Nader Motee

Amirhossein Mollaei Khass, Vivek Pandey, Guangyi Liu et al.

Multi-agent Next-Best-View (NBV) selection for safe path planning in uncertain and unknown environments requires informative, safety-aware, and efficient coordination. Centralized approaches rely on sharing raw sensor data or significant communication overhead, resulting in limited scalability. We propose a distributed, risk-aware multi-agent NBV framework in which each robot maintains a private local 3D Gaussian Splatting map and the team jointly maximizes expected information gain (EIG) restricted to masked zones along planned trajectories. The resulting distributed objective is solved by Consensus ADMM (C-ADMM) over a communication graph, with each robot exchanging only candidate viewpoints, planned trajectory descriptors, and scalar EIG contributions. Collision risk along each trajectory is modeled via Average Value-at-Risk (AV@R) over the local 3DGS map and used both to shape the masking radius and to score planned paths. Experiments in Gibson environments at multiple team sizes show that the distributed formulation approaches the centralized baseline in mapping quality and trajectory safety while reducing communication by orders of magnitude.

Milad Siami, Nader Motee

In this paper, we develop a novel unified methodology for performance and robustness analysis of linear dynamical networks. We introduce the notion of systemic measures for the class of first--order linear consensus networks. We classify two important types of performance and robustness measures according to their functional properties: convex systemic measures and Schur--convex systemic measures. It is shown that a viable systemic measure should satisfy several fundamental properties such as homogeneity, monotonicity, convexity, and orthogonal invariance. In order to support our proposed unified framework, we verify functional properties of several existing performance and robustness measures from the literature and show that they all belong to the class of systemic measures. Moreover, we introduce new classes of systemic measures based on (a version of) the well--known Riemann zeta function, input--output system norms, and etc. Then, it is shown that for a given linear dynamical network one can take several different strategies to optimize a given performance and robustness systemic measure via convex optimization. Finally, we characterized an interesting fundamental limit on the best achievable value of a given systemic measure after adding some certain number of new weighted edges to the underlying graph of the network.

Christoforos Somarakis, Yaser Ghaedsharaf, Nader Motee

We quantify the value-at-risk of inter-vehicle collision and detachment for a class of platoons, which are governed by second-order dynamics in presence of communication time-delay and exogenous stochastic noise. Closed-form expressions for the risk measures are obtained as functions of Laplacian eigen-spectrum as well as their fine explicit approximations using rational polynomial functions. We quantify several hard limits and fundamental tradeoffs among the risk measures, network connectivity, communication time-delay, and statistics of exogenous stochastic noise. Simultaneous presence of stochastic noise and time delay in a platoon imposes some idiosyncratic limitations on the behavior of collision and detachment risks, for instance, weakening (improving) network connectivity may result in lower (higher) levels of risk. Furthermore, a thorough risk analysis and comparison have been conducted for networks with specific graph topology. We support our theoretical findings via extensive simulations.

Yaser Ghaedsharaf, Milad Siami, Christoforos Somarakis et al.

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.

Guangyi Liu, Arash Amini, Martin Takac et al.

For a given stable recurrent neural network (RNN) that is trained to perform a classification task using sequential inputs, we quantify explicit robustness bounds as a function of trainable weight matrices. The sequential inputs can be perturbed in various ways, e.g., streaming images can be deformed due to robot motion or imperfect camera lens. Using the notion of the Voronoi diagram and Lipschitz properties of stable RNNs, we provide a thorough analysis and characterize the maximum allowable perturbations while guaranteeing the full accuracy of the classification task. We illustrate and validate our theoretical results using a map dataset with clouds as well as the MNIST dataset.

Hossein K. Mousavi, Qiyu Sun, Nader Motee

Designing sparse sampling strategies is one of the important components in having resilient estimation and control in networked systems as they make network design problems more cost-effective due to their reduced sampling requirements and less fragile to where and when samples are collected. It is shown that under what conditions taking coarse samples from a network will contain the same amount of information as a more finer set of samples. Our goal is to estimate initial condition of linear time-invariant networks using a set of noisy measurements. The observability condition is reformulated as the frame condition, where one can easily trace location and time stamps of each sample. We compare estimation quality of various sampling strategies using estimation measures, which depend on spectrum of the corresponding frame operators. Using properties of the minimal polynomial of the state matrix, deterministic and randomized methods are suggested to construct observability frames. Intrinsic tradeoffs assert that collecting samples from fewer subsystems dictates taking more samples (in average) per subsystem. Three scalable algorithms are developed to generate sparse space-time sampling strategies with explicit error bounds.

Guangyi Liu, Disha Kamale, Cristian-Ioan Vasile et al.

We develop a novel framework to assess the risk of misperception in a traffic sign classification task in the presence of exogenous noise. We consider the problem in an autonomous driving setting, where visual input quality gradually improves due to improved resolution, and less noise since the distance to traffic signs decreases. Using the estimated perception statistics obtained using the standard classification algorithms, we aim to quantify the risk of misperception to mitigate the effects of imperfect visual observation. By exploring perception outputs, their expected high-level actions, and potential costs, we show the closed-form representation of the conditional value-at-risk (CVaR) of misperception. Several case studies support the effectiveness of our proposed methodology.

Christoforos Somarakis, Nader Motee

The focus of this paper is to quantify measures of aggregate fluctuations for a class of consensus-seeking multiagent networks subject to exogenous noise with alpha-stable distributions. This type of noise is generated by a class of random measures with heavy-tailed probability distributions. We define a cumulative scale parameter using scale parameters of probability distributions of the output variables, as a measure of aggregate fluctuation. Although this class of measures can be characterized implicitly in closed-form in steady-state, finding their explicit forms in terms of network parameters is, in general, almost impossible. We obtain several tractable upper bounds in terms of Laplacian spectrum and statistics of the input noise. Our results suggest that relying on Gaussian-based optimal design algorithms will result in non-optimal solutions for networks that are driven by non-Gaussian noise inputs with alpha-stable distributions. The manuscript has been submitted for publication to IEEE Transactions on Control of Network Systems. It is the extended version of preliminary paper included in the proceedings of the 2018 American Control Conference.

MirSaleh Bahavarnia, Hossein K. Mousavi, Nader Motee

We propose a self-triggered control algorithm to reduce onboard processor usage, communication bandwidth, and energy consumption across a linear time-invariant networked control system. We formulate an optimal control problem by penalizing the l0-measures of the feedback gain and the vector of control inputs and maximizing the dwell time between the consecutive triggering times. It is shown that the corresponding l1-relaxation of the optimal control problem is feasible and results in a stabilizing feedback control law with guaranteed performance bounds, while providing a sparse schedule for collecting samples from sensors, communication with other subsystems, and activating the input actuators.

Milad Siami, Nader Motee

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.

Arash Amini, Qiyu Sun, Nader Motee

We consider a class of stochastic dynamical networks whose governing dynamics can be modeled using a coupling function. It is shown that the dynamics of such networks can generate geometrically ergodic trajectories under some reasonable assumptions. We show that a general class of coupling functions can be learned using only one sample trajectory from the network. This is practically plausible as in numerous applications it is desired to run an experiment only once but for a longer period of time, rather than repeating the same experiment multiple times from different initial conditions. Building upon ideas from the concentration inequalities for geometrically ergodic Markov chains, we formulate several results about the convergence of the empirical estimator to the true coupling function. Our theoretical findings are supported by extensive simulation results.

Amirhossein Mollaei Khass, Athanasios Cosse, Vivek Pandey et al.

Active perception in uncertain environments requires robots to navigate safely while acquiring informative observations to reduce map uncertainty. These objectives inherently conflict, as informative viewpoints often lie near uncertain regions with higher collision risk. To address this challenge, we develop a conflict-aware active perception and control framework for robotic systems operating in environments represented by 3D Gaussian Splatting (3DGS). Safety is enforced using a Control Barrier Function (CBF) derived from an Average Value-at-Risk AV@R collision-risk metric that accounts for geometric uncertainty and guarantees forward invariance of a safe set. To improve perception, we propose a risk-aware Expected Information Gain (EIG) formulation for selecting the next-best-view and introduce perception barrier functions that align the camera orientation with the local information-ascent direction. To obtain a tractable formulation for these conflicting safety and perception objectives, we propose a unified safety-critical, perception-aware quadratic program that enforces safety as a hard constraint while relaxing perception constraints through slack variables. Simulation results demonstrate that the proposed method improves both safety and information acquisition compared to existing 3DGS-based approaches.

Vivek Pandey, Nader Motee

Safe operation of connected vehicle platoons under stochastic disturbances and time-delayed dynamics requires accurate quantification of rare but dangerous events, such as inter-vehicle collisions. We propose a rigorous framework for quantifying the risk of inter-vehicle collisions in connected vehicle platoons subject to time-delayed stochastic dynamics. We adopt the \emph{entropic value-at-risk} (EVaR) as a conservative metric to capture \emph{risk due to extreme events}, highlighting its advantages over conventional Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). By expressing the inter-vehicle distance covariance in terms of the Laplacian eigenvalues of the communication network, we derive \emph{network-and time-delay-induced bounds} on both the minimum inherent risk and the worst-case risk. Specifically, the algebraic connectivity dictates the maximum EVaR, while the largest Laplacian eigenvalue determines the minimum risk inherently induced by the network structure. Numerical simulations illustrate how network topology and time delay shape collision risk, offering actionable insights for the safe design of vehicle platoons operating under stochastic disturbances.

Guangyi Liu, Vivek Pandey, Christoforos Somarakis et al.

We develop a framework for studying and quantifying the risk of cascading failures in time-delay consensus networks, motivated by a team of agents attempting temporal rendezvous under stochastic disturbances and communication delays. To assess how failures at one or multiple agents amplify the risk of deviation across the network, we employ the Average Value-at-Risk as a systemic measure of cascading uncertainty. Closed-form expressions reveal explicit dependencies of the risk of cascading failure on the Laplacian spectrum, communication delay, and noise statistics. We further establish fundamental lower bounds that characterize the best-achievable network performance under time-delay constraints. These bounds serve as feasibility certificates for assessing whether a desired safety or performance goal can be achieved without exhaustive search across all possible topologies. In addition, we develop an efficient single-step update law that enables scalable propagation of conditional risk as new failures are detected. Analytical and numerical studies demonstrate significant computational savings and confirm the tightness of the theoretical limits across diverse network configurations.

Amirhossein Mollaei Khass, Guangyi Liu, Vivek Pandey et al.

Safe navigation in uncertain environments requires planning methods that integrate risk aversion with active perception. In this work, we present a unified framework that refines a coarse reference path by constructing tail-sensitive risk maps from Average Value-at-Risk statistics on an online-updated 3D Gaussian-splat Radiance Field. These maps enable the generation of locally safe and feasible trajectories. In parallel, we formulate Next-Best-View (NBV) selection as an optimization problem on the SE(3) pose manifold, where Riemannian gradient descent maximizes an expected information gain objective to reduce uncertainty most critical for imminent motion. Our approach advances the state-of-the-art by coupling risk-averse path refinement with NBV planning, while introducing scalable gradient decompositions that support efficient online updates in complex environments. We demonstrate the effectiveness of the proposed framework through extensive computational studies.

Arash Amini, Guangyi Liu, Nader Motee

Recurrent Neural networks (RNN) have shown promising potential for learning dynamics of sequential data. However, artificial neural networks are known to exhibit poor robustness in presence of input noise, where the sequential architecture of RNNs exacerbates the problem. In this paper, we will use ideas from control and estimation theories to propose a tractable robustness analysis for RNN models that are subject to input noise. The variance of the output of the noisy system is adopted as a robustness measure to quantify the impact of noise on learning. It is shown that the robustness measure can be estimated efficiently using linearization techniques. Using these results, we proposed a learning method to enhance robustness of a RNN with respect to exogenous Gaussian noise with known statistics. Our extensive simulations on benchmark problems reveal that our proposed methodology significantly improves robustness of recurrent neural networks.

Guangyi Liu, Arash Amini, Martin Takáč et al.

We consider the problem of classifying a map using a team of communicating robots. It is assumed that all robots have localized visual sensing capabilities and can exchange their information with neighboring robots. Using a graph decomposition technique, we proposed an offline learning structure that makes every robot capable of communicating with and fusing information from its neighbors to plan its next move towards the most informative parts of the environment for map classification purposes. The main idea is to decompose a given undirected graph into a union of directed star graphs and train robots w.r.t a bounded number of star graphs. This will significantly reduce the computational cost of offline training and makes learning scalable (independent of the number of robots). Our approach is particularly useful for fast map classification in large environments using a large number of communicating robots. We validate the usefulness of our proposed methodology through extensive simulations.

Hossein K. Mousavi, Guangyi Liu, Weihang Yuan et al.

We propose a planning and perception mechanism for a robot (agent), that can only observe the underlying environment partially, in order to solve an image classification problem. A three-layer architecture is suggested that consists of a meta-layer that decides the intermediate goals, an action-layer that selects local actions as the agent navigates towards a goal, and a classification-layer that evaluates the reward and makes a prediction. We design and implement these layers using deep reinforcement learning. A generalized policy gradient algorithm is utilized to learn the parameters of these layers to maximize the expected reward. Our proposed methodology is tested on the MNIST dataset of handwritten digits, which provides us with a level of explainability while interpreting the agent's intermediate goals and course of action.

Hossein K. Mousavi, Mohammadreza Nazari, Martin Takáč et al.

We investigate a classification problem using multiple mobile agents capable of collecting (partial) pose-dependent observations of an unknown environment. The objective is to classify an image over a finite time horizon. We propose a network architecture on how agents should form a local belief, take local actions, and extract relevant features from their raw partial observations. Agents are allowed to exchange information with their neighboring agents to update their own beliefs. It is shown how reinforcement learning techniques can be utilized to achieve decentralized implementation of the classification problem by running a decentralized consensus protocol. Our experimental results on the MNIST handwritten digit dataset demonstrates the effectiveness of our proposed framework.

Hossein K. Mousavi, Nader Motee

We consider the visual feature selection to improve the estimation quality required for the accurate navigation of a robot. We build upon a key property that asserts: contributions of trackable features (landmarks) appear linearly in the information matrix of the corresponding estimation problem. We utilize standard models for motion and vision system using a camera to formulate the feature selection problem over moving finite time horizons. A scalable randomized sampling algorithm is proposed to select more informative features (and ignore the rest) to achieve a superior position estimation quality. We provide probabilistic performance guarantees for our method. The time-complexity of our feature selection algorithm is linear in the number of candidate features, which is practically plausible and outperforms existing greedy methods that scale quadratically with the number of candidates features. Our numerical simulations confirm that not only the execution time of our proposed method is comparably less than that of the greedy method, but also the resulting estimation quality is very close to the greedy method.

Hossein K. Mousavi, Christoforos Somarakis, Qiyu Sun et al.

Spectral decomposition of dynamical systems is a popular methodology to investigate the fundamental qualitative and quantitative properties of these systems and their solutions. In this chapter, we consider a class of nonlinear cooperative protocols, which consist of multiple agents that are coupled together via an undirected state-dependent graph. We develop a representation of the system solution by decomposing the nonlinear system utilizing ideas from the Koopman operator theory and its spectral analysis. We use recent results on the extensions of the well-known Hartman theorem for hyperbolic systems to establish a connection between the original nonlinear dynamics and the linearized dynamics in terms of Koopman spectral properties. The expected value of the output energy of the nonlinear protocol, which is related to the notions of coherence and robustness in dynamical networks, is evaluated and characterized in terms of Koopman eigenvalues, eigenfunctions, and modes. Spectral representation of the performance measure enables us to develop algorithmic methods to assess the performance of this class of nonlinear dynamical networks as a function of their graph topology. Finally, we propose a scalable computational method for approximation of the components of the Koopman mode decomposition, which is necessary to evaluate the systemic performance measure of the nonlinear dynamic network.

Yaser Ghaedsharaf, Milad Siami, Christoforos Somarakis et al.

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.

Christoforos Somarakis, Yaser Ghaedsharaf, Nader Motee

For the class of noisy time-delay linear consensus networks, we obtain explicit formulas for risk of large fluctuations of a scalar observable as a function of Laplacian spectrum and its eigenvectors. It is shown that there is an intrinsic tradeoff between risk and effective resistance of the underlying coupling graph of the network. The main implication is that increasing network connectivity, increases the risk of large fluctuations. For vector-valued observables, we obtain computationally tractable lower and upper bounds for joint risk measures. Then, we study behavior of risk measures for networks with specific graph topologies and show how risk scales with network size.

Milad Siami, Nader Motee

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.

Milad Siami, Nader Motee, Gentian Buzi et al.

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.

Milad Siami, Nader Motee

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.