arXiv subjects

Anastasia Bizyaeva

Publications and source records attributed to Anastasia Bizyaeva.

At least 19 recordsLinked to original sources

arXiv2026

Census-Based Population Autonomy For Distributed Robotic Teaming

Collaborating teams of robots show promise due to their ability to complete missions more efficiently and with improved robustness, attributes that are particularly useful for systems operating in marine environments. A key issue is how to model, analyze, and design these multi-robot systems to realize the full benefits of collaboration, a challenging task since the domain of multi-robot autonomy encompasses both collective and individual behaviors. This paper introduces a layered model of multi-robot autonomy that uses the principle of census, or a weighted count of the inputs from neighbors, for collective decision-making about teaming, coupled with multi-objective behavior optimization for individual decision-making about actions. The census component is expressed as a nonlinear opinion dynamics model and the multi-objective behavior optimization is accomplished using interval programming. This model can be reduced to recover foundational algorithms in distributed optimization and control, while the full model enables new types of collective behaviors that are useful in real-world scenarios. To illustrate these points, a new method for distributed optimization of subgroup allocation is introduced where robots use a gradient descent algorithm to minimize portions of the cost functions that are locally known, while being influenced by the opinion states from neighbors to account for the unobserved costs. With this method the group can collectively use the information contained in the Hessian matrix of the total global cost. The utility of this model is experimentally validated in three categorically different experiments with fleets of autonomous surface vehicles: an adaptive sampling scenario, a high value unit protection scenario, and a competitive game of capture the flag.

cs.RO↗

arXiv2026

A KKL Observer Perspective on Reservoir Computing

Reservoir computing (RC) is a machine learning technique for data-driven modeling of dynamics for forecasting and control, primarily studied in computer science and physics literature with promising applications in neural network learning, physical computing, and neuroscience. Why reservoirs learn and how to choose good reservoir architectures are considered important open questions. We show that the RC problem is mathematically an extension of a classic problem in systems and control theory, the Kazantzis-Kravaris-Luenberger (KKL) observer design problem. As a consequence, many of the questions considered open for RC stand to benefit from a large body of theory in the mature KKL literature, non-exhaustively including on questions of embedding, transverse stability, local and global uniqueness guarantees, and effective data-driven solution constructions. Elaborating on this connection, we show that the surprising forecasting ability of reservoirs is in fact a direct consequence of the well-known observer internal model principle, derive an upper bound on the prediction error over a fixed forecast horizon, and provide a partial explanation for why linear readout training in RC works reasonably well. This work illustrates how classical ideas from systems and control can provide strong theoretical backing and open new questions for modern machine learning methods.

eess.SY↗

arXiv2026

Optimality of delayed reward attainment under uncertainty

Decision making under uncertainty requires balancing the value of additional information against the cost of delaying the decision until that information becomes available. This challenge is especially prevalent for embodied decisions such as those faced by animals moving between food sources and robots selecting navigation targets, where movement through space shapes both the quality of information and the cost of acting. We consider a version of this problem, where the decision is on choosing among rewards of uncertain value, and those rewards can only be attained through changing the decision maker's state sufficiently. Our focus is on interactions between reward learning and state evolution, restated as a deterministic optimal control problem with two terminal alternatives, one with a known reward and the other learned gradually through noisy observations. We demonstrate that delayed reward attainment is often optimal in a variety of systems, especially so when the alternatives are initially difficult to distinguish and the cost of waiting is relatively low. For a subset of problems, we also derive sufficient conditions that allow shortening the planning horizon a priori, guaranteeing that further observations would not affect the value function. Finally, when observation quality depends on the state, we show that it is often optimal for a controller to evolve the state strategically toward more informative sensing locations before making a decision, in line with the behavior broadly observed in biological and engineered systems.

math.OC↗

arXiv2026

Explicit Second-Order Bounds on the Domain of Validity for Lyapunov-Schmidt Reduction

Lyapunov-Schmidt reduction is a widely used dimensionality reduction technique for bifurcation analysis in high-dimensional systems. While classical formulations guarantee the local existence of reduced-order equations, they typically lack explicit quantitative estimates on the size of the neighbourhoods in which these representations faithfully capture the full bifurcation structure. In recent work, we have addressed this limitation by deriving bounds on the domain of validity of this reduction using first-order conditions on the vector field together with a quantitative result for the implicit function theorem. In this article we explore beyond, and adopt second-order conditions that incorporate the Hessians of the vector field to develop these bounds, and obtain a new set of results. We then investigate the applicability of these newly derived bounds to Hopfield-like networked dynamical systems, evaluate these bounds for pitchfork bifurcations on connected regular graphs, and finally examine the relationship between the two certified domains for this class of systems.

eess.SY↗

arXiv2026

On Dominant Manifolds in Reservoir Computing Networks

Understanding how training shapes the geometry of recurrent network dynamics is a central problem in time-series modeling. We study the emergence of low-dimensional dominant manifolds in the training of Reservoir Computing (RC) networks for temporal forecasting tasks. For a general linear continuous-time reservoir in the infinite-data limit, we show that the training data generate an invariant subspace of the trained reservoir, whose dimension equals the number of dominant modes. We then specialize to a simplified diagonal linear reservoir, where we link the dominant eigenvalues and eigenvectors to the spectrum of a backward Dynamic Mode Decomposition matrix, which yields a finite-dimensional approximation of the backward-time Koopman operator of the system generating the training data. We illustrate the emergence of these dominant modes during training in simulation, and discuss how the analysis may be extended to nonlinear RC via tangent dynamics and differential p-dominance.

cs.LG↗

arXiv2026

Constraint-Induced Redistribution of Social Influence in Nonlinear Opinion Dynamics

We study how intrinsic hard constraints on the decision dynamics of social agents shape collective decisions on multiple alternatives in a heterogeneous group. Such constraints may arise due to structural and behavioral limitations, such as adherence to belief systems in social networks or hardware limitations in autonomous networks. In this work, agent constraints are encoded as projections in a multi-alternative nonlinear opinion dynamics framework. We prove that projections induce an invariant subspace on which the constraints are always satisfied and study the dynamics of networked opinions on this subspace. We then show that heterogeneous pairwise alignments between individuals' constraint vectors generate an effective weighted social graph on the invariant subspace, even when agents exchange opinions over an unweighted communication graph in practice. With analysis and simulation studies, we illustrate how the effective constraint-induced weighted graph reshapes the centrality of agents in the decision process and the group's sensitivity to distributed inputs.

math.OC↗

arXiv2026

Behavior of Nonlinear Opinion Dynamics over Large Networks

Opinion dynamics have been studied for decades across disciplines, with much of the theoretical literature focusing on behaviors such as consensus, polarization, and clustering. Although classic models can exhibit more complex opinion patterns in simulations, quantifying such distributions is not fully understood. To address this question, in this paper, we study the behavior of nonlinear opinion dynamics over large-scale networks using graphons, which capture the underlying network structure. In the model, agents update their opinions according to a nonlinear rule that includes saturation effects in interactions. The network is represented by random graphs generated from a graphon, and a corresponding nonlinear dynamical model is introduced over the graphon. We show that the graphon dynamics approximate the finite-dimensional system, when the network size is large. Leveraging spectral approximation results for random graphs, we further show that the equilibria of the nonlinear model can also be approximated by those of the continuum limit. This result enables a quantitative characterization of the opinion distribution based on the underlying graphon structure. The theoretical results are illustrated by numerical simulation.

eess.SY↗

arXiv2026

Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification

We introduce Fourier Weak SINDy, a minimal noise-robust and interpretable derivative-free equation learning method that combines weak-form sparse equation learning with spectral density estimation for data-driven test function selection. By using orthogonal sinusoidal test functions inspired by their prevalence in Modulating Function-based system identification, the weak-form sparse regression problem reduces to a regression over Fourier coefficients. Dominant frequencies are then selected via multitaper estimation of the frequency spectrum of the data. This formulation unifies weak-form learning and spectral estimation within a compact and flexible framework. We illustrate the effectiveness of this approach in numerical experiments across multiple chaotic and hyperchaotic ODE benchmarks.

cs.LG↗

arXiv2026

Bounds of Validity for Bifurcations of Equilibria in a Class of Networked Dynamical Systems

Local bifurcation analysis plays a central role in understanding qualitative transitions in networked nonlinear dynamical systems, including dynamic neural network and opinion dynamics models. In this article we establish explicit bounds of validity for the classification of bifurcation diagrams in two classes of continuous-time networked dynamical systems, analogous in structure to the Hopfield and the Firing Rate dynamic neural network models. Our approach leverages recent advances in computing the bounds for the validity of Lyapunov-Schmidt reduction, a reduction method widely employed in nonlinear systems analysis. Using these bounds we rigorously characterize neighbourhoods around bifurcation points where predictions from reduced-order bifurcation equations remain reliable. We further demonstrate how these bounds can be applied to an illustrative family of nonlinear opinion dynamics on k-regular graphs, which emerges as a special case of the general framework. These results provide new analytical tools for quantifying the robustness of bifurcation phenomena in dynamics over networked systems and highlight the interplay between network structure and nonlinear dynamical behaviour.

eess.SY↗

arXiv2026

From Vision to Decision: Neuromorphic Control for Autonomous Navigation and Tracking

Robotic navigation has historically struggled to reconcile reactive, sensor-based control with the decisive capabilities of model-based planners. This duality becomes critical when the absence of a predominant option among goals leads to indecision, challenging reactive systems to break symmetries without computationally-intense planners. We propose a parsimonious neuromorphic control framework that bridges this gap for vision-guided navigation and tracking. Image pixels from an onboard camera are encoded as inputs to dynamic neuronal populations that directly transform visual target excitation into egocentric motion commands. A dynamic bifurcation mechanism resolves indecision by delaying commitment until a critical point induced by the environmental geometry. Inspired by recently proposed mechanistic models of animal cognition and opinion dynamics, the neuromorphic controller provides real-time autonomy with a minimal computational burden, a small number of interpretable parameters, and can be seamlessly integrated with application-specific image processing pipelines. We validate our approach in simulation environments as well as on an experimental quadrotor platform.

cs.RO↗

arXiv2025

Mixed-feedback oscillations in the foraging dynamics of arboreal turtle ants

We propose and analyze a model for the dynamics of the flow into and out of a nest for the arboreal turtle ant $\textit{Cephalotes goniodontus}$ during foraging to investigate a possible mechanism for the emergence of oscillations. In our model, there is mixed dynamic feedback between the flow of ants between different behavioral compartments and the amount of pheromone along trails. On one hand, the ants deposit pheromone along the trail, which provides a positive feedback by increasing rates of return to the nest. On the other hand, pheromone evaporation is a source of negative feedback, as it depletes the pheromone and inhibits the return rate. We prove that the model is globally asymptotically stable in the absence of pheromone feedback. Then we show that pheromone feedback can lead to a loss of stability of the equilibrium and onset of sustained oscillations in the flow in and out of the nest via a Hopf bifurcation. This analysis sheds light on a potential key mechanism that enables arboreal turtle ants to effectively optimize their trail networks to minimize traveled path lengths and eliminate graph cycles.

q-bio.PE↗

arXiv2025

Bifurcation analysis of an opinion dynamics model coupled with an environmental dynamics

We consider an opinion dynamics model coupled with an environmental dynamics. Based on a forward invariance argument, we can simplify the analysis of the asymptotic behavior to the case when all the opinions in the social network are synchronized. Our goal is to emphasize the role of the trust given to the environmental signal in the asymptotic behavior of the opinion dynamics and implicitly of the coupled system. To do that, we conduct a bifurcation analysis of the system around the origin when the trust parameter is varying. Specific conditions are presented for both pitchfork and Hopf bifurcation. Numerical illustration completes the theoretical findings.

eess.SY↗

arXiv2025

Opinion-driven risk perception and reaction in SIS epidemics

We present and analyze a mathematical model to study the feedback between behavior and epidemic spread in a population that is actively assessing and reacting to risk of infection. In our model, a population dynamically forms an opinion that reflects its willingness to engage in risky behavior (e.g., not wearing a mask in a crowded area) or reduce it (e.g., social distancing). We consider SIS epidemic dynamics in which the contact rate within a population adapts as a function of its opinion. For the new coupled model, we prove the existence of two distinct parameter regimes. One regime corresponds to a low baseline infectiousness, and the equilibria of the epidemic spread are identical to those of the standard SIS model. The other regime corresponds to a high baseline infectiousness, and there is a bistability between two new endemic equilibria that reflect an initial preference towards either risk seeking behavior or risk aversion. We prove that risk seeking behavior increases the steady-state infection level in the population compared to the baseline SIS model, whereas risk aversion decreases it. When a population is highly reactive to extreme opinions, we show how risk aversion enables the complete eradication of infection in the population. Extensions of the model to a network of populations or individuals are explored numerically.

math.DS↗

arXiv2024

Adaptive bias for dissensus in nonlinear opinion dynamics with application to evolutionary division of labor games

This paper addresses the problem of adaptively controlling the bias parameter in nonlinear opinion dynamics (NOD) to allocate agents into groups of arbitrary sizes for the purpose of maximizing collective rewards. In previous work, an algorithm based on the coupling of NOD with an multi-objective behavior optimization was successfully deployed as part of a multi-robot system in an autonomous task allocation field experiment. Motivated by the field results, in this paper we propose and analyze a new task allocation model that synthesizes NOD with an evolutionary game framework. We prove sufficient conditions under which it is possible to control the opinion state in the group to a desired allocation of agents between two tasks through an adaptive bias using decentralized feedback. We then verify the theoretical results with a simulation study of a collaborative evolutionary division of labor game.

eess.SY↗

arXiv2024

Spatially-invariant opinion dynamics on the circle

We propose and analyze a nonlinear opinion dynamics model for an agent making decisions about a continuous distribution of options in the presence of input. Inspired by perceptual decision-making, we develop new theory for opinion formation in response to inputs about options distributed on the circle. Options on the circle can represent, e.g., the possible directions of perceived objects and resulting heading directions in planar robotic navigation problems. Interactions among options are encoded through a spatially invariant kernel, which we design to ensure that only a small (finite) subset of options can be favored over the continuum. We leverage the spatial invariance of the model linearization to design flexible, distributed opinion-forming behaviors using spatiotemporal frequency domain and bifurcation analysis. We illustrate our model's versatility with an application to robotic navigation in crowded spaces.

math.AP↗

arXiv2024

Active risk aversion in SIS epidemics on networks

We present and analyze an actively controlled Susceptible-Infected-Susceptible (actSIS) model of interconnected populations to study how risk aversion strategies, such as social distancing, affect network epidemics. A population using a risk aversion strategy reduces its contact rate with other populations when it perceives an increase in infection risk. The network actSIS model relies on two distinct networks. One is a physical contact network that defines which populations come into contact with which other populations and thus how infection spreads. The other is a communication network, such as an online social network, that defines which populations observe the infection level of which other populations and thus how information spreads. We prove that the model, with these two networks and populations using risk aversion strategies, exhibits a transcritical bifurcation in which an endemic equilibrium emerges. For regular graphs, we prove that the endemic infection level is uniform across populations and reduced by the risk aversion strategy, relative to the network SIS endemic level. We show that when communication is sufficiently sparse, this initially stable equilibrium loses stability in a secondary bifurcation. Simulations show that a new stable solution emerges with nonuniform infection levels.

q-bio.PE↗

arXiv2024

Fast-and-flexible decision-making with modulatory interactions

Multi-agent systems in biology, society, and engineering are capable of making decisions through the dynamic interaction of their elements. Nonlinearity of the interactions is key for the speed, robustness, and flexibility of multi-agent decision-making. In this work we introduce modulatory, that is, multiplicative, in contrast to additive, interactions in a nonlinear opinion dynamics model of fast-and-flexible decision-making. The original model is nonlinear because network interactions, although additive, are saturated. Modulatory interactions introduce an extra source of nonlinearity that greatly enriches the model decision-making behavior in a mathematically tractable way. Modulatory interactions are widespread in both biological and social decision-making networks; our model provides new tools to understand the role of these interactions in networked decision-making and to engineer them in artificial systems.

math.DS↗

arXiv2024

Estimates on the domain of validity for Lyapunov-Schmidt reduction

Lyapunov-Schmidt reduction is a dimensionality reduction technique in nonlinear systems analysis that is commonly utilised in the study of bifurcation problems in high-dimensional systems. The method is a systematic procedure for reducing the dimensionality of systems of algebraic equations that have singular points, preserving essential features of their solution sets. In this article, we establish estimates for the region of validity of the reduction by leveraging recently derived bounds on the Implicit Function Theorem. We then apply these bounds to an illustrative example of a two-dimensional system with a pitchfork bifurcation.

eess.SY↗