arXiv subjects

Milad Siami

Publications and source records attributed to Milad Siami.

At least 37 records · Page 2Linked to original sources

arXiv2024

Robustness Evaluation of Machine Learning Models for Robot Arm Action Recognition in Noisy Environments

In the realm of robot action recognition, identifying distinct but spatially proximate arm movements using vision systems in noisy environments poses a significant challenge. This paper studies robot arm action recognition in noisy environments using machine learning techniques. Specifically, a vision system is used to track the robot's movements followed by a deep learning model to extract the arm's key points. Through a comparative analysis of machine learning methods, the effectiveness and robustness of this model are assessed in noisy environments. A case study was conducted using the Tic-Tac-Toe game in a 3-by-3 grid environment, where the focus is to accurately identify the actions of the arms in selecting specific locations within this constrained environment. Experimental results show that our approach can achieve precise key point detection and action classification despite the addition of noise and uncertainties to the dataset.

cs.CV↗

arXiv2023

Robot Motion Prediction by Channel State Information

Autonomous robotic systems have gained a lot of attention, in recent years. However, accurate prediction of robot motion in indoor environments with limited visibility is challenging. While vision-based and light detection and ranging (LiDAR) sensors are commonly used for motion detection and localization of robotic arms, they are privacy-invasive and depend on a clear line-of-sight (LOS) for precise measurements. In cases where additional sensors are not available or LOS is not possible, these technologies may not be the best option. This paper proposes a novel method that employs channel state information (CSI) from WiFi signals affected by robotic arm motion. We developed a convolutional neural network (CNN) model to classify four different activities of a Franka Emika robotic arm. The implemented method seeks to accurately predict robot motion even in scenarios in which the robot is obscured by obstacles, without relying on any attached or internal sensors.

cs.RO↗

arXiv2023

On the ISS Property of the Gradient Flow for Single Hidden-Layer Neural Networks with Linear Activations

Recent research in neural networks and machine learning suggests that using many more parameters than strictly required by the initial complexity of a regression problem can result in more accurate or faster-converging models -- contrary to classical statistical belief. This phenomenon, sometimes known as ``benign overfitting'', raises questions regarding in what other ways might overparameterization affect the properties of a learning problem. In this work, we investigate the effects of overfitting on the robustness of gradient-descent training when subject to uncertainty on the gradient estimation. This uncertainty arises naturally if the gradient is estimated from noisy data or directly measured. Our object of study is a linear neural network with a single, arbitrarily wide, hidden layer and an arbitrary number of inputs and outputs. In this paper we solve the problem for the case where the input and output of our neural-network are one-dimensional, deriving sufficient conditions for robustness of our system based on necessary and sufficient conditions for convergence in the undisturbed case. We then show that the general overparametrized formulation introduces a set of spurious equilibria which lay outside the set where the loss function is minimized, and discuss directions of future work that might extend our current results for more general formulations.

cs.LG↗

arXiv2023

Edge Selection in Bilinear Dynamical Networks

We develop some basic principles for the design and robustness analysis of a continuous-time bilinear dynamical network, where an attacker can manipulate the strength of the interconnections/edges between some of the agents/nodes. We formulate the edge protection optimization problem of picking a limited number of attack-free edges and minimizing the impact of the attack over the bilinear dynamical network.In particular, the $\mathcal{H}_2$-norm of bilinear systems is known to capture robustness and performance properties analogous to its linear counterpart and provides valuable insights for identifying which edges are most sensitive to attacks. The exact optimization problem is combinatorial in the number of edges, and brute-force approaches show poor scalability. However, we show that the $\mathcal{H}_2$-norm as a cost function is supermodular and, therefore, allows for efficient greedy approximations of the optimal solution. We illustrate and compare the effectiveness of our theoretical findings via numerical simulations.

eess.SY↗

arXiv2020

Centrality-Based Traffic Restriction in Delayed Epidemic Networks

During an epidemic, infectious individuals might not be detectable until some time after becoming infected. The studies show that carriers with mild or no symptoms are the main contributors to the transmission of a virus within the population. The average time it takes to develop the symptoms causes a delay in the spread dynamics of the disease. When considering the influence of delay on the disease propagation in epidemic networks, depending on the value of the time-delay and the network topology, the peak of epidemic could be considerably different in time, duration, and intensity. Motivated by the recent worldwide outbreak of the COVID-19 virus and the topological extent in which this virus has spread over the course of a few months, this study aims to highlight the effect of time-delay in the progress of such infectious diseases in the meta-population networks rather than individuals or a single population. In this regard, the notions of epidemic network centrality in terms of the underlying interaction graph of the network, structure of the uncertainties, and symptom development duration are investigated to establish a centrality-based analysis of the disease evolution. A convex traffic volume optimization method is then developed to control the outbreak. The control process is done by identifying the sub-populations with the highest centrality and then isolating them while maintaining the same overall traffic volume (motivated by economic considerations) in the meta-population level. The numerical results, along with the theoretical expectations, highlight the impact of time-delay as well as the importance of considering the worst-case scenarios in investigating the most effective methods of epidemic containment.

eess.SY↗

arXiv2020

Stability and Robustness Analysis of Commensurate Fractional-order Networks

Motivated by biochemical reaction networks, a generalization of the classical secant condition for the stability analysis of cyclic interconnected commensurate fractional-order systems is provided. The main result presents a sufficient condition for stability of networks of cyclic interconnection of fractional-order systems when the digraph describing the network conforms to a single circuit. The condition becomes necessary under a special situation where coupling weights are uniform. We then investigate the robustness of fractional-order linear networks. Robustness performance of a fractional-order linear network is quantified using the $\mathcal{H}_2$-norm of the dynamical system. Finally, the theoretical results are confirmed via some numerical illustrations.

math.DS↗

arXiv2020

Deterministic and Randomized Actuator Scheduling With Guaranteed Performance Bounds

In this paper, we investigate the problem of actuator selection for linear dynamical systems. We develop a framework to design a sparse actuator schedule for a given large-scale linear system with guaranteed performance bounds using deterministic polynomial-time and randomized approximately linear-time algorithms. First, we introduce systemic controllability metrics for linear dynamical systems that are monotone and homogeneous with respect to the controllability Gramian. We show that several popular and widely used optimization criteria in the literature belong to this class of controllability metrics. Our main result is to provide a polynomial-time actuator schedule that on average selects only a constant number of actuators at each time step, independent of the dimension, to furnish a guaranteed approximation of the controllability metrics in comparison to when all actuators are in use. Our results naturally apply to the dual problem of sensor selection, in which we provide a guaranteed approximation to the observability Gramian. We illustrate the effectiveness of our theoretical findings via several numerical simulations using benchmark examples.

eess.SY↗

arXiv2020

A Separation Theorem for Joint Sensor and Actuator Scheduling with Guaranteed Performance Bounds

We study the problem of jointly designing a sparse sensor and actuator schedule for linear dynamical systems while guaranteeing a control/estimation performance that approximates the fully sensed/actuated setting. We further prove a separation principle, showing that the problem can be decomposed into finding sensor and actuator schedules separately. However, it is shown that this problem cannot be efficiently solved or approximated in polynomial, or even quasi-polynomial time for time-invariant sensor/actuator schedules; instead, we develop deterministic polynomial-time algorithms for a time-varying sensor/actuator schedule with guaranteed approximation bounds. Our main result is to provide a polynomial-time joint actuator and sensor schedule that on average selects only a constant number of sensors and actuators at each time step, irrespective of the dimension of the system. The key idea is to sparsify the controllability and observability Gramians while providing approximation guarantees for Hankel singular values. This idea is inspired by recent results in theoretical computer science literature on sparsification.

eess.SY↗

arXiv2019

Competitive Contagion with Sparse Seeding

This paper studies a strategic model of marketing and product diffusion in social networks. We consider two firms offering substitutable products which can improve their market share by seeding the key individuals in the market. Consumers update their consumption level for each of the two products as the best response to the consumption of their neighbors in the previous period. This results in linear update dynamics for the product consumption. Each consumer receives externality from the consumption of each neighbor where the strength of the externality is higher for consumption of the products of the same firm. We represent the above setting as a duopoly game between the firms and introduce a novel framework that allows for sparse seeding to emerge as an equilibrium strategy. We then study the effect of the network structure on the optimal seeding strategies and the extent to which the strategies can be sparsified. In particular, we derive conditions under which near Nash equilibrium strategies can asymptotically lead to sparse seeding in large populations. The results are illustrated using a core-periphery network.

cs.SI↗

arXiv2019

Centrality in Time-Delay Consensus Networks with Structured Uncertainties

We investigate notions of network centrality in terms of the underlying coupling graph of the network, structure of exogenous uncertainties, and communication time-delay. Our focus is on time-delay linear consensus networks, where uncertainty is modeled by structured additive noise on the dynamics of agents. The centrality measures are defined using the $\mathcal H_2$-norm of the network. We quantify the centrality measures as functions of time-delay, the graph Laplacian, and the covariance matrix of the input noise. Several practically relevant uncertainty structures are considered, where we discuss two notions of centrality: one w.r.t intensity of the noise and the other one w.r.t coupling strength between the agents. Furthermore, explicit formulas for the centrality measures are obtained for all types of uncertainty structures. Lastly, we rank agents and communication links based on their centrality indices and highlight the role of time-delay and uncertainty structure in each scenario. Our counter intuitive grasp is that some of centrality measures are highly volatile with respect to time-delay.

eess.SY↗

arXiv2018

Performance Improvement in Noisy Linear Consensus Networks with Time-Delay

We analyze performance of a class of time-delay first-order consensus networks from a graph topological perspective and present methods to improve it. The performance is measured by network's square of H-2 norm and it is shown that it is a convex function of Laplacian eigenvalues and the coupling weights of the underlying graph of the network. First, we propose a tight convex, but simple, approximation of the performance measure in order to achieve lower complexity in our design problems by eliminating the need for eigen-decomposition. The effect of time-delay reincarnates itself in the form of non-monotonicity, which results in nonintuitive behaviors of the performance as a function of graph topology. Next, we present three methods to improve the performance by growing, re-weighting, or sparsifying the underlying graph of the network. It is shown that our suggested algorithms provide near-optimal solutions with lower complexity with respect to existing methods in literature.

eess.SY↗

arXiv2017

Abstraction of Linear Consensus Networks with Guaranteed Systemic Performance Measures

A proper abstraction of a large-scale linear consensus network with a dense coupling graph is one whose number of coupling links is proportional to its number of subsystems and its performance is comparable to the original network. Optimal design problems for an abstracted network are more amenable to efficient optimization algorithms. From the implementation point of view, maintaining such networks are usually more favorable and cost effective due to their reduced communication requirements across a network. Therefore, approximating a given dense linear consensus network by a suitable abstract network is an important analysis and synthesis problem. In this paper, we develop a framework to compute an abstraction of a given large-scale linear consensus network with guaranteed performance bounds using a nearly-linear time algorithm. First, the existence of abstractions of a given network is proven. Then, we present an efficient and fast algorithm for computing a proper abstraction of a given network. Finally, we illustrate the effectiveness of our theoretical findings via several numerical simulations.

eess.SY↗

arXiv2017

Fundamental Limits and Tradeoffs in Autocatalytic Pathways

This paper develops some basic principles to study autocatalytic networks and exploit their structural properties in order to characterize their inherent fundamental limits and tradeoffs. In a dynamical system with autocatalytic structure, the system's output is necessary to catalyze its own production. We consider a simplified model of Glycolysis pathway as our motivating application. First, the properties of these class of pathways are investigated through a simplified two-state model, which is obtained by lumping all the intermediate reactions into a single intermediate reaction. Then, we generalize our results to autocatalytic pathways that are composed of a chain of enzymatically catalyzed intermediate reactions. We explicitly derive a hard limit on the minimum achievable $\mathcal L_2$-gain disturbance attenuation and a hard limit on its minimum required output energy. Finally, we show how these resulting hard limits lead to some fundamental tradeoffs between transient and steady-state behavior of the network and its net production.

eess.SY↗

arXiv2017

Structural Analysis and Optimal Design of Distributed System Throttlers

In this paper, we investigate the performance analysis and synthesis of distributed system throttlers (DST). A throttler is a mechanism that limits the flow rate of incoming metrics, e.g., byte per second, network bandwidth usage, capacity, traffic, etc. This can be used to protect a service's backend/clients from getting overloaded, or to reduce the effects of uncertainties in demand for shared services. We study performance deterioration of DSTs subject to demand uncertainty. We then consider network synthesis problems that aim to improve the performance of noisy DSTs via communication link modifications as well as server update cycle modifications.

eess.SY↗

arXiv2017

Growing Linear Consensus Networks Endowed by Spectral Systemic Performance Measures

We propose an axiomatic approach for design and performance analysis of noisy linear consensus networks by introducing a notion of systemic performance measure. This class of measures are spectral functions of Laplacian eigenvalues of the network that are monotone, convex, and orthogonally invariant with respect to the Laplacian matrix of the network. It is shown that several existing gold-standard and widely used performance measures in the literature belong to this new class of measures. We build upon this new notion and investigate a general form of combinatorial problem of growing a linear consensus network via minimizing a given systemic performance measure. Two efficient polynomial-time approximation algorithms are devised to tackle this network synthesis problem: a linearization-based method and a simple greedy algorithm based on rank-one updates. Several theoretical fundamental limits on the best achievable performance for the combinatorial problem is derived that assist us to evaluate optimality gaps of our proposed algorithms. A detailed complexity analysis confirms the effectiveness and viability of our algorithms to handle large-scale consensus networks.

math.OC↗

arXiv2015

Scaling Laws for Disturbance Propagation in Cyclic Dynamical Networks

Our goal is to analyze performance of stable linear dynamical networks subject to external stochastic disturbances. The square of the $\mathcal H_2$-norm of the network is used as a performance measure to quantify the expected steady-state dispersion of the outputs of the network. We show that this performance measure can be tightly bounded from below and above by some spectral functions of the state-space matrices of the network. This result is applied to a class of cyclic linear networks and shown that their performance measure scale quadratically with the network size.

eess.SY↗

arXiv2014

Fundamental Limits and Tradeoffs on Disturbance Propagation in Large-Scale Dynamical Networks

We consider performance deterioration of interconnected linear dynamical networks subject to exogenous stochastic disturbances. The focus of this paper is on first-order and second-order linear consensus networks. We employ the expected value of the steady state dispersion of the state of the entire network as a performance measure and develop a graph-theoretic methodology to relate structural specifications of the underlying graphs of the network to the performance measure. We explicitly quantify several inherent fundamental limits on the best achievable levels of performance in linear consensus networks and show that these limits of performance are merely imposed by the specific structure of the underlying graphs. Furthermore, we discover new connections between notions of sparsity and the performance measure. Particularly, we characterize several fundamental tradeoffs that reveal interplay between the performance measure and various sparsity measures of a linear consensus network. At the end, we apply our results to two real-world dynamical networks and provide energy interpretations for the proposed performance measures. It is shown that the total power loss in synchronous power networks and total kinetic energy of a network of autonomous vehicles in a formation are viable performance measure for these networks and fundamental limits on these measures quantify the best achievable levels of energy-efficiency in these dynamical networks.

math.OC↗

arXiv2014

Eminence Grise Coalitions: On the Shaping of Public Opinion

We consider a network of evolving opinions. It includes multiple individuals with first-order opinion dynamics defined in continuous time and evolving based on a general exogenously defined time-varying underlying graph. In such a network, for an arbitrary fixed initial time, a subset of individuals forms an eminence grise coalition, abbreviated as EGC, if the individuals in that subset are capable of leading the entire network to agreeing on any desired opinion, through a cooperative choice of their own initial opinions. In this endeavor, the coalition members are assumed to have access to full profile of the underlying graph of the network as well as the initial opinions of all other individuals. While the complete coalition of individuals always qualifies as an EGC, we establish the existence of a minimum size EGC for an arbitrary time-varying network; also, we develop a non-trivial set of upper and lower bounds on that size. As a result, we show that, even when the underlying graph does not guarantee convergence to a global or multiple consensus, a generally restricted coalition of agents can steer public opinion towards a desired global consensus without affecting any of the predefined graph interactions, provided they can cooperatively adjust their own initial opinions. Geometric insights into the structure of EGC's are given. The results are also extended to the discrete time case where the relation with Decomposition-Separation Theorem is also made explicit.

math.DS↗