arXiv subjects

Karl H. Johansson

Publications and source records attributed to Karl H. Johansson.

At least 91 records · Page 5Linked to original sources

arXiv2025

Adding links wisely: how an influencer seeks for leadership in opinion dynamics?

This paper investigates the problem of leadership development for an external influencer using the Friedkin-Johnsen (FJ) opinion dynamics model, where the influencer is modeled as a fully stubborn agent and leadership is quantified by social power. The influencer seeks to maximize her social power by strategically adding a limited number of links to regular agents. This optimization problem is shown to be equivalent to maximizing the absorbing probability to the influencer in an augmented Markov chain. The resulting objective function is both monotone and submodular, enabling the use of a greedy algorithm to compute an approximate solution. To handle large-scale networks efficiently, a random walk sampling over the Markov chain is employed to reduce computational complexity. Analytical characterizations of the solution are provided for both low and high stubbornness of regular agents. Specific network topologies are also examined: for complete graphs with rank-one weight matrices, the problem reduces to a hyperbolic 0-1 programmming problem, which is solvable in polynomial time; for symmetric ring graphs with circulant weight matrices and uniform agent stubbornness, the optimal strategy involves selecting agents that are sufficiently dispersed across the network. Numerical simulations are presented for illustration.

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arXiv2025

Parallel Model Predictive Control for Deterministic Systems

In this note, we consider infinite horizon optimal control problems with deterministic systems. Since exact solutions to these problems are often intractable, we propose a parallel model predictive control (MPC) method that provides an approximate solution. Our method computes multiple lookahead minimization problems at each time, where each minimization may involve a different number of lookahead steps, and terminal cost and constraint. The policy computed via parallel MPC applies the first control of the lookahead minimization with the lowest cost. We show that the proposed method can harnesses the power of multiple computing units. Moreover, we prove that the policy computed via parallel MPC has better performance guarantee than that computed via the single lookahead minimization involved in parallel MPC.

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arXiv2025

Distributed Optimization with Efficient Communication, Event-Triggered Solution Enhancement, and Operation Stopping

In modern large-scale systems with sensor networks and IoT devices it is essential to collaboratively solve complex problems while utilizing network resources efficiently. In our paper we present three distributed optimization algorithms that exhibit efficient communication among nodes. Our first algorithm presents a simple quantized averaged gradient procedure for distributed optimization, which is shown to converge to a neighborhood of the optimal solution. Our second algorithm incorporates a novel event-triggered refinement mechanism, which refines the utilized quantization level to enhance the precision of the estimated optimal solution. It enables nodes to terminate their operation according to predefined performance guarantees. Our third algorithm is tailored to operate in environments where each message consists of only a few bits. It incorporates a novel event-triggered mechanism for adjusting the quantizer basis and quantization level, allowing nodes to collaboratively decide operation termination based on predefined performance criteria. We analyze the three algorithms and establish their linear convergence. Finally, an application on distributed sensor fusion for target localization is used to demonstrate their favorable performance compared to existing algorithms in the literature.

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arXiv2025

A Centralized Planning and Distributed Execution Method for Shape Filling with Homogeneous Mobile Robots

The pattern formation task is commonly seen in a multi-robot system. In this paper, we study the problem of forming complex shapes with functionally limited mobile robots, which have to rely on other robots to precisely locate themselves. The goal is to decide whether a given shape can be filled by a given set of robots; in case the answer is yes, to complete a shape formation process as fast as possible with a minimum amount of communication. Traditional approaches either require global coordinates for each robot or are prone to failure when attempting to form complex shapes beyond the capability of given approaches - the latter calls for a decision procedure that can tell whether a target shape can be formed before the actual shape-forming process starts. In this paper, we develop a method that does not require global coordinate information during the execution process and can effectively decide whether it is feasible to form the desired shape. The latter is achieved via a planning procedure that is capable of handling a variety of complex shapes, in particular, those with holes, and assigning a simple piece of scheduling information to each robot, facilitating subsequent distributed execution, which does not rely on the coordinates of all robots but only those of neighboring ones. The effectiveness of our shape-forming approach is vividly illustrated in several simulation case studies.

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arXiv2025

Distributed Prescribed-Time Observer for Nonlinear Systems in Block-Triangular Form

This paper proposes a distributed prescribed-time observer for nonlinear systems representable in a block-triangular observable canonical form. Using a weighted average of neighbor estimates exchanged over a strongly connected digraph, each observer estimates the system state despite the limited observability of local sensor measurements. The proposed design guarantees that distributed state estimation errors converge to zero at a user-specified convergence time, irrespective of observers' initial conditions. To achieve this prescribed-time convergence, distributed observers implement time-varying local output injection gains that monotonically increase and approach infinity at the prescribed time. The theoretical convergence is rigorously proven and validated through numerical simulations, where some implementation issues due to increasing gains have also been clarified.

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arXiv2025

Cloud-Fog Automation: The New Paradigm towards Autonomous Industrial Cyber-Physical Systems

Autonomous Industrial Cyber-Physical Systems (ICPS) represent a future vision where industrial systems achieve full autonomy, integrating physical processes seamlessly with communication, computing and control technologies while holistically embedding intelligence. Cloud-Fog Automation is a new digitalized industrial automation reference architecture that has been recently proposed. This architecture is a fundamental paradigm shift from the traditional International Society of Automation (ISA)-95 model to accelerate the convergence and synergy of communication, computing, and control towards a fully autonomous ICPS. With the deployment of new wireless technologies to enable almost-deterministic ultra-reliable low-latency communications, a joint design of optimal control and computing has become increasingly important in modern ICPS. It is also imperative that system-wide cyber-physical security are critically enforced. Despite recent advancements in the field, there are still significant research gaps and open technical challenges. Therefore, a deliberate rethink in co-designing and synergizing communications, computing, and control (which we term "3C co-design") is required. In this paper, we position Cloud-Fog Automation with 3C co-design as the new paradigm to realize the vision of autonomous ICPS. We articulate the state-of-the-art and future directions in the field, and specifically discuss how goal-oriented communication, virtualization-empowered computing, and Quality of Service (QoS)-aware control can drive Cloud-Fog Automation towards a fully autonomous ICPS, while accounting for system-wide cyber-physical security.

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arXiv2025

Sequential Binary Hypothesis Testing with Competing Agents under Information Asymmetry

This paper concerns sequential hypothesis testing in competitive multi-agent systems where agents exchange potentially manipulated information. Specifically, a two-agent scenario is studied where each agent aims to correctly infer the true state of nature while optimizing decision speed and accuracy. At each iteration, agents collect private observations, update their beliefs, and share (possibly corrupted) belief signals with their counterparts before deciding whether to stop and declare a state, or continue gathering more information. The analysis yields three main results: (1)~when agents share information strategically, the optimal signaling policy involves equal-probability randomization between truthful and inverted beliefs; (2)~agents maximize performance by relying solely on their own observations for belief updating while using received information only to anticipate their counterpart's stopping decision; and (3)~the agent reaching their confidence threshold first cause the other agent to achieve a higher conditional probability of error. Numerical simulations further demonstrate that agents with higher KL divergence in their conditional distributions gain competitive advantage. Furthermore, our results establish that information sharing -- despite strategic manipulation -- reduces overall system stopping time compared to non-interactive scenarios, which highlights the inherent value of communication even in this competitive setup.

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arXiv2025

Reduced Network Cumulative Constraint Violation for Distributed Bandit Convex Optimization under Slater Condition

This paper studies the distributed bandit convex optimization problem with time-varying inequality constraints, where the goal is to minimize network regret and cumulative constraint violation. To calculate network cumulative constraint violation, existing distributed bandit online algorithms solving this problem directly use the clipped constraint function to replace its original constraint function. However, the use of the clipping operation renders Slater condition (i.e, there exists a point that strictly satisfies the inequality constraints at all iterations) ineffective to achieve reduced network cumulative constraint violation. To tackle this challenge, we propose a new distributed bandit online primal-dual algorithm. If local loss functions are convex, we show that the proposed algorithm establishes sublinear network regret and cumulative constraint violation bounds. When Slater condition holds, the network cumulative constraint violation bound is reduced. In addition, if local loss functions are strongly convex, for the case where strongly convex parameters are unknown, the network regret bound is reduced. For the case where strongly convex parameters are known, the network regret and cumulative constraint violation bounds are further reduced. To the best of our knowledge, this paper is among the first to establish reduced (network) cumulative constraint violation bounds for (distributed) bandit convex optimization with time-varying constraints under Slater condition. Finally, a numerical example is provided to verify the theoretical results.

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arXiv2025

Task Allocation for Multi-agent Systems via Unequal-dimensional Optimal Transport

We consider a probabilistic model for large-scale task allocation problems for multi-agent systems, aiming to determine an optimal deployment strategy that minimizes the overall transport cost. Specifically, we assign transportation agents to delivery tasks with given pick-up and drop-off locations, pairing the spatial distribution of transport resources with the joint distribution of task origins and destinations. This aligns with the optimal mass transport framework where the problem and is in the unequal-dimensional setting. The task allocation problem can be thus seen as a linear programming problem that minimizes a quadratic transport cost functional, optimizing the energy of all transport units. The problem is motivated by time-sensitive medical deliveries using drones, such as emergency equipment and blood transport. In this paper, we establish the existence, uniqueness, and smoothness of the optimal solution, and illustrate its properties through numerical simulations.

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arXiv2025

Quantized Distributed Nonconvex Optimization Algorithms with Linear Convergence under the Polyak--$Ł$ojasiewicz Condition

This paper considers distributed optimization for minimizing the average of local nonconvex cost functions, by using local information exchange over undirected communication networks. To reduce the required communication capacity, we introduce an encoder--decoder scheme. By integrating them with distributed gradient tracking and proportional integral algorithms, respectively, we then propose two quantized distributed nonconvex optimization algorithms. Assuming the global cost function satisfies the Polyak--Łojasiewicz condition, which does not require the global cost function to be convex and the global minimizer is not necessarily unique, we show that our proposed algorithms linearly converge to a global optimal point and that larger quantization level leads to faster convergence speed. Moreover, we show that a low data rate is sufficient to guarantee linear convergence when the algorithm parameters are properly chosen. The theoretical results are illustrated by numerical examples.

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arXiv2025

Compressed Gradient Tracking Algorithms for Distributed Nonconvex Optimization

In this paper, we study the distributed nonconvex optimization problem, which aims to minimize the average value of the local nonconvex cost functions using local information exchange. To reduce the communication overhead, we introduce three general classes of compressors, i.e., compressors with bounded relative compression error, compressors with globally bounded absolute compression error, and compressors with locally bounded absolute compression error. By integrating them with distributed gradient tracking algorithm, we then propose three compressed distributed nonconvex optimization algorithms. For each algorithm, we design a novel Lyapunov function to demonstrate its sublinear convergence to a stationary point if the local cost functions are smooth. Furthermore, when the global cost function satisfies the Polyak--Łojasiewicz (P--Ł) condition, we show that our proposed algorithms linearly converge to a global optimal point. It is worth noting that, for compressors with bounded relative compression error and globally bounded absolute compression error, our proposed algorithms' parameters do not require prior knowledge of the P--Ł constant. The theoretical results are illustrated by numerical examples, which demonstrate the effectiveness of the proposed algorithms in significantly reducing the communication burden while maintaining the convergence performance. Moreover, simulation results show that the proposed algorithms outperform state-of-the-art compressed distributed nonconvex optimization algorithms.

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arXiv2025

A continuous-time violation-free multi-agent optimization algorithm and its applications to safe distributed control

In this work, we propose a continuous-time distributed optimization algorithm with guaranteed zero coupling constraint violation and apply it to safe distributed control in the presence of multiple control barrier functions (CBF). The optimization problem is defined over a network that collectively minimizes a separable cost function with coupled linear constraints. An equivalent optimization problem with auxiliary decision variables and a decoupling structure is proposed. A sensitivity analysis demonstrates that the subgradient information can be computed using local information. This then leads to a subgradient algorithm for updating the auxiliary variables. A case with sparse coupling constraints is further considered, and it is shown to have better memory and communication efficiency. For the specific case of a CBF-induced time-varying quadratic program (QP), an update law is proposed that achieves finite-time convergence. Numerical results involving a static resource allocation problem and a safe coordination problem for a multi-agent system demonstrate the efficiency and effectiveness of our proposed algorithms.

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arXiv2025

Optimization and Learning in Open Multi-Agent Systems

Modern artificial intelligence relies on networks of agents that collect data, process information, and exchange it with neighbors to collaboratively solve optimization and learning problems. This article introduces a novel distributed algorithm to address a broad class of these problems in "open networks", where the number of participating agents may vary due to several factors, such as autonomous decisions, heterogeneous resource availability, or DoS attacks. Extending the current literature, the convergence analysis of the proposed algorithm is based on the newly developed "Theory of Open Operators", which characterizes an operator as open when the set of components to be updated changes over time, yielding to time-varying operators acting on sequences of points of different dimensions and compositions. The mathematical tools and convergence results developed here provide a general framework for evaluating distributed algorithms in open networks, allowing to characterize their performance in terms of the punctual distance from the optimal solution, in contrast with regret-based metrics that assess cumulative performance over a finite-time horizon. As illustrative examples, the proposed algorithm is used to solve dynamic consensus or tracking problems on different metrics of interest, such as average, median, and min/max value, as well as classification problems with logistic loss functions.

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arXiv2024

Enhancing Privacy in Federated Learning through Local Training

In this paper we propose the federated learning algorithm Fed-PLT to overcome the challenges of (i) expensive communications and (ii) privacy preservation. We address (i) by allowing for both partial participation and local training, which significantly reduce the number of communication rounds between the central coordinator and computing agents. The algorithm matches the state of the art in the sense that the use of local training demonstrably does not impact accuracy. Additionally, agents have the flexibility to choose from various local training solvers, such as (stochastic) gradient descent and accelerated gradient descent. Further, we investigate how employing local training can enhance privacy, addressing point (ii). In particular, we derive differential privacy bounds and highlight their dependence on the number of local training epochs. We assess the effectiveness of the proposed algorithm by comparing it to alternative techniques, considering both theoretical analysis and numerical results from a classification task.

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arXiv2024

Distributed Optimization with Finite Bit Adaptive Quantization for Efficient Communication and Precision Enhancement

In realistic distributed optimization scenarios, individual nodes possess only partial information and communicate over bandwidth constrained channels. For this reason, the development of efficient distributed algorithms is essential. In our paper we addresses the challenge of unconstrained distributed optimization. In our scenario each node's local function exhibits strong convexity with Lipschitz continuous gradients. The exchange of information between nodes occurs through $3$-bit bandwidth-limited channels (i.e., nodes exchange messages represented by a only $3$-bits). Our proposed algorithm respects the network's bandwidth constraints by leveraging zoom-in and zoom-out operations to adjust quantizer parameters dynamically. We show that during our algorithm's operation nodes are able to converge to the exact optimal solution. Furthermore, we show that our algorithm achieves a linear convergence rate to the optimal solution. We conclude the paper with simulations that highlight our algorithm's unique characteristics.

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arXiv2024

Hierarchical Federated ADMM

In this paper, we depart from the widely-used gradient descent-based hierarchical federated learning (FL) algorithms to develop a novel hierarchical FL framework based on the alternating direction method of multipliers (ADMM). Within this framework, we propose two novel FL algorithms, which both use ADMM in the top layer: one that employs ADMM in the lower layer and another that uses the conventional gradient descent-based approach. The proposed framework enhances privacy, and experiments demonstrate the superiority of the proposed algorithms compared to the conventional algorithms in terms of learning convergence and accuracy. Additionally, gradient descent on the lower layer performs well even if the number of local steps is very limited, while ADMM on both layers lead to better performance otherwise.

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arXiv2024

Learning Communities from Equilibria of Nonlinear Opinion Dynamics

This paper studies community detection for a nonlinear opinion dynamics model from its equilibria. It is assumed that the underlying network is generated from a stochastic block model with two communities, where agents are assigned with community labels and edges are added independently based on these labels. Agents update their opinions following a nonlinear rule that incorporates saturation effects on interactions. It is shown that clustering based on a single equilibrium can detect most community labels (i.e., achieving almost exact recovery), if the two communities differ in size and link probabilities. When the two communities are identical in size and link probabilities, and the inter-community connections are denser than intra-community ones, the algorithm can achieve almost exact recovery under negative influence weights but fails under positive influence weights. Utilizing fixed point equations and spectral methods, we also propose a detection algorithm based on multiple equilibria, which can detect communities with positive influence weights. Numerical experiments demonstrate the performance of the proposed algorithms.

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arXiv2024

Byzantine-Robust and Communication-Efficient Distributed Learning via Compressed Momentum Filtering

Distributed learning has become the standard approach for training large-scale machine learning models across private data silos. While distributed learning enhances privacy preservation and training efficiency, it faces critical challenges related to Byzantine robustness and communication reduction. Existing Byzantine-robust and communication-efficient methods rely on full gradient information either at every iteration or at certain iterations with a probability, and they only converge to an unnecessarily large neighborhood around the solution. Motivated by these issues, we propose a novel Byzantine-robust and communication-efficient stochastic distributed learning method that imposes no requirements on batch size and converges to a smaller neighborhood around the optimal solution than all existing methods, aligning with the theoretical lower bound. Our key innovation is leveraging Polyak Momentum to mitigate the noise caused by both biased compressors and stochastic gradients, thus defending against Byzantine workers under information compression. We provide proof of tight complexity bounds for our algorithm in the context of non-convex smooth loss functions, demonstrating that these bounds match the lower bounds in Byzantine-free scenarios. Finally, we validate the practical significance of our algorithm through an extensive series of experiments, benchmarking its performance on both binary classification and image classification tasks.

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