arXiv subjects

Gustav Nilsson

Publications and source records attributed to Gustav Nilsson.

27 records · Page 2Linked to original sources

arXiv2021

The Strong Integral Input-to-State Stability Property in Dynamical Flow Networks

Dynamical flow networks serve as macroscopic models for, e.g., transportation networks, queuing networks, and distribution networks. While the flow dynamics in such networks follow the conservation of mass on the links, the outflow from each link is often non-linear due to, e.g., flow capacity constraints and simultaneous service rate constraints. Such non-linear constraints imply a limit on the magnitude of exogenous inflow that is able to be accommodated by the network before it becomes overloaded and its state trajectory diverges. This paper shows how the Strong integral Input-to-State Stability (Strong iISS) property allows for quantifying the effects of the exogenous inflow on the flow dynamics. The Strong iISS property enables a unified stability analysis of classes of dynamical flow networks that were only partly analyzable before, such as networks with cycles, multi-commodity flow networks and networks with non-monotone flow dynamics. We present sufficient conditions on the maximum magnitude of exogenous inflow to guarantee input-to-state stability for a dynamical flow network, and we also present cases when this sufficient condition is necessary. The conditions are exemplified on a few existing dynamical flow network models, specifically, fluid queuing models with time-varying exogenous inflows and multi-commodity flow models.

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arXiv2021

Capacity-Constrained Urban Air Mobility Scheduling

This paper studies the problem of scheduling urban air mobility trips when travel times are uncertain and capacity at destinations is limited. Urban air mobility, in which air transportation is used for relatively short trips within a city or region, is emerging as a possible component in future transportation networks. Destinations in urban air mobility networks, called vertiports or vertistops, typically have limited landing capacity, and, for safety, it must be guaranteed that an air vehicle will be able to land before it can be allowed to take off. We first present a tractable model of urban air mobility networks that accounts for limited landing capacity and uncertain travel times between destinations with lower and upper travel time bounds. We then establish theoretical bounds on the achievable throughput of the network. Next, we present a tractable algorithm for scheduling trips to satisfy safety constraints and arrival deadlines. The algorithm allows for dynamically updating the schedule to accommodate, e.g., new demands over time. The paper concludes with case studies that demonstrate the algorithm on two networks.

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arXiv2021

On the Impact of the Capacity Drop Phenomenon for Freeway Traffic Flow Control

Capacity drop is an empirically observed phenomenon in vehicular traffic flow on freeways whereby, after a critical density is reached, a state of congestion sets in, but the freeway does not become decongested again until the density drops well below the critical density. This introduces a hysteresis effect so that it is easier to enter the congested state than to leave it. However, many existing first-order models of traffic flow, particularly those used for control design, ignore capacity drop, leading to suboptimal controllers. In this paper, we consider a cell transmission model of traffic flow that incorporates capacity drop to study the problem of optimal freeway ramp metering. We show that, if capacity drop is ignored in the control design, then the resulting controller, obtained via a convex program, may be significantly suboptimal. We then propose an alternative model predictive controller that accounts for capacity drop via a mixed integer linear program and show that, for sufficiently large rollout horizon, this controller is optimal. We also compare these approaches to a heuristic hand-crafted controller that is viewed as a modification of an integral feedback controller to account for capacity drop. This heuristic controller outperforms the controller that ignores capacity drop but underperforms compared to the proposed alternative model predictive controller. These results suggest that it is generally important to include capacity drop in the controller design process, and we demonstrate this insight on several case studies.

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arXiv2020

Resource Aware Pricing for Electric Vehicle Charging

Electric vehicle charging facilities offer electric charge and parking to users for a fee. Both parking availability and electric charge capacity are constrained resources, and as the demand for charging facilities grows with increasing electric vehicle adoption, so too does the potential for exceeding these resource limitations. In this paper, we study how prices set by the charging facility impact the likelihood that resource constraints are exceeded. Specifically, we present probabilistic bounds on the number of charging spots and the total power supply needed at a facility based on the characteristics of the arriving vehicles. We assume the charging facility either offers a set of distinct and fixed charging rates to each user or allows the user to decide a charging deadline, from which a charging rate is determined. Users arrive randomly, requiring a random amount of charge. Additionally, each user has a random impatience factor that quantifies their value of time, and a random desired time to stay at a particular location. Assuming rational user behavior, and with knowledge of the probability distribution of the random parameters, we present high-confidence bounds on the total number of vehicles parked at the station and the aggregate power use of all vehicles actively charging. We demonstrate how these bounds can be used by a charging facility to determine appropriate prices and investigate through a Monte-Carlo simulation case study the tightness of the bounds.

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arXiv2020

Data Augmentation of IMU Signals and Evaluation via a Semi-Supervised Classification of Driving Behavior

Over the past years, interest in classifying drivers' behavior from data has surged. Such interest is particularly relevant for car insurance companies who, due to privacy constraints, often only have access to data from Inertial Measurement Units (IMU) or similar. In this paper, we present a semi-supervised learning solution to classify portions of trips according to whether drivers are driving aggressively or normally based on such IMU data. Since the amount of labeled IMU data is limited and costly to generate, we utilize Recurrent Conditional Generative Adversarial Networks (RCGAN) to generate more labeled data. Our results show that, by utilizing RCGAN-generated labeled data, the classification of the drivers is improved in 79% of the cases, compared to when the drivers are classified with no generated data.

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arXiv2020

Extent-Compatible Control Barrier Functions

Safety requirements in dynamical systems are commonly enforced with set invariance constraints over a safe region of the state space. Control barrier functions, which are Lyapunov-like functions for guaranteeing set invariance, are an effective tool to enforce such constraints and guarantee safety when the system is represented as a point in the state space. In this paper, we introduce extent-compatible control barrier functions as a tool to enforce safety for the system including its volume (extent) in the physical world. In order to implement the extent-compatible control barrier functions framework, a sum-of-squares based optimization program is proposed. Since sum-of-squares programs can be computationally prohibitive, we additionally introduce a sampling based method in order to retain the computational advantage of a traditional barrier function based quadratic program controller. We prove that the proposed sampling based controller retains the guarantee for safety. Simulation and robotic implementation results are also provided.

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arXiv2020

On the Well-Posedness of Dynamical Flow Networks With Feedback-Controlled Outflows

We study the well-posedness of a class of dynamical flow network systems describing the dynamical mass balance among a finite number of cells exchanging flow of a commodity between themselves and with the external environment. Systems in the considered class are described as differential inclusions whereby the routing matrix is constant and the outflow from each cell in the network is limited by a control that is a Lipschitz continuous function of the state of the network. In many applications, such as queueing systems and traffic signal control, it is common that an empty queue can be allowed to have more outflow than the mass in the queue. While models for this scenario have previously been presented for open-loop outflow controls, this result ensures the existence and uniqueness of solutions for the network flow dynamics in the case Lipschitz continuous feedback controllers.

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arXiv2019

Generalized Proportional Allocation Policies for Robust Control of Dynamical Flow Networks

We study a robust control problem for dynamical flow networks. In the considered dynamical models, traffic flows along the links of a transportation network --modeled as a capacited multigraph-- and queues up at the nodes, whereby control policies determine which incoming queues at a node are to be allocated service simultaneously, within some predetermined scheduling constraints. We first prove a fundamental performance limitation by showing that for a dynamical flow network to be stabilizable by some control policy it is necessary that the exogenous inflows belong to a certain stability region, that is determined by the network topology, link capacities, and scheduling constraints. Then, we introduce a family of distributed controls, referred to as Generalized Proportional Allocation (GPA) policies, and prove that they stabilize a dynamical transportation network whenever the exogenous inflows belong to such stability region. The proposed GPA control policies are decentralized and fully scalable as they rely on local feedback information only. Differently from previously studied maximally stabilizing control strategies, the GPA control policies do not require any global information about the network topology, the exogenous inflows, or the routing, which makes them robust to demand variations and unpredicted changes in the link capacities or the routing decisions. Moreover, the proposed GPA control policies also take into account the overhead time while switching between services. Our theoretical results find one application in the control of urban traffic networks with signalized intersections, where vehicles have to queue up at junctions and the traffic signal controls determine the green light allocation to the different incoming lanes.

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arXiv2019

A Micro-Simulation Study of the Generalized Proportional Allocation Traffic Signal Control

In this paper, we study the problem of determining phase activations for signalized junctions by utilizing feedback, more specifically, by measure the queue-lengths on the incoming lanes to each junction. The controller we are investigating is the Generalized Proportional Allocation (GPA) controller, which has previously been shown to have desired stability and throughput properties in a continuous averaged dynamical model for queueing networks. In this paper, we provide and implement two discretized versions of the GPA controller in the SUMO micro simulator. We also compare the GPA controllers with the MaxPressure controller, a controller that requires more information than the GPA, in an artificial Manhattan-like grid. To show that the GPA controller is easy to implement in a real scenario, we also implement it in a previously published realistic traffic scenario for the city of Luxembourg and compare its performance with the static controller provided with the scenario. The simulations show that the GPA performs better than a static controller for the Luxembourg scenario, and better than the MaxPressure pressure controller in the Manhattan-grid when the demands are low.

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