arXiv subjects

Bassam Bamieh

Publications and source records attributed to Bassam Bamieh.

At least 19 recordsLinked to original sources

arXiv2026

On Distributed Control of Continuum Swarms: Local Controllers as Differential Operators

We study the problem of distributed control of large-scale robotic swarms which can be modeled as continuum densities evolving under the continuity equation. We propose a formalization of distributed controllers as (generally nonlinear) spatial differential operators, in which control inputs depend only on local information about the state and environment. This perspective yields a fully local, PDE-based framework for analysis and design. We apply this framework to the problem of stabilizing a swarm density around an arbitrary target density, and investigate fundamental limitations of low-spatial-order distributed controllers in achieving this goal. In particular, we show that controllers which act in a purely pointwise manner are incompatible with natural system symmetries and strong forms of stability, and must rely on mixing-type behavior to achieve stabilization. In contrast, we present a simple first-order control law which achieves stabilization and enjoys substantially stronger properties.

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arXiv2026

Spiking control systems for soft robotics: a rhythmic case study in a soft robotic crawler

Inspired by spiking neural feedback, we propose a spiking controller to engineer the locomotion of a soft robotic crawler. Its bistability, akin to neural fast positive feedback, combined with a sensorimotor slow negative feedback loop, generates rhythmic spiking and self-sustained peristaltic locomotion. We analytically characterize the local equilibrium bifurcations induced by the sensorimotor gain and complement this analysis through numerical continuation of periodic orbits. The resulting bifurcation diagram reveals the emergence of qualitatively distinct solutions, including resting and crawling behaviors. For a representative regime with separated mechanical and electrical timescales, Geometric Singular Perturbation Theory reveals the geometry of the relaxation oscillations leading to endogenous crawling. Within this singularly perturbed regime, we formulate and analytically solve an optimization problem, proving that locomotion speed is maximized at mechanical resonance through a matching of neuromechanical scales. Given the importance and ubiquity of rhythms and waves in soft-bodied locomotion, we envision that spiking control systems could be utilized in a variety of soft-robotic morphologies and modular distributed architectures.

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arXiv2026

Mean-Field Oscillator Ising Machines: Gradient Flows and Classification of Limit Solutions

Oscillator Ising Machines (OIMs) have emerged as promising computational architectures for approximating solutions to combinatorial optimization problems. We derive and analyze the mean-field limit of an OIM model and show that it inherits the gradient-flow structure of the finite-dimensional dynamics. We identify conditions under which this mean-field evolution admits an Eulerian formulation as a gradient flow on the Wasserstein space of probability measures, and contrast this with a Lagrangian formulation which is always available. The gradient-flow structure strongly constrains the long-time dynamics and enables a complete classification of limit solutions and their stability in the symmetric case. In particular, all limit solutions are fixed points whose phases cluster into at most four groups, and for almost all parameter values, only binarized fixed points -- those with clusters at $0$ and/or $π$ -- can be stable. Since binarized states are exactly those for which a feasible solution to the original problem can be read out, this shows that feasible solutions can almost always be recovered. We provide tight bounds on the parameter thresholds for which fixed points in this binarized family are stable, thereby identifying the threshold for binarization in this model. We also present numerical evidence that the mean-field model correctly predicts behavioral regimes in large random networks, including Erdős-Rényi networks.

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arXiv2026

Least-Squares State Estimation, LQR and LQ-Tracking

This note is a tutorial on the Least-Squares State Estimator (LSSE) (the deterministic version of the Kalman-Bucy filter) and related topics. The LSSE is formulated as finding the state trajectory consistent with the system's equations with the minimal amount of L2 process and measurement uncertainty. As stated, this is an input-signal design problem with linear dynamics and affine-quadratic objective in the state and inputs, and therefore a deterministic optimal control problem. We explore its relations to other problems such as the Linear Quadratic Regulator (LQR) with initial or final conditions, as well as the Linear Quadratic (LQ)-tracking problem. Several related topics such as the use of homogeneous coordinates and time reversal in optimal control are explored. The emergence of dynamical controllers/estimators in both LQ-tracking and LSSE as opposed to memoryless ones (as in LQR) is highlighted. It is seen to be a consequence of the affine-quadratic, rather than a purely quadratic form of the cost objective. The relations with the stochastic version of the Kalman-Bucy filter are explicitly highlighted, as well as characterizations in terms of certainty (information) matrices, versus covariance matrices.

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arXiv2026

On the connection between input-output resonances and internal modes of linear time-invariant systems

It is shown that in general, there is no connection between the location of the internal modes of a Linear Time-Invariant (LTI) system and the shape of its input-output frequency response. In particular, it is shown that resonance peaks of the frequency response do not necessarily correspond to under-damped internal modes. This phenomenon, though rare, can occur in high (or infinite) dimensional LTI systems. In the Single Input Single Output (SISO) case, this phenomenon can be attributed to the location of system zeros, while in certain Multi Input Multi Output (MIMO) cases without system zeros, it can be attributed to the non-normality of the matrix generating the internal dynamics.

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arXiv2026

An iterative tangential interpolation algorithm for model reduction of MIMO systems

We consider model reduction of large-scale multi-input, multi-output (MIMO) systems using tangential interpolation in the frequency domain. Our scheme is related to the recently-developed Adaptive Antoulas--Anderson (AAA) algorithm, which is an iterative algorithm that uses concepts from the Loewner framework. Our algorithm has two main features. The first is the use of freedom in interpolation weight matrices to optimize a proxy for an $H_2$ system error. The second is the use of low-rank interpolation, where we iteratively add low-order interpolation data based on several criteria including minimizing maximum errors. We show there is freedom in the interpolation point selection method, leading to multiple algorithms that have trade-offs between computational complexity and approximation performance. We prove that a weighted $H_2$ norm of a representative error system is monotonically decreasing as interpolation points are added. Finally, we provide computational results and some comparisons with prior work, demonstrating performance on par with standard model reduction methods.

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arXiv2025

Optimal Assignment and Motion Control in Two-Class Continuum Swarms

We consider optimal swarm control problems where two different classes of agents are present. Continuum idealizations of large-scale swarms are used where the dynamics describe the evolution of the spatially-distributed densities of each agent class. The problem formulation we adopt is motivated by applications where agents of one class are assigned to agents of the other class, which we refer to as demand and resource agents respectively. Assignments have costs related to the distances between mutually assigned agents, and the overall cost of an assignment is quantified by a Wasserstein distance between the densities of the two agent classes. When agents can move, the assignment cost can decrease at the expense of a physical motion cost, and this tradeoff sets up a nonlinear infinite-dimensional optimal control problem. We show that in one spatial dimension, this problem can be converted to an infinite-dimensional, but decoupled, linear-quadratic (LQ) tracking problem when expressed in terms of the quantile functions of the respective agent densities. Solutions are given in the general one-dimensional case, as well as in the special cases of constant and periodically time-varying demands.

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arXiv2025

On the Gaussian Limit of the Output of IIR Filters

We study the asymptotic distribution of the output of a stable Linear Time-Invariant (LTI) system driven by a non-Gaussian stochastic input. Motivated by longstanding heuristics in the stochastic describing function method, we rigorously characterize when the output process becomes approximately Gaussian, even when the input is not. Using the Wasserstein-1 distance as a quantitative measure of non-Gaussianity, we derive upper bounds on the distance between the appropriately scaled output and a standard normal distribution. These bounds are obtained via Stein's method and depend explicitly on the system's impulse response and the dependence structure of the input process. We show that when the dominant pole of the system approaches the edge of stability and the input satisfies one of the following conditions: (i) independence, (ii) positive correlation with a real and positive dominant pole, or (iii) sufficient correlation decay, the output converges to a standard normal distribution at rate $O(1/\sqrt{t})$. We also present counterexamples where convergence fails, thereby motivating the stated assumptions. Our results provide a rigorous foundation for the widespread observation that outputs of low-pass LTI systems tend to be approximately Gaussian.

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arXiv2025

An Interpolation-based Scheme for Rapid Frequency-Domain System Identification

We present a frequency-domain system identification scheme based on barycentric interpolation and weight optimization. The scheme is related to the Adaptive Antoulas-Anderson (AAA) algorithm for model reduction, but uses an adaptive algorithm for selection of frequency points for interrogating the system response, as would be required in identification versus model reduction. The scheme is particularly suited for systems in which any one sinusoidal response run is long or expensive, and thus there is an incentive to reduce the total number of such runs. Two key features of our algorithm are the use of transient data in sinusoidal runs to both optimize the barycentric weights, and automated next-frequency selection on an adaptive grid. Both are done with error criteria that are proxies for a system's $H^2$ and $H^\infty$ norms respectively. Furthermore, the optimization problem we formulate is convex, and can optionally guarantee stability of the identified system. Computational results on a high-order, lightly damped structural system highlights the efficacy of this scheme.

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arXiv2025

Incompressible Optimal Transport and Applications in Fluid Mixing

The problem of incompressible fluid mixing arises in numerous engineering applications and has been well-studied over the years, yet many open questions remain. This paper aims to address the question "what do efficient flow fields for mixing look like, and how do they behave?" We approach this question by developing a framework which is inspired by the dynamic and geometric approach to optimal mass transport. Specifically, we formulate the fluid mixing problem as an optimal control problem where the dynamics are given by the continuity equation together with an incompressibility constraint. We show that within this framework, the set of reachable fluid configurations can formally be endowed with the structure of an infinite-dimensional Riemannian manifold, with a metric which is induced by the control effort, and that flow fields which are maximally efficient at mixing correspond to geodesics in this Riemannian space.

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arXiv2025

Localization Phenomena in Large-Scale Networked Systems: Robustness and Fragility of Dynamics

We study phenomena where some eigenvectors of a graph Laplacian are largely confined in small subsets of the graph. These localization phenomena are similar to those generally termed Anderson Localization in the Physics literature, and are related to the complexity of the structure of large graphs in still unexplored ways. Using spectral perturbation theory and pseudo-spectrum analysis, we explain how the presence of localized eigenvectors gives rise to fragilities (low robustness margins) to unmodeled node or link dynamics. Our analysis is demonstrated by examples of networks with relatively low complexity, but with features that appear to induce eigenvector localization. The implications of this newly-discovered fragility phenomenon are briefly discussed.

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arXiv2025

Optimal gait design for nonlinear soft robotic crawlers

Soft robots offer a frontier in robotics with enormous potential for safe human-robot interaction and agility in uncertain environments. A stepping stone towards unlocking their potential is a control theory tailored to soft robotics, including a principled framework for gait design. We analyze the problem of optimal gait design for a soft crawling body - the crawler. The crawler is an elastic body with the control signal defined as actuation forces between segments of the body. We consider the simplest such crawler: a two-segmented body with a passive mechanical connection modeling the viscoelastic body dynamics and a symmetric control force modeling actuation between the two body segments. The model accounts for the nonlinear asymmetric friction with the ground, which together with the symmetric actuation forces enable the crawler's locomotion. Using a describing-function analysis, we show that when the body is forced sinusoidally, the optimal actuator contraction frequency corresponds to the body's natural frequency when operating with only passive dynamics. We then use the framework of Optimal Periodic Control (OPC) to design optimal force cycles of arbitrary waveform and the corresponding crawling gaits. We provide a hill-climbing algorithm to solve the OPC problem numerically. Our proposed methods and results inform the design of optimal forcing and gaits for more complex and multi-segmented crawling soft bodies.

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arXiv2024

Optimal estimation in spatially distributed systems: how far to share measurements from?

We consider the centralized optimal estimation problem in spatially distributed systems. We use the setting of spatially invariant systems as an idealization for which concrete and detailed results are given. Such estimators are known to have a degree of spatial localization in the sense that the estimator gains decay in space, with the spatial decay rates serving as a proxy for how far measurements need to be shared in an optimal distributed estimator. In particular, we examine the dependence of spatial decay rates on problem specifications such as system dynamics, measurement and process noise variances, as well as their spatial autocorrelations. We propose non-dimensional parameters that characterize the decay rates as a function of problem specifications. In particular, we find an interesting matching condition between the characteristic lengthscale of the dynamics and the measurement noise correlation lengthscale for which the optimal centralized estimator is completely decentralized. A new technique - termed the Branch Point Locus - is introduced to quantify spatial decay rates in terms of analyticity regions in the complex spatial frequency plane. Our results are illustrated through two case studies of systems with dynamics modeled by diffusion and the Swift-Hohenberg equation, respectively.

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arXiv2024

Causal Tracking of Distributions in Wasserstein Space: A Model Predictive Control Scheme

We consider a problem of optimal swarm tracking which can be formulated as a tracking problem for distributions in the Wasserstein space. Optimal solutions to this problem are non-causal and require knowing the time-trajectory of the reference distribution in advance. We propose a scheme where these non-causal solutions can be used together with a predictive model for the reference to achieve causal tracking of a priori-unknown references. We develop a model-predictive control scheme built around the simple case where the reference is constant-in-time. A computational algorithm based on particle methods and discrete optimal mass transport is presented, and numerical simulations are provided for various classes of reference signals. The results demonstrate that the proposed control algorithm achieves reasonable performance even when using simple predictive models.

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arXiv2024

An Implicit Function Method for Computing the Stability Boundaries of Hill's Equation

Hill's equation is a common model of a time-periodic system that can undergo parametric resonance for certain choices of system parameters. For most kinds of parametric forcing, stable regions in its two-dimensional parameter space need to be identified numerically, typically by applying a matrix trace criterion. By integrating ODEs derived from the stability criterion, we present an alternative, more accurate and computationally efficient numerical method for determining the stability boundaries of Hill's equation in parameter space. This method works similarly to determine stability boundaries for the closely related problem of vibrational stabilization of the linearized Katpiza pendulum. Additionally, we derive a stability criterion for the damped Hill's equation in terms of a matrix trace criterion on an equivalent undamped system. In doing so we generalize the method of this paper to compute stability boundaries for parametric resonance in the presence of damping.

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arXiv2024

Parametric Resonance in Networked Oscillators

We investigate parametric resonance in oscillator networks subjected to periodically time-varying oscillations in the edge strengths. Such models are inspired by the well-known parametric resonance phenomena for single oscillators, as well as the potential rich phenomenology when such parametric excitations are present in a variety of applications like deep brain stimulation, AC power transmission networks, as well as vehicular flocking formations. We consider cases where a single edge, a subgraph, or the entire network is subjected to forcing, and in each case, we characterize an interesting interplay between the parametric resonance modes and the eigenvalues/vectors of the graph Laplacian. Our analysis is based on a novel treatment of multiple-scale perturbation analysis that we develop for the underlying high-dimensional dynamic equations.

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arXiv2024

Excitable crawling

We propose and analyze the suitability of a spiking controller to engineer the locomotion of a soft robotic crawler. Inspired by the FitzHugh-Nagumo model of neural excitability, we design a bistable controller with an electrical flipflop circuit representation capable of generating spikes on-demand when coupled to the passive crawler mechanics. A proprioceptive sensory signal from the crawler mechanics turns bistability of the controller into a rhythmic spiking. The output voltage, in turn, activates the crawler's actuators to generate movement through peristaltic waves. We show through geometric analysis that this control strategy achieves endogenous crawling. The electro-mechanical sensorimotor interconnection provides embodied negative feedback regulation, facilitating locomotion. Dimensional analysis provides insights on the characteristic scales in the crawler's mechanical and electrical dynamics, and how they determine the crawling gait. Adaptive control of the electrical scales to optimally match the mechanical scales can be envisioned to achieve further efficiency, as in homeostatic regulation of neuronal circuits. Our approach can scale up to multiple sensorimotor loops inspired by biological central pattern generators.

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arXiv2024

A Convex Parameterization of Controllers Constrained to use only Relative Measurements

The optimal controller design problem for systems equipped with sensors that measure only relative, rather than absolute, quantities is considered. This relative measurement structure is formulated as a design constraint; it is demonstrated that the resulting constrained controller design problem can be written as a convex program. Certain additional network structural constraints can be incorporated into this formulation, making it especially useful in distributed or networked settings. An illustrative example highlights the advantage of the proposed methodology over the standard formulation of the output feedback controller design problem. A numerical example is provided.

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