Proper selection of the time period for application of the control action optimally is important: depending on the particular MSA this period should be either short or long or intermediate. We also consider the case that the transmissibility increases in time (due e.g. to increasingly colder weather), for which we find that the optimal control solution yields progressively stricter measures of social distancing. {We finally compute the optimal control solution for a model modified to incorporate the effects of vaccinations on the population and we see that depending on a number of factors, social distancing measures could be optimally reduced during the period over which vaccines are administered to the population.

q-bio.PE↗

arXiv2021

Reservoir Computers Modal Decomposition and Optimization

The topology of a network associated with a reservoir computer is often taken so that the connectivity and the weights are chosen randomly. Optimization is hardly considered as the parameter space is typically too large. Here we investigate this problem for a class of reservoir computers for which we obtain a decomposition of the reservoir dynamics into modes, which can be computed independently of one another. Each mode depends on an eigenvalue of the network adjacency matrix. We then take a parametric approach in which the eigenvalues are parameters that can be appropriately designed and optimized. In addition, we introduce the application of a time shift to each individual mode. We show that manipulations of the individual modes, either in terms of the eigenvalues or the time shifts, can lead to dramatic reductions in the training error.

cond-mat.dis-nn↗

arXiv2019

Stability Analysis of Reservoir Computers Dynamics via Lyapunov Functions

A Lyapunov design method is used to analyze the nonlinear stability of a generic reservoir computer for both the cases of continuous-time and discrete-time dynamics. Using this method, for a given nonlinear reservoir computer, a radial region of stability around a fixed point is analytically determined. We see that the training error of the reservoir computer is lower in the region where the analysis predicts global stability but is also affected by the particular choice of the individual dynamics for the reservoir systems. For the case that the dynamics is polynomial, it appears to be important for the polynomial to have nonzero coefficients corresponding to at least one odd power (e.g., linear term) and one even power (e.g., quadratic term).

eess.SY↗

arXiv2018

Optimal Regulation of Blood Glucose Level in Type I Diabetes using Insulin and Glucagon

The Glucose-Insulin-Glucagon nonlinear model [1-4] accurately describes how the body responds to exogenously supplied insulin and glucagon in patients affected by Type I diabetes. Based on this model, we design infusion rates of either insulin (monotherapy) or insulin and glucagon (dual therapy) that can optimally maintain the blood glucose level within desired limits after consumption of a meal and prevent the onset of both hypoglycemia and hyperglycemia. This problem is formulated as a nonlinear optimal control problem, which we solve using the numerical optimal control package PSOPT. Interestingly, in the case of monotherapy, we find the optimal solution is close to the standard method of insulin based glucose regulation, which is to assume a variable amount of insulin half an hour before each meal. We also find that the optimal dual therapy (that uses both insulin and glucagon) is better able to regulate glucose as compared to using insulin alone. We also propose an ad-hoc rule for both the dosage and the time of delivery of insulin and glucagon.

q-bio.TO↗

arXiv2018

Prediction of Optimal Drug Schedules for Controlling Autophagy

The effects of molecularly targeted drug perturbations on cellular activities and fates are difficult to predict using intuition alone because of the complex behaviors of cellular regulatory networks. An approach to overcoming this problem is to develop mathematical models for predicting drug effects. Such an approach beckons for co-development of computational methods for extracting insights useful for guiding therapy selection and optimizing drug scheduling. Here, we present and evaluate a generalizable strategy for identifying drug dosing schedules that minimize the amount of drug needed to achieve sustained suppression or elevation of an important cellular activity/process, the recycling of cytoplasmic contents through (macro)autophagy. Therapeutic targeting of autophagy is currently being evaluated in diverse clinical trials but without the benefit of a control engineering perspective. Using a nonlinear ordinary differential equation (ODE) model that accounts for activating and inhibiting influences among protein and lipid kinases that regulate autophagy (MTORC1, ULK1, AMPK and VPS34) and methods guaranteed to find locally optimal control strategies, we find optimal drug dosing schedules (open-loop controllers) for each of six classes of drugs and drug pairs. Our approach is generalizable to designing monotherapy and multi therapy drug schedules that affect different cell signaling networks of interest.

eess.SY↗

arXiv2018

Optimal Control of Networks in the presence of Attackers and Defenders

We consider the problem of a dynamical network whose dynamics is subject to external perturbations (`attacks') locally applied at a subset of the network nodes. We assume that the network has an ability to defend itself against attacks with appropriate countermeasures, which we model as actuators located at (another) subset of the network nodes. We derive the optimal defense strategy as an optimal control problem. We see that the network topology, as well as the distribution of attackers and defenders over the network affect the optimal control solution and the minimum control energy. We study the optimal control defense strategy for several network topologies, including chain networks, star networks, ring networks, and scale free networks.

eess.SY↗

arXiv2017

Locally Optimal Control of Complex Networks

It has recently been shown that the minimum energy solution of the control problem for a linear system produces a control trajectory that is nonlocal. An issue then arises when the dynamics represents a linearization of the underlying nonlinear dynamics of the system where the linearization is only valid in a local region of the state space. Here we provide a solution to the problem of optimally controlling a linearized system by deriving a time-varying set that represents all possible control trajectories parameterized by time and energy. As long as the control action terminus is defined within this set, the control trajectory is guaranteed to be local. If the desired terminus of the control action is far from the initial state, a series of local control actions can be performed in series, re-linearizing the dynamics at each new position.

math.OC↗

arXiv2017

Observability of Nonlinear Complex Networks in the Presence of Symmetries: A Graphical Approach

Reconstructing the states of the nodes of a dynamical network is a problem of fundamental importance in the study of neuronal and genetic networks. An underlying related problem is that of observability, i.e., identifying the conditions under which such a reconstruction is possible. In this paper we study observability of complex dynamical networks, where we consider the effects of network symmetries on observability. We present an efficient algorithm that returns a minimal set of necessary sensor nodes for observability in the presence of symmetries.

nlin.PS↗

arXiv2016

Energy Scaling of Targeted Optimal Control of Complex Networks

Recently it has been shown that the control energy required to control a dynamical complex network is prohibitively large when there are only a few control inputs. Most methods to reduce the control energy have focused on where, in the network, to place additional control inputs. Here, in contrast, we show that by controlling the states of a subset of the nodes of a network, rather than the state of every node, while holding the number of control signals constant, the required energy to control a portion of the network can be reduced substantially. The energy requirements exponentially decay with the number of target nodes, suggesting that large networks can be controlled by a relatively small number of inputs as long as the target set is appropriately sized. We validate our conclusions in model and real networks to arrive at an energy scaling law to better design control objectives regardless of system size, energy restrictions, state restrictions, input node choices and target node choices.

eess.SY↗

arXiv2013

Numerical Solutions of Fredholm Integral Equations Using Bernstein Polynomials

In this paper, Bernstein piecewise polynomials are used to solve the integral equations numerically. A matrix formulation is given for a non-singular linear Fredholm Integral Equation by the technique of Galerkin method. In the Galerkin method, the Bernstein polynomials are used as the approximation of basis functions. Examples are considered to verify the effectiveness of the proposed derivations, and the numerical solutions guarantee the desired accuracy.

math.NA↗

arXiv2013

Numerical solutions of a class of second order boundary value problems on using Bernoulli Polynomials

The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with Dirichlet, Neumann and Robin boundary conditions. We use the Bernoulli polynomials as linear combination to the approximate solutions of 2nd order boundary value problems. Here the Bernoulli polynomials over the interval [0, 1] are chosen as trial functions so that care has been taken to satisfy the corresponding homogeneous form of the Dirichlet boundary conditions in the Galerkin weighted residual method. In addition to that the given differential equation over arbitrary finite domain [a, b] and the boundary conditions are converted into its equivalent form over the interval [0, 1]. All the formulas are verified by considering numerical examples. The approximate solutions are compared with the exact solutions, and also with the solutions of the existing methods. A reliable good accuracy is obtained in all cases.

math.NA↗