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Karl H. Johansson

Publications and source records attributed to Karl H. Johansson.

At least 19 recordsLinked to original sources
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.

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arXiv2026

Noisy-Space Policy Gradient for Diffusion Policies in Offline Reinforcement Learning

Diffusion policies offer a powerful and expressive parameterization for continuous control. Yet, their integration with reinforcement learning remains conceptually and algorithmically challenging. In this work, we address this gap by introducing a noisy-space action-value (Q-)function that assigns values to diffusion latents through the distribution of executed actions induced by the denoising process. We show that this construction admits a precise semantic interpretation and derive a noisy-space policy gradient (NSPG) that optimizes noisy latents using only clean action-space value estimates. Building on this result, we formulate a KL-regularized policy improvement over noisy latents and show that the resulting objective admits a diffusion-compatible regression form, avoiding backpropagation through the denoising process. Empirical results on state-based D4RL benchmarks and vision-based OGBench tasks demonstrate that the proposed noisy-space objective provides a principled and effective basis for training diffusion policies in offline reinforcement learning. Project webpage: https://mahmoud-selim.github.io/NSPG/

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arXiv2026

Distributed risk-averse optimization via CVaR

Distributed systems often operate under uncertainty, where minimizing expected loss may overlook rare but severe events. This paper studies a distributed risk-averse convex optimization problem in which agents cooperatively minimize the average of local conditional value-at-risk (CVaR) objectives over a time-varying network. Each agent has access only to noisy evaluations of its local loss function, rather than to its CVaR objective or gradient. We therefore develop a zeroth-order algorithm that uses sampled losses to construct empirical CVaR estimates and their gradient estimates. At each iteration, agents combine neighboring decisions and perform a local update. Under convexity and Lipschitz continuity assumptions, we prove that the agents reach exact asymptotic consensus. We also establish a finite-time expected suboptimality bound for the weighted ergodic iterate. With diminishing step sizes and fixed sample sizes, the local last iterates converge almost surely to a common optimum, and their limiting expected CVaR gap is bounded in terms of the smoothing and finite-sample errors. This distributed bound matches the parameter dependence of the centralized benchmark provided in this paper. Finally, simulations on a distributed sensor network estimation problem illustrate the efficacy of the method.

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arXiv2026

Demonstration of Space Robot Teleoperation over a Lossy and Delayed Network using ATMOS

We present a demonstration showcasing the Autonomy Testbed for Multi-purpose Orbiting Systems (ATMOS), a planar spacecraft-analog robot designed for hardware-in-the-loop evaluation of guidance and control strategies in microgravity-like conditions. Using ATMOS as the physical test platform, we investigate the design, analysis, and performance evaluation of control architectures for remotely operated spacecraft under round-trip communication delays. In this work, we develop and experimentally validate a control strategy that combines state prediction and trajectory tracking control to perform a docking maneuver, accounting for time-varying random communication latency between ground operators and the ATMOS system. The demonstration includes a long-distance remote control experiment between Seoul and Stockholm, introducing realistic intercontinental delays and variability. The results highlight the capability of ATMOS to support rapid, reliable, and cost-effective testing of spacecraft teleoperation concepts, establishing a first step toward robust validation of on-orbit operations in microgravity-like environments.

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arXiv2026

From Noisy Data to Hierarchical Control: A Model-Order-Reduction Framework

This paper develops a direct data-driven framework for constructing reduced-order models (ROMs) of discrete-time linear dynamical systems with unknown dynamics and process disturbances. The proposed scheme enables controller synthesis on the ROM and its refinement to the original system via an interface function designed using noisy data. To achieve this, the notion of simulation functions (SFs) is employed to establish a formal relation between the original system and its ROM, yielding a quantitative bound on the mismatch between their output trajectories. To construct such relations and interface functions, we rely on data collected from the unknown system. In particular, using noise-corrupted input-state data gathered along a single trajectory of the system, and without identifying the original dynamics, we propose data-dependent conditions, cast as a semidefinite program, for the simultaneous construction of ROMs, SFs, and interface functions. Through a case study, we demonstrate that data-driven controller synthesis on the ROM, combined with controller refinement via the interface function, enables the satisfaction of complex logic specifications.

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arXiv2026

Iterative Training of Physics-Informed Neural Networks with Fourier-enhanced Features

Spectral bias, the tendency of neural networks to learn low-frequency features first, is a well-known issue with many training algorithms for physics-informed neural networks (PINNs). To overcome this issue, we propose IFeF-PINN, an algorithm for iterative training of PINNs with Fourier-enhanced features. The key idea is to enrich the latent space using high-frequency components through Random Fourier Features. This creates a two-stage training problem: (i) estimate a basis in the feature space, and (ii) perform regression to determine the coefficients of the enhanced basis functions. For an underlying linear model, it is shown that the latter problem is convex, and we prove that the iterative training scheme converges. Furthermore, we empirically establish that Random Fourier Features enhance the expressive capacity of the network, enabling accurate approximation of high-frequency PDEs. Through extensive numerical evaluation on classical benchmark problems, the superior performance of our method over state-of-the-art algorithms is shown, and the improved approximation across the frequency domain is illustrated.

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arXiv2026

Alternating Levenberg-Marquardt Training of Physics-Informed Neural Networks with Fourier-Enhanced Features

Physics-informed neural networks (PINNs) often fail to accurately resolve partial differential equations (PDEs) with high-frequency or multi-scale solutions, as well as strongly nonlinear problems. Two factors underlie this difficulty: spectral bias, the tendency of neural networks to underfit high-frequency features; and representation-coefficient coupling, the entanglement of representation learning and coefficient fitting within a single nonconvex optimization objective. In this work, we propose the Fourier-enhanced alternating Levenberg--Marquardt PINN (FALM-PINN), an optimization framework that decouples representation learning from coefficient fitting. The upper-level problem learns a Fourier-enhanced basis that enriches the latent space with high-frequency components, while the lower-level problem resolves the coupling by fitting the projection coefficients on this basis, solving a nonlinear least-squares problem with the Levenberg--Marquardt algorithm. The framework applies to general nonlinear and coupled PDE systems, and reduces to a single-step convex optimization problem for linear PDEs. We prove global convergence of the alternating training scheme in both cases. Numerical examples on multiple challenging high-frequency and nonlinear PDEs show that FALM-PINN achieves relative $L^2$ errors up to two orders of magnitude lower than state-of-the-art baselines.

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arXiv2026

Secure Set-based State Estimation for Safety-Critical Applications under Adversarial Attacks on Sensors

Set-based state estimation provides guaranteed state inclusion certificates that are crucial for the safety verification of dynamical systems. However, when system sensors are subject to cyberattacks, maintaining both safety and security guarantees becomes a fundamental challenge. Existing point-based secure state estimation methods cannot adequately address this challenge because they cannot provide state inclusion certificates. This paper introduces a novel approach that simultaneously ensures safety guarantees through guaranteed state inclusion and security guarantees against sensor attacks, without imposing conservative restrictions on system operation. We propose a Secure Set-based State Estimation (S3E) algorithm that maintains the true system state within the estimated set under sensor attacks, provided the initialization set contains the initial state and the system remains observable from the uncompromised sensor subset. The algorithm provides the estimated set as a collection of constrained zonotopes (agreement sets), which can be used as robust certificates to verify whether the system adheres to safety constraints. Furthermore, we demonstrate that the estimated set remains unaffected by attack signals of sufficiently large magnitude and also establish sufficient conditions for attack detection, identification, and filtering. This compels the attacker to inject only signals of small magnitudes to evade detection, thus preserving the accuracy of the estimated set. To address the computational complexity of the algorithm, we offer several strategies for complexity-performance tradeoffs. The efficacy of the proposed algorithm is illustrated through several examples, including its application to a three-story building model.

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arXiv2026

MetaKoopman: Bayesian Meta-Learning of Koopman Operators for Modeling Structured Dynamics under Distribution Shifts

Modeling and forecasting nonlinear dynamics under distribution shifts is essential for robust decision-making in real-world systems. In this work, we propose MetaKoopman, a Bayesian meta-learning framework for modeling nonlinear dynamics through linear latent representations. MetaKoopman learns a Matrix Normal-Inverse Wishart (MNIW) prior over the Koopman operator, enabling closed-form Bayesian updates conditioned on recent trajectory segments. Moreover, it provides a closed-form posterior predictive distribution over future state trajectories, capturing both epistemic and aleatoric uncertainty in the learned dynamics. We evaluate MetaKoopman on a full-scale autonomous truck and trailer system across a wide range of adverse winter scenarios, including snow, ice, and mixed-friction conditions, as well as in simulated control tasks with diverse distribution shifts. MetaKoopman consistently outperforms prior approaches in multi-step prediction accuracy, uncertainty calibration, and robustness to distributional shifts. Field experiments further demonstrate its effectiveness in dynamically feasible motion planning, particularly during evasive maneuvers and operation at the limits of traction. Project website: https://mahmoud-selim.github.io/MetaKoopman/

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arXiv2026

Decentralized Linearized Consensus ADMM with Efficient Quantized Communication

Distributed optimization offers significant advantages over centralized methods in terms of scalability and robustness when solving large-scale problems. In this paper, we propose a novel decentralized optimization algorithm that integrates Inexact Consensus ADMM (IC-ADMM) with a finite-time decentralized quantized communication algorithm. The proposed method enjoys three main benefits: (i) it operates on directed communication graphs, (ii) it requires only quantized local information instead of exact values, and (iii) it does not rely on solving the local subproblems exactly. Under the assumption that each node's local objective is strongly convex and L-smooth, the algorithm is guaranteed to achieve global linear convergence to a neighborhood of the optimal solution. Extensive numerical experiments demonstrate its advantages over existing methods in terms of convergence speed and communication efficiency.

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arXiv2026

CADMM-Prox: A Bi-level Consensus ADMM for Non-smooth Non-convex Distributed Consensus Optimization

Non-smooth and non-convex optimization problems are pervasive in machine learning, control, and signal processing, due to the need for sparse solutions and the inherently non-convex nature of many objective functions. In this paper, we study non-smooth and non-convex distributed optimization problems. We propose a novel bi-level Consensus Alternating Direction Method of Multipliers (ADMM) algorithm, termed CADMM-Prox. The proposed algorithm integrates classical Consensus ADMM with a proximal mechanism by introducing a sufficiently large proximal term associated with an outer-level variable. Under the mild assumption that the local objective functions are semi-convex, CADMM-Prox is guaranteed to converge globally to a neighborhood of a Clarke stationary point. Numerical experiments on a phase retrieval problem demonstrate that our proposed method exhibits more stable convergence behavior compared with baseline algorithm.

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arXiv2026

On Optimal Event-Triggered Distributed Control for Stochastic Multi-Agent Systems via Reinforcement Learning

We propose a reinforcement learning (RL) based optimal distributed control algorithm for the multi-agent systems (MASs) with stochastic uncertainties. Unlike existing methods, during the optimized backstepping design process, we use the actor-critic-identifier structure. The actor neural network is used to reflect control behavior, the critic neural network works to evaluate control performance and the unknown stochastic uncertainties are handled by identifier neural network. Furthermore, a low-pass filter effectively suppresses problems stemming from non-affine nonlinear faults and a hybrid event-triggered control (ETC) strategy is proposed to reduce control frequency. We analyze our algorithm's operation, and we provide a Lyapunov-based stability proof that guarantees all errors are bounded, ensuring precise tracking between the leader and followers. We validate its correctness in a single-axis robotic manipulator simulation and finally, we compare against the non-optimal control algorithm highlighting our optimal control algorithm's operational advantages.

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arXiv2026

Approximate Simulation-Based Verification of Compatibility of the Friedkin-Johnsen Model with Binary Observations

We consider a verification problem for opinion dynamics based on binary observations. The opinion dynamics is governed by a Friedkin-Johnsen (FJ) model, where only a sequence of binary outputs is available instead of the agents' continuous opinions. At every time-step we observe a binarized output for each agent depending on whether the opinion exceeds a fixed threshold. The objective is to verify whether an FJ model with a given set of stubbornness parameters and initial opinions can generate the observed binary outputs up to a small error. The FJ model is formulated as a transition system, and an approximate simulation relation of two transition systems is defined in terms of the proximity of their opinion trajectories and output sequences. We then construct a finite set of abstract FJ models by simplifying the influence matrix and discretizing the stubbornness parameters and the initial opinions. It is shown that the abstraction approximately simulates any concrete FJ model with continuous parameters and initial opinions, and is itself approximately simulated by some concrete FJ model. These results ensure that consistency verification can be performed over the finite abstraction. Specifically, by checking whether an abstract model satisfies the observation constraints, we can conclude whether the corresponding family of concrete FJ models is consistent with the binary observations. Finally, numerical experiments are presented to illustrate the proposed verification framework.

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arXiv2026

Security Index from Input/Output Data: Theory and Computation

The concept of a security index quantifies the minimum number of components that must be compromised to carry out a stealth attack. This metric enables system operators to assess the security risk of each component and implement countermeasures accordingly. In this paper, we introduce a data-driven security index that can be computed solely from input/output data when the system model is unknown. We show a sufficient condition under which the data-driven security index coincides with the model-based security index, which implies that the exact risk level of each component can be identified solely from data. We also provide an algorithm for computing the data-driven security index.

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arXiv2026

Distributed Traffic State Estimation in Connected Vehicle and Roadside Infrastructure Networks

This paper proposes a distributed traffic state estimation framework that combines infrastructure sensors and connected vehicles as cooperative sensing nodes. Using Vehicle-to-Everything (V2X) communication, nearby nodes exchange local estimates and update them through a distributed Kalman filter designed for a second-order macroscopic traffic flow model. A consensus step fuses heterogeneous information across the network, while projection steps enforce physically consistent traffic states. We evaluate the method on HighD and NGSIM data, and on microscopic SUMO simulations that capture transient congestion. The results show accurate reconstruction of highway traffic states and detection of nonlinear shockwave dynamics, even with sparse infrastructure sensing and intermittent vehicular connectivity. A statistical analysis further shows how CV penetration rate, V2X communication range, and infrastructure deployment affect estimation accuracy. In particular, with 10% CV penetration, V2X ranges of 300-400 m, and sparse infrastructure deployment, the combined infrastructure-vehicle configuration consistently outperforms approaches that rely only on infrastructure or only on connected vehicles.

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arXiv2026

Wasserstein Robust Performative Prediction via Lagrangian Relaxation

In machine learning, predictive models are trained on historical data. Their deployment may incentivize agents to strategically adapt their behavior, thereby inducing a model-dependent distribution shift. This phenomenon is known as performativity. This paper develops a Wasserstein distributionally robust framework for performative prediction, where the predictive model only has access to limited data. Using these data, we construct an ambiguity set centered on the empirical distribution, and optimize the predictive model against the worst-case distribution. Furthermore, we reformulate the objective as a tractable min-max optimization problem via Lagrangian relaxation, and allow the penalty to depend on the prediction model. Based on this, we develop distributionally robust repeated risk minimization (DR-RRM) and repeated gradient descent (DR-RGD) algorithms to iteratively find a performative stable point amid distributional shifts and model retraining. We theoretically show that both algorithms converge to a stable point linearly under standard regularity conditions. When accounting for approximation errors in the optimization problems, both algorithms converge to a neighborhood of the stable point. Additionally, we establish theoretical bounds on the suboptimality gap between the stable point and the global performative optimum. Finally, numerical simulations of a dynamic credit scoring problem demonstrate the efficacy of the method.

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arXiv2026

Distributed Resilient State Estimation and Control with Strategically Implemented Security Measures

This paper addresses the problem of distributed resilient state estimation and control for linear time-invariant systems in the presence of malicious false data injection sensor attacks and bounded noise. We consider a system operator (defender) capable of deploying cybersecurity measures to counteract the sensor compromises. Although such measures enhance resilience against adversarial attacks, they may incur substantial costs; hence, it is crucial to select countermeasures to balance resilience gains and cost efficiency strategically. We first demonstrate that the system's resilience against attacks is maximized through the appropriate implementation of security measures, implying that no attacker can execute undetectable sensor attacks. Building on this analysis, we propose an algorithm that identifies the optimal security measure. While determining this measure is NP-hard in general, we also derive sufficient conditions under which efficient computation is feasible. Furthermore, we develop a distributed resilient state estimation and control scheme informed by the optimal security measure and establish conditions that guarantee bounded estimation and control errors. Finally, we validate the efficacy of our approach via numerical simulations of a vehicle platooning scenario.

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arXiv2026

Unified Communication Compression Beyond Global Error Bounds for Distributed Nonconvex Optimization

In this paper, we propose a unified compression algorithm for distributed nonconvex opitmization with both the locally- and globally-bounded communication compressors, including 1-bit compressors, saturating quantizers, and the globally-bounded compressors with both relative and absolute compression errors, as well as additional arbitrary bounded noise. We provide a rigorous convergence analysis in nonconvex settings and establish linear convergence under the Polyak-Lojasiewicz (P-L) condition. Notably, we establish an $\mathcal{O}(1/\sqrt{T})$ convergence rate for the locally-bounded class in the distributed nonconvex setting, matching that achieved by the centralized algorithms with 1-bit compressors, where $T$ denotes the total number of iterations. Moreover, one initial uncompressed communication round further yields an order-wise improvement to $\mathcal{O}(1/T^{2/3})$. For the P-L setting and the globally-bounded class, we recover state-of-the-art convergence rates.

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