arXiv subjects

Karl H. Johansson

Publications and source records attributed to Karl H. Johansson.

At least 55 records · Page 3Linked to original sources

arXiv2026

Data-Driven Nonconvex Reachability Analysis using Exact Set Propagation

This paper studies deterministic data-driven reachability analysis for dynamical systems with unknown dynamics and nonconvex reachable sets. Existing deterministic data-driven approaches typically employ zonotopic set representations, for which the multiplication between a zonotopic model set and a zonotopic state set cannot be represented algebraically exactly, thereby necessitating over-approximation steps in reachable-set propagation. To remove this structural source of conservatism, we introduce constrained polynomial matrix zonotopes (CPMZs) to represent data-consistent model sets, and show that the multiplication between a CPMZ model set and a constrained polynomial zonotope (CPZ) state set admits an algebraically exact CPZ representation. This property enables set propagation entirely within the CPZ representation, thereby avoiding propagation-induced over-approximation and even retaining the ability to represent nonconvex reachable sets. Moreover, we develop set-theoretic results that enable the intersection of data-consistent model sets as new data become available, yielding the proposed online refinement scheme that progressively tightens the data-consistent model set and, in turn, the resulting reachable set. Beyond linear systems, we extend the proposed framework to polynomial dynamics and develop additional set-theoretic results that enable both model-based and data-driven reachability analysis within the same algebraic representation. By deriving algebraically exact CPZ representations for monomials and their compositions, reachable-set propagation can be carried out directly at the set level without resorting to interval arithmetic or relaxation-based bounding techniques. Numerical examples for both linear and polynomial systems demonstrate a significant reduction in conservatism compared to state-of-the-art deterministic data-driven reachability methods.

eess.SY↗

arXiv2026

Communication-Efficient Distributed Learning with Differential Privacy

We address nonconvex learning problems over undirected networks. In particular, we focus on the challenge of designing an algorithm that is both communication-efficient and that guarantees the privacy of the agents' data. The first goal is achieved through a local training approach, which reduces communication frequency. The second goal is achieved by perturbing gradients during local training, specifically through gradient clipping and additive noise. We prove that the resulting algorithm converges to a stationary point of the problem within a bounded distance. Additionally, we provide theoretical privacy guarantees within a differential privacy framework that ensure agents' training data cannot be inferred from the trained model shared over the network. We show the algorithm's superior performance on a classification task under the same privacy budget, compared with state-of-the-art methods.

cs.LG↗

arXiv2026

Secure Filtering against Spatio-Temporal False Data Attacks under Asynchronous Sampling

This paper addresses the secure state estimation problem for continuous linear time-invariant systems with non-periodic and asynchronous sampled measurements, where the sensors need to transmit not only measurements but also sampling time-stamps to the fusion center. This measurement and communication setup is well-suited for operating large-scale control systems and, at the same time, introduces new vulnerabilities that can be exploited by adversaries through (i) manipulation of measurements, (ii) manipulation of time-stamps, (iii) elimination of measurements, (iv) generation of completely new false measurements, or a combination of these attacks. To mitigate these attacks, we propose a decentralized estimation algorithm in which each sensor maintains its local state estimate asynchronously based on its measurements. The local states are synchronized through time prediction and fused after time-stamp alignment. In the absence of attacks, state estimates are proven to recover the optimal Kalman estimates by solving a weighted least square problem. In the presence of attacks, solving this weighted least square problem with the aid of $\ell_1$ regularization provides secure state estimates with uniformly bounded error under an observability redundancy assumption. The effectiveness of the proposed algorithm is demonstrated using a benchmark example of the IEEE 14-bus system.

eess.SY↗

arXiv2026

On a Co-evolving Opinion-Leadership Model in Social Networks

Leadership in social groups is often a dynamic characteristic that emerges from interactions and opinion exchange. Empirical evidence suggests that individuals with strong opinions tend to gain influence, at the same time maintaining alignment with the social context is crucial for sustained leadership. Motivated by the social psychology literature that supports these empirical observations, we propose a novel dynamical system in which opinions and leadership co-evolve within a social network. Our model extends the Friedkin-Johnsen framework by making susceptibility to peer influence time-dependent, turning it into the leadership variable. Leadership strengthens when an agent holds strong yet socially aligned opinions, and declines when such alignment is lost, capturing the trade-off between conviction and social acceptance. After illustrating the emergent behavior of this complex system, we formally analyze the coupled dynamics, establishing sufficient conditions for convergence to a non-trivial equilibrium, and examining two time-scale separation regimes reflecting scenarios where opinion and leadership evolve at different speeds.

physics.soc-ph↗

arXiv2026

RHYME-XT: A Neural Operator for Spatiotemporal Control Systems

We propose RHYME-XT, an operator-learning framework for surrogate modeling of spatiotemporal control systems governed by input-affine nonlinear partial integro-differential equations (PIDEs) with localized rhythmic behavior. RHYME-XT uses a Galerkin projection to approximate the infinite-dimensional PIDE on a learned finite-dimensional subspace with spatial basis functions parameterized by a neural network. This yields a projected system of ODEs driven by projected inputs. Instead of integrating this non-autonomous system, we directly learn its flow map using an architecture for learning flow functions, avoiding costly computations while obtaining a continuous-time and discretization-invariant representation. Experiments on a neural field PIDE show that RHYME-XT outperforms a state-of-the-art neural operator and is able to transfer knowledge effectively across models trained on different datasets, through a fine-tuning process.

cs.LG↗

arXiv2026

Data-Driven Model Order Reduction of Nonlinear Systems with Noisy Data

Model order reduction techniques simplify high-dimensional dynamical systems by deriving lower-dimensional models that retain essential system characteristics. These techniques are crucial for the controller design of complex systems while significantly reducing computational costs. Nevertheless, constructing effective reduced-order models (ROMs) poses considerable challenges, particularly for nonlinear dynamical systems. These challenges are further exacerbated when the actual system model is unavailable, a scenario frequently encountered in real-world applications. In this work, we propose a data-driven framework for constructing ROMs of nonlinear dynamical systems with unknown mathematical models, enabling controller synthesis directly from the resulting ROMs. We establish similarity relations between the output trajectories of the original systems and those of their ROMs by employing the notion of simulation functions (SFs), thereby enabling a formal characterization of their closeness. To achieve this, we collect one set of noise-corrupted input-state data from the system during a finite-time experiment, upon which we propose conditions to construct both ROMs and SFs simultaneously. These conditions are formulated as data-dependent semidefinite programs. We demonstrate that the data-driven ROMs obtained can be employed to synthesize controllers for the original unknown systems, ensuring that they satisfy high-level logic specifications. This is accomplished by first designing controllers for the data-driven ROMs and then translating the results back to the original systems via interface functions, designed directly from the proposed data-dependent conditions. We evaluate the efficacy of our data-driven framework through two case studies, including a challenging benchmark from the model reduction literature: a circuit of chained inverter gates with 20 state variables.

eess.SY↗

arXiv2026

Faster shortest-path algorithms using the acyclic-connected tree

We provide a method to obtain beyond-worst-case time complexity for any single-source-shortest-path (SSSP) algorithm by exploiting modular structures in graphs. The key novelty is a graph decomposition, called the acyclic-connected (A-C) tree, which breaks up a graph into a recursively nested sequence of strongly connected components in topological order. The A-C tree is optimal in the sense that it maximally decomposes the graph, formalised by a parameter called nesting width, measuring the extent to which a graph can be decomposed. We show how to compute the A-C tree in linear time, allowing it to be used as a preprocessing step for SSSP. Indeed, we transform any SSSP algorithm by first computing the A-C tree, and then running the SSSP algorithm in a careful recursive manner on the A-C tree. We illustrate this with two state-of-the-art algorithms: Dijkstra's algorithm and the recent sparse graph algorithm of Duan et al., obtaining improved time complexities of $O(m+n\log(\mathrm{nw}(G)))$ and $O(mα(n)+m\log^{2/3}(\mathrm{nw}(G)))$, respectively, where $\mathrm{nw}(G) \leq n$ is the nesting width of the graph $G$, and $α(n)$ is the extremely slow-growing inverse Ackermann function. Some classes of graphs, such as directed acyclic graphs, have bounded nesting width, and we obtain linear-time SSSP algorithms for these graphs.

cs.DS↗

arXiv2026

Toward Wireless Human-Machine Collaboration in the 6G Era

The next industrial revolution, Industry 5.0, will be driven by advanced technologies that foster human-machine collaboration (HMC). It will leverage human creativity, judgment, and dexterity with the machine's strength, precision, and speed to improve productivity, quality of life, and sustainability. Wireless communications, empowered by the emerging capabilities of sixth-generation (6G) wireless networks, will play a central role in enabling flexible, scalable, and low-cost deployment of geographically distributed HMC systems. In this article, we first introduce the generic architecture and key components of wireless HMC (WHMC). We then present the network topologies of WHMC and highlight impactful applications across various industry sectors. Driven by the prospective applications, we elaborate on new performance metrics that researchers and practitioners may consider during the exploration and implementation of WHMC and discuss new design methodologies. We then summarize the communication requirements and review promising state-of-the-art technologies that can support WHMC. Finally, we present a proof-of-concept case study and identify several open challenges.

eess.SY↗

arXiv2026

Efficient Tail-Aware Generative Optimization via Flow Model Fine-Tuning

Fine-tuning pre-trained diffusion and flow models to optimize downstream utilities is central to real-world deployment. Existing entropy-regularized methods primarily maximize expected reward, providing no mechanism to shape tail behavior. However, tail control is often essential: the lower tail determines reliability by limiting low-reward failures, while the upper tail enables discovery by prioritizing rare, high-reward outcomes. In this work, we present Tail-aware Flow Fine-Tuning (TFFT), a principled and efficient distributional fine-tuning algorithm based on the Conditional Value-at-Risk (CVaR). We address two distinct tail-shaping goals: right-CVaR for seeking novel samples in the high-reward tail and left-CVaR for controlling worst-case samples in the low-reward tail. Unlike prior approaches that rely on non-linear optimization, we leverage the variational dual formulation of CVaR to decompose it into a decoupled two-stage procedure: a lightweight one-dimensional threshold optimization step, and a single entropy-regularized fine-tuning process via a specific pseudo-reward. This decomposition achieves CVaR fine-tuning efficiently with computational cost comparable to standard expected fine-tuning methods. We demonstrate the effectiveness of TFFT across illustrative experiments, high-dimensional text-to-image generation, and molecular design.

cs.LG↗

arXiv2026

Temporally Flexible Transport Scheduling on Networks with Departure-Arrival Constriction and Nodal Capacity Limits

We investigate the optimal transport (OT) problem over networks, wherein supply and demand are conceptualized as temporal marginals governing departure rates of particles from source nodes and arrival rates at sink nodes. This setting extends the classical OT framework, where all mass is conventionally assumed to depart at $t = 0$ and arrive at $t = t_f$. Our generalization accommodates departures and arrivals at specified times, referred as departure--arrival(DA) constraints. In particular, we impose nodal-temporal flux constraints at source and sink nodes, characterizing two distinct scenarios: (i) Independent DA constraints, where departure and arrival rates are prescribed independently, and (ii) Coupled DA constraints, where each particle's transportation time span is explicitly specified. We establish that OT with independent DA constraints admits a multi-marginal optimal transport formulation, while the coupled DA case aligns with the unequal-dimensional OT framework. For line graphs, we analyze the existence and uniqueness of the solution path. For general graphs, we use a constructive path-based reduction and optimize over a prescribed set of paths. From a computational perspective, we consider entropic regularization of the original problem to efficiently provide solutions based on multi-marginal Sinkhorn method, making use of the graphical structure of the cost to further improve scalability. Our numerical simulation further illustrates the linear convergence rate in terms of marginal violation.

math.OC↗

arXiv2026

Pareto-optimal Trade-offs Between Communication and Computation with Flexible Gradient Tracking

This paper addresses distributed stochastic optimization problems under non-i.i.d. data, focusing on the inherent trade-offs between communication and computational efficiency. To this end, we propose FlexGT, a flexible snapshot gradient tracking method that enables tunable numbers of local updates and neighbor communications per round, thereby adapting efficiently to diverse system resource conditions. Leveraging a unified convergence analysis framework, we derive tight communication and computational complexity for FlexGT with explicit dependence on objective properties and certain tunable parameters. Moreover, we introduce an accelerated variant, termed Acc-FlexGT, and prove that, with prior knowledge of the graph, it achieves Pareto-optimal trade-offs between communication and computation. Particularly, in the nonconvex case, Acc-FlexGT achieves the optimal iteration complexity of $\tilde{\mathcal{O}}\left( \left( Lσ^2 \right) /\left( nε^2 \right) +L/\left( ε\sqrt{1-\sqrt{ρ_W}} \right) \right) $ and optimal communication complexity of $\tilde{\mathcal{O}}\left( L/\left( ε\sqrt{1-\sqrt{ρ_W}} \right) \right)$ for appropriately chosen numbers of local updates, matching existing lower bounds up to logarithmic factors. And, it improves the existing results for the strongly convex case by a factor of $\tilde{\mathcal{O}} \left( 1/\sqrtε \right)$, where $ε$ is the targeted accuracy, $n$ the number of nodes, $L$ the Lipschitz constant, $ρ_W$ the connectivity of the graph, and $σ$ the stochastic gradient variance. Numerical experiments corroborate the theoretical results and demonstrate the effectiveness of the proposed methods.

math.OC↗

arXiv2026

Detection and Identification of Sensor Attacks Using Partially Attack-Free Data

In this paper, we investigate data-driven attack detection and identification in a model-free setting. We consider a practically motivated scenario in which the available dataset may be compromised by malicious sensor attacks, but contains an unknown, contiguous, partially attack-free interval. The control input is assumed to include a small stochastic watermarking signal. Under these assumptions, we establish sufficient conditions for attack detection and identification from partially attack-free data. We also develop data-driven detection and identification procedures and characterize their computational complexity. Notably, the proposed framework does not impose a limit on the number of compromised sensors; thus, it can detect and identify attacks even when all sensor outputs are compromised outside the attack-free interval, provided that the attack-free interval is sufficiently long. Finally, we demonstrate the effectiveness of the proposed framework via numerical simulations.

eess.SY↗

arXiv2026

On a Coupled Adoption-Opinion Framework for Competing Innovations

In this paper, we propose a two-layer adoption-opinion model to study the diffusion of two competing technologies within a population whose opinions evolve under social influence and adoption-driven feedback. After adopting one technology, individuals may become dissatisfied and switch to the alternative. We prove the existence and uniqueness of the adoption-diffused equilibrium, showing that both technologies coexist and that neither partial-adoption nor monopoly can arise. Numerical simulations show that while opinions shape the equilibrium adoption levels, the relative market share between the two technologies depends solely on their user-experience. As a consequence, interventions that symmetrically boost opinions or adoption can disproportionately favor the higher-quality technology, illustrating how symmetric control actions may generate asymmetric outcomes.

eess.SY↗

arXiv2026

Communication-Efficient Stochastic Distributed Learning

We address distributed learning problems, both nonconvex and convex, over undirected networks. In particular, we design a novel algorithm based on the distributed Alternating Direction Method of Multipliers (ADMM) to address the challenges of high communication costs, and large datasets. Our design tackles these challenges i) by enabling the agents to perform multiple local training steps between each round of communications; and ii) by allowing the agents to employ stochastic gradients while carrying out local computations. We show that the proposed algorithm converges to a neighborhood of a stationary point, for nonconvex problems, and of an optimal point, for convex problems. We also propose a variant of the algorithm to incorporate variance reduction thus achieving exact convergence. We show that the resulting algorithm indeed converges to a stationary (or optimal) point, and moreover that local training accelerates convergence. We thoroughly compare the proposed algorithms with the state of the art, both theoretically and through numerical results.

cs.LG↗

arXiv2025

Risk-Averse Learning with Varying Risk Levels

In safety-critical decision-making, the environment may evolve over time, and the learner adjusts its risk level accordingly. This work investigates risk-averse online optimization in dynamic environments with varying risk levels, employing Conditional Value-at-Risk (CVaR) as the risk measure. To capture the dynamics of the environment and risk levels, we employ the function variation metric and introduce a novel risk-level variation metric. Two information settings are considered: a first-order scenario, where the learner observes both function values and their gradients; and a zeroth-order scenario, where only function evaluations are available. For both cases, we develop risk-averse learning algorithms with a limited sampling budget and analyze their dynamic regret bounds in terms of function variation, risk-level variation, and the total number of samples. The regret analysis demonstrates the adaptability of the algorithms in non-stationary and risk-sensitive settings. Finally, numerical experiments are presented to demonstrate the efficacy of the methods.

math.OC↗

arXiv2025

Personalized and Resilient Distributed Learning Through Opinion Dynamics

In this paper, we address two practical challenges of distributed learning in multi-agent network systems, namely personalization and resilience. Personalization is the need of heterogeneous agents to learn local models tailored to their own data and tasks, while still generalizing well; on the other hand, the learning process must be resilient to cyberattacks or anomalous training data to avoid disruption. Motivated by a conceptual affinity between these two requirements, we devise a distributed learning algorithm that combines distributed gradient descent and the Friedkin-Johnsen model of opinion dynamics to fulfill both of them. We quantify its convergence speed and the neighborhood that contains the final learned models, which can be easily controlled by tuning the algorithm parameters to enforce a more personalized/resilient behavior. We numerically showcase the effectiveness of our algorithm on synthetic and real-world distributed learning tasks, where it achieves high global accuracy both for personalized models and with malicious agents compared to standard strategies.

cs.MA↗

arXiv2025

Data-Driven Nonconvex Reachability Analysis using Exact Multiplication

This paper addresses a fundamental challenge in data-driven reachability analysis: accurately representing and propagating non-convex reachable sets. We propose a novel approach using constrained polynomial zonotopes to describe reachable sets for unknown LTI systems. Unlike constrained zonotopes commonly used in existing literature, constrained polynomial zonotopes are closed under multiplication with constrained matrix zonotopes. We leverage this property to develop an exact multiplication method that preserves the non-convex geometry of reachable sets without resorting to approximations. We demonstrate that our approach provides tighter over-approximations of reachable sets for LTI systems compared to conventional methods.

eess.SY↗

arXiv2025

Jointly Computation- and Communication-Efficient Distributed Learning

We address distributed learning problems over undirected networks. Specifically, we focus on designing a novel ADMM-based algorithm that is jointly computation- and communication-efficient. Our design guarantees computational efficiency by allowing agents to use stochastic gradients during local training. Moreover, communication efficiency is achieved as follows: i) the agents perform multiple training epochs between communication rounds, and ii) compressed transmissions are used. We prove exact linear convergence of the algorithm in the strongly convex setting. We corroborate our theoretical results by numerical comparisons with state of the art techniques on a classification task.

cs.LG↗