arXiv subjects

Karl Henrik Johansson

Publications and source records attributed to Karl Henrik Johansson.

At least 109 records · Page 6Linked to original sources

arXiv2021

Strategic Hub-Based Platoon Coordination under Uncertain Travel Times

We study the strategic interaction among vehicles in a non-cooperative platoon coordination game. Vehicles have predefined routes in a transportation network with a set of hubs where vehicles can wait for other vehicles to form platoons. Vehicles decide on their waiting times at hubs and the utility function of each vehicle includes both the benefit from platooning and the cost of waiting. We show that the platoon coordination game is a potential game when the travel times are either deterministic or stochastic, and the vehicles decide on their waiting times at the beginning of their journeys. We also propose two feedback solutions for the coordination problem when the travel times are stochastic and vehicles are allowed to update their strategies along their routes. The solutions are evaluated in a simulation study over the Swedish road network. It is shown that uncertainty in travel times affects the total benefit of platooning drastically and the benefit from platooning in the system increases significantly when utilizing feedback solutions.

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arXiv2021

Verifying Compositional Refinement of Assume/Guarantee Contracts using Linear Programming

Verifying specifications for large-scale modern engineering systems can be a time-consuming task, as most formal verification methods are limited to systems of modest size. Recently, contract-based design and verification has been proposed as a modular framework for specifications, and linear-programming-based techniques have been presented for verifying that a given system satisfies a given contract. In this paper, we extend this assume/guarantee framework by presenting necessary and sufficient conditions for a collection of contracts on individual components to refine a contract on the composed system. These conditions can be verified by solving linear programs, whose number grows linearly with the number of specifications defined by the contracts. We exemplify the tools developed using a case study considering safety in a car-following scenario, where noise and time-varying delay are considered.

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arXiv2021

Set-Membership Estimation in Shared Situational Awareness for Automated Vehicles in Occluded Scenarios

One of the main challenges in developing autonomous transport systems based on connected and automated vehicles is the comprehension and understanding of the environment around each vehicle. In many situations, the understanding is limited to the information gathered by the sensors mounted on the ego-vehicle, and it might be severely affected by occlusion caused by other vehicles or fixed obstacles along the road. Situational awareness is the ability to perceive and comprehend a traffic situation and to predict the intent of vehicles and road users in the surrounding of the ego-vehicle. The main objective of this paper is to propose a framework for how to automatically increase the situational awareness for an automatic bus in a realistic scenario when a pedestrian behind a parked truck might decide to walk across the road. Depending on the ego-vehicle's ability to fuse information from sensors in other vehicles or in the infrastructure, shared situational awareness is developed using a set-based estimation technique that provides robust guarantees for the location of the pedestrian. A two-level information fusion architecture is adopted, where sensor measurements are fused locally, and then the corresponding estimates are shared between vehicles and units in the infrastructure. Thanks to the provided safety guarantees, it is possible to appropriately adjust the ego-vehicle speed to maintain a proper safety margin. It is also argued that the framework is suitable for handling sensor failures and false detections in a systematic way. Three scenarios of growing information complexity are considered throughout the study. Simulations show how the increased situational awareness allows the ego-vehicle to maintain a reasonable speed without sacrificing safety.

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arXiv2020

Community Detection for Gossip Dynamics with Stubborn Agents

We consider a community detection problem for gossip dynamics with stubborn agents in this paper. It is assumed that the communication probability matrix for agent pairs has a block structure. More specifically, we assume that the network can be divided into two communities, and the communication probability of two agents depends on whether they are in the same community. Stability of the model is investigated, and expectation of stationary distribution is characterized, indicating under the block assumption, the stationary behaviors of agents in the same community are similar. It is also shown that agents in different communities display distinct behaviors if and only if state averages of stubborn agents in different communities are not identical. A community detection algorithm is then proposed to recover community structure and to estimate communication probability parameters. It is verified that the community detection part converges in finite time, and the parameter estimation part converges almost surely. Simulations are given to illustrate algorithm performance.

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arXiv2020

Causality Graph of Vehicular Traffic Flow

In an intelligent transportation system, the effects and relations of traffic flow at different points in a network are valuable features which can be exploited for control system design and traffic forecasting. In this paper, we define the notion of causality based on the directed information, a well-established data-driven measure, to represent the effective connectivity among nodes of a vehicular traffic network. This notion indicates whether the traffic flow at any given point affects another point's flow in the future and, more importantly, reveals the extent of this effect. In contrast with conventional methods to express connections in a network, it is not limited to linear models and normality conditions. In this work, directed information is used to determine the underlying graph structure of a network, denoted directed information graph, which expresses the causal relations among nodes in the network. We devise an algorithm to estimate the extent of the effects in each link and build the graph. The performance of the algorithm is then analyzed with synthetic data and real aggregated data of vehicular traffic.

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arXiv2020

Analysis and distributed control of periodic epidemic processes

This paper studies epidemic processes over discrete-time periodic time-varying networks. We focus on the susceptible-infected-susceptible (SIS) model that accounts for a (possibly) mutating virus. We say that an agent is in the disease-free state if it is not infected by the virus. Our objective is to devise a control strategy which ensures that all agents in a network exponentially (resp. asymptotically) converge to the disease-free equilibrium (DFE). Towards this end, we first provide a) sufficient conditions for exponential (resp. asymptotic) convergence to the DFE; and b) a necessary and sufficient condition for asymptotic convergence to the DFE. The sufficient condition for global exponential stability (GES) (resp. global asymptotic stability (GAS)) of the DFE is in terms of the joint spectral radius of a set of suitably-defined matrices, whereas the necessary and sufficient condition for GAS of the DFE involves the spectral radius of an appropriately-defined product of matrices. Subsequently, we leverage the stability results in order to design a distributed control strategy for eradicating the epidemic.

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arXiv2020

Distributed Design of Glocal Controllers via Hierarchical Model Decomposition

This paper proposes a distributed design method of controllers having a glocal (global/local) information structure for large-scale network systems. Distributed design, independent design of all subcontrollers that constitute a structured controller, facilitates scalable controller synthesis. While existing distributed design methods confine attention to the decentralized or distributed information structures, this study addresses distributed design of glocal-structured controllers. Glocal control exploits the nature that network system's behavior can typically be represented as a superposition of spatially local fluctuations and global interarea oscillations by incorporating a global coordinating subcontroller with local decentralized subcontrollers. The key idea to distributed design of glocal controllers is to represent the original network system as a hierarchical cascaded system composed of reduced-order models representing the global and local dynamics, referred to as hierarchical model decomposition. Distributed design is achieved by independently designing and implementing subcontrollers for the reduced-order models while preserving the cascade structure. This paper provides a condition for existence of the hierarchical model decomposition, a specific representation of the hierarchical system, a clustering method appropriate for the proposed approach, and a robust extension. Numerical examples of a power grid evidence the practical relevance of the proposed method.

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arXiv2020

Data-Driven Distributed Mitigation Strategies and Analysis of Mutating Epidemic Processes

In this paper we study a discrete-time SIS (susceptible-infected-susceptible) model, where the infection and healing parameters and the underlying network may change over time. We provide conditions for the model to be well-defined and study its stability. For systems with homogeneous infection rates over symmetric graphs,we provide a sufficient condition for global exponential stability (GES) of the healthy state, that is, where the virus is eradicated. For systems with heterogeneous virus spread over directed graphs, provided that the variation is not too fast, a sufficient condition for GES of the healthy state is established.

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arXiv2020

Numerical Investigation of Traffic State Reconstruction and Control Using Connected Automated Vehicles

In this paper we present a numerical study on control and observation of traffic flow using Lagrangian measurements and actuators. We investigate the effect of some basic control and observation schemes using probe and actuated vehicles within the flow. The aim is to show the effect of the state reconstruction on the efficiency of the control, compared to the case using full information about the traffic. The effectiveness of the proposed state reconstruction and control algorithms is demonstrated in simulations. They show that control using the reconstructed state approaches the full-information control when the gap between the connected vehicles is not too large, reducing the delay by more than $60\%$ when the gap between the sensor vehicles is $1.25$~km on average, compared to a delay reduction of almost $80\%$ in the full-information control case. %It shows that the reconstruction is well achieved if the distance between two connected and autonomous vehicles is not too large (more than 1 vehicle per kilometer). %We also show that it is possible to further improve the control performance by employing a simple adaptive probe vehicle selection scheme. Moreover, we propose a simple scheme for selecting which vehicles to use as sensors, in order to reduce the communication burden. Numerical simulations demonstrate that %It also demonstrates that it is possible to reduce the communication burden using a triggering mechanism with with this triggering mechanism, the delay is reduced by around $65\%$, compared to a reduction of $72\%$ if all connected vehicles are communicating at all times.

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arXiv2020

Control Limitations due to Zero Dynamics in a Single-Machine Infinite Bus Network

In this work, fundamental control limitations for rotor angle stability are considered. Limitations are identified by characterizing open-loop transfer function zeros for input-output combinations of certain power system configurations. Of particular interest are non-minimum phase (NMP) zeros that limit the achievable performance of the closed-loop system. By studying a single-machine infinite bus power system model, analytic conditions for the presence of NMP zeros are derived. They are shown to be closely linked to the destabilizing effect of automatic voltage regulators (AVRs). Depending on the control loop, it is found that NMP zeros may persist in the system even if the closed-loop system is stabilized through feedback control. A simulation study shows that NMP zeros introduced by AVR limit the achievable performance and stabilization using feedback control.

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arXiv2020

Dynamic Traffic Reconstruction using Probe Vehicles

This article deals with the observation problem in traffic flow theory. The model used is the semilinear viscous Burgers equation. Instead of using the traditional fixed sensors to estimate the state of the traffic at given points, the measurements here are obtained from Probe Vehicles (PVs). We propose then a moving dynamic boundary observer whose boundaries are defined by the trajectories of the PVs. The main result of this article is the exponential convergence of the observation error, and, in some cases, its finite-time convergence. Finally, numerical simulations show that it is possible to observe the traffic in the congested, free-flow, and mixed regimes provided that the number of PVs is large enough.

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arXiv2020

Linear System Identification Under Multiplicative Noise from Multiple Trajectory Data

The study of multiplicative noise models has a long history in control theory but is re-emerging in the context of complex networked systems and systems with learning-based control. We consider linear system identification with multiplicative noise from multiple state-input trajectory data. We propose exploratory input signals along with a least-squares algorithm to simultaneously estimate nominal system parameters and multiplicative noise covariance matrices. Identifiability of the covariance structure and asymptotic consistency of the least-squares estimator are demonstrated by analyzing first and second moment dynamics of the system. The results are illustrated by numerical simulations.

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arXiv2020

An Optimal Linear Attack Strategy on Remote State Estimation

This work considers the problem of designing an attack strategy on remote state estimation under the condition of strict stealthiness and $ε$-stealthiness of the attack. An attacker is assumed to be able to launch a linear attack to modify sensor data. A metric based on Kullback-Leibler divergence is adopted to quantify the stealthiness of the attack. We propose a generalized linear attack based on past attack signals and the latest innovation. We prove that the proposed approach can obtain an attack that can cause more estimation performance loss than linear attack strategies recently studied in the literature. The result thus provides a bound on the tradeoff between available information and attack performance, which is useful in the development of mitigation strategies. Finally, some numerical examples are given to evaluate the performance of the proposed strategy.

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arXiv2020

Coordinating Vehicle Platoons for Highway Bottleneck Decongestion and Throughput Improvement

Truck platooning is a technology that is expected to become widespread in the coming years. Apart from the numerous benefits that it brings, its potential effects on the overall traffic situation need to be studied further, especially at bottlenecks and ramps. Assuming we can control the platoons from the infrastructure, they can be used as controlled moving bottlenecks, actuating control actions on the rest of the traffic, and potentially improving the throughput of the whole system. In this paper, we use a multi-class cell transmission model to capture the interaction between truck platoons and background traffic, and propose a corresponding queuing model, which we use for control design. We use platoon speeds, and the number of lanes platoons occupy as control inputs, and design a control strategy for throughput improvement of a highway section with a bottleneck. By postponing and shaping the inflow to the bottleneck, we are able to avoid traffic breakdown and capacity drop, which significantly reduces the total time spent of all vehicles. We derived the estimated improvement in throughput that is achieved by applying the proposed control law, and then tested it in a simulation study and found that the median delay of all vehicles by 75.6% compared to the uncontrolled case. Notably, although they are slowed down while actuating control actions, platooned vehicles experience less delay compared to the case without control, since they avoid going through congestion at the bottleneck.

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arXiv2020

Analysis of free recall dynamics of an abstract working memory model

This paper analyzes the free recall dynamics of a working memory model. Free recalling is the reactivation of a stored pattern in the memory in the absence of the pattern. Our free recall model is based on an abstract model of a modular neural network composed on $N$ modules, hypercolumns, each of which is a bundle of minicolumns. This paper considers a network of $N$ modules, each consisting of two minicolumns, over a complete graph topology. We analyze the free recall dynamics assuming a constant, and homogeneous coupling between the network modules. We obtain a sufficient condition for synchronization of network's minicolumns whose activities are positively correlated. Furthermore, for the synchronized network, the bifurcation analysis of one module is presented. This analysis gives a necessary condition for having a stable limit cycle as the attractor of each module. The latter implies recalling a stored pattern. Numerical results are provided to verify the theoretical analysis.

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arXiv2020

Linearly Solvable Mean-Field Traffic Routing Games

We consider a dynamic traffic routing game over an urban road network involving a large number of drivers in which each driver selecting a particular route is subject to a penalty that is affine in the logarithm of the number of drivers selecting the same route. We show that the mean-field approximation of such a game leads to the so-called linearly solvable Markov decision process, implying that its mean-field equilibrium (MFE) can be found simply by solving a finite-dimensional linear system backward in time. Based on this backward-only characterization, it is further shown that the obtained MFE has the notable property of strong time-consistency. A connection between the obtained MFE and a particular class of fictitious play is also discussed.

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arXiv2019

Recursive Network Estimation From Binary-Valued Observation Data

This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which agents exchange and display binary outputs. Sufficient conditions are given to ensure stability of the observation sequence and identifiability of the system parameters. It is shown that stability and identifiability can be guaranteed under the assumption of independent standard Gaussian disturbances. Via a maximum likelihood approach, the estimation problem is transformed into an optimization problem, and it is verified that its solution is the true parameter vector under the independent standard Gaussian assumption. A recursive algorithm for the estimation problem is then proposed based on stochastic approximation techniques. Its strong consistency is established and convergence rate analyzed. Finally, numerical simulations are conducted to illustrate the results and to show that the proposed algorithm is insensitive to small unmodeled factors.

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arXiv2019

Learning Optimal Scheduling Policy for Remote State Estimation under Uncertain Channel Condition

We consider optimal sensor scheduling with unknown communication channel statistics. We formulate two types of scheduling problems with the communication rate being a soft or hard constraint, respectively. We first present some structural results on the optimal scheduling policy using dynamic programming and assuming the channel statistics is known. We prove that the Q-factor is monotonic and submodular, which leads to the threshold-like structures in both types of problems. Then we develop a stochastic approximation and parameter learning frameworks to deal with the two scheduling problems with unknown channel statistics. We utilize their structures to design specialized learning algorithms. We prove the convergence of these algorithms. Performance improvement compared with the standard Q-learning algorithm is shown through numerical examples.

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