arXiv subjects

Stephanie Stockar

Publications and source records attributed to Stephanie Stockar.

At least 19 recordsLinked to original sources

arXiv2026

Real-Time In-Domain Congestion Control for the LWR Traffic Model via Control Barrier Functions

This paper presents a control barrier function-based method for real-time in-domain congestion control of the Lighthill-Whitham-Richards traffic model. Traffic congestion is formulated as a distributed safety control problem, leading to a infinite-dimensional optimization problem. Through the discretization and Karush-Kuhn-Tucker (KKT) analysis, the problem is converted into a high-dimensional quadratic program. A structure-exploiting primal-dual active set algorithm is then developed to compute the safe control input in real time, with convergence guarantees. Numerical simulations with different nominal controllers demonstrate the effectiveness and real-time feasibility of the proposed approach.

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arXiv2026

A Continuification Approach to CAV Control in Mixed Traffic via Variable Speed Limits

This paper presents a method for controlling traffic via the use of connected and automated vehicles (CAVs) acting as moving bottlenecks. Current methods for moving bottleneck control use a couple PDE-ODE model, based on the Lighthill-Whitham-Richard (LWR) model, to represent the influence of the CAV. Control of the CAV is normally achieved by designing the control on the ODE which models the speed of the moving bottleneck. The proposed method in this paper instead looks to reduce the computational burden of controlling multiple CAVs by designing the moving bottleneck controller first on the PDE. The original control designed on the PDE is a linear quadratic regulator (LQR) that determines the optimal variable speed limit (VSL) for the entire length of freeway in order to regulate density to a desired setpoint. Then, a continuification approach is utilized to determine the input speed for each CAV. Results show that multiple CAVs can be controlled via this method, with minimal computational burden, and that as the number of CAVs increases the solution approaches the global optimal solution determined by the LQR.

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arXiv2026

Optimal Finite-Horizon LQR Control for Traffic Flow via Variable Speed Limits

This article presents a finite-horizon linear quadratic regulator for the control of the first-order Lighthill-Whitham-Richards traffic model with a triangular fundamental diagram. The in-domain control action is realized through variable speed limits implemented as a source term in the governing hyperbolic partial differential equation. Unlike prior studies on infinite-horizon formulations, this article develops a finite-horizon LQR framework, deriving a space and time varying state feedback function for hyperbolic PDEs. The solution to the finite time optimal control problem relies on the solution of another PDE, called the Riccati PDE. The resulting nonlinear Riccati PDE is solved analytically via the parametric method of characteristics. The Riccati PDE solution is a function of both time and space, as well as the traffic regime. A sensitivity analysis demonstrates the effects of the LQR parameters for both the infinite and finite time horizon problem in different traffic situations, while siulations validate the finite-horizon LQR's ability to guarentee finite-time convergence. Comapred to the infinite-horizon LQR, the proposed approach achieves significantly improved control performance across various scenarios, making it particularly suitable for time-sensitive traffic management applications.

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arXiv2026

Sensitivity Analysis of Performance-Based Partitioning in District Heating Networks

The paper presents a sensitivity analysis of the factors affecting the optimal partitioning of a district heating network for distributed control. Leveraging a physics-based, distributed model predictive control framework and a performance-based partitioning method, this work studies the relationship between variations in system parameters and the resulting optimal partition, providing insight into the robustness of a nominally designed partition to perturbed operating conditions. The enabling methodology is a learning-enhanced branch and bound method that culls the search space, reducing the number of partitions evaluated for each case. The sensitivity of the nominally optimal partition is characterized across twelve parameter variations, including supply temperature, operating season, building flexibility, pipe characteristics, and building type. This simulation study shows that a well-designed nominal partition exhibits an average cost increase of only 2.8% relative to centralized control across eleven of the twelve cases, with three cases identifying the nominal partition as globally optimal under the perturbed conditions. The robustness study is followed by an analysis of the sensitivity of the optimality loss metric (OLM), revealing that, in five of twelve cases, the case-specific OLM-minimizing partitions underperform the nominally optimal one due to shifts in the relative magnitude of heat loss versus flexibility costs. This indicates that proper tuning of cost function weights and initial conditions for the performance optimization problem is essential for reliable partition selection, and that seasonal repartitioning is warranted when demand profiles deviate substantially from the nominal, as observed in the November operating case.

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arXiv2025

Constrained Control of PDE Traffic Flow via Spatial Control Barrier Functions

In this paper, a constrained control approach to variable speed limit (VSL) control for macroscopic partial differential equations (PDE) traffic models is developed. Control Lyapunov function (CLF) theory for ordinary differential equations (ODE) is extended to account for spatially and temporally varying states and control inputs. The stabilizing CLF is then unified with safety constraints through the introduction of spatially varying control barrier functions (sCBF). These methods are applied to in-domain VSL control of the Lighthill-Whitham-Richards (LWR) model to regulate traffic density to a desired profile while ensuring the density remains below prescribed limits enforced by the sCBF. Results show that incorporating constrained control minimally affects the stabilizing control input while successfully maintaining the density with the defined safe set.

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arXiv2025

Traffic-Aware Eco-Driving Control in CAVs via Learning-based Terminal Cost Model

Connected and Automated Vehicles (CAVs) offer significant potential for improving energy efficiency and lowering vehicle emissions through eco-driving technologies. Control algorithms in CAVs leverage look-ahead route information and Vehicle-to-Everything (V2X) communication to optimize vehicle performance. However, existing eco-driving strategies often neglect macroscopic traffic effects, such as upstream traffic jams, that occur outside the optimization horizon but significantly impact vehicle energy efficiency. This work presents a novel Neural Network (NN)-based methodology to approximate the terminal cost within a model predictive control (MPC) problem framework, explicitly incorporating upstream traffic dynamics. By incorporating traffic jams into the optimization process, the proposed traffic-aware approach yields more energy-efficient speed trajectories compared to traffic-agnostic methods, with minimal impact on travel time. The framework is scalable for real-time implementation while effectively addressing uncertainties from dynamic traffic conditions and macroscopic traffic events.

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arXiv2025

Optimality Loss Minimization in Distributed Control with Application to District Heating

This paper presents a novel partitioning method designed to minimize control performance degradation resulting from partitioning a system for distributed control while maintaining the computational benefits of these methods. A game-theoretic performance metric, the modified Price of Anarchy, is introduced and is used in a generalizable partitioning metric to quantify optimality losses in a distributed controller. By finding the partition that minimizes the partitioning metric, the best-performing distributed control design is chosen. The presented partitioning metric is control-design agnostic, making it broadly applicable to many control design problems. In this paper, the developed metric is used to minimize the performance losses in the distributed control of a demand-flexible District Heating Network. The final distributed controller is provably feasible and stable. In simulation, this novel partitioning performed similarly to the centralized controller, increasing overall heat losses by only 1.9%, as compared to a similarly-sized baseline partition, which resulted in a 22% increase in losses.

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arXiv2025

Epsilon-Neighborhood Decision-Boundary Governed Estimation (EDGE) of 2D Black Box Classifier Functions

Accurately estimating decision boundaries in black box systems is critical when ensuring safety, quality, and feasibility in real-world applications. However, existing methods iteratively refine boundary estimates by sampling in regions of uncertainty, without providing guarantees on the closeness to the decision boundary and also result in unnecessary exploration that is especially disadvantageous when evaluations are costly. This paper presents $\varepsilon$-Neighborhood Decision-Boundary Governed Estimation (EDGE), a sample efficient and function-agnostic algorithm that leverages the intermediate value theorem to estimate the location of the decision boundary of a black box binary classifier within a user-specified $\varepsilon$-neighborhood. To demonstrate applicability, a case study is presented of an electric grid stability problem with uncertain renewable power injection. Evaluations are conducted on three test functions, where it is seen that the EDGE algorithm demonstrates superior sample efficiency and better boundary approximation than adaptive sampling techniques and grid-based searches.

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arXiv2025

Koopman-Based Methods for EV Climate Dynamics: Comparing eDMD Approaches

In this paper, data-driven algorithms based on Koopman Operator Theory are applied to identify and predict the nonlinear dynamics of a vapor compression system and cabin temperature in a light-duty electric vehicle. By leveraging a high-fidelity nonlinear HVAC model, the system behavior is captured in a lifted higher-dimensional state space, enabling a linear representation. A comparative analysis of three Koopman-based system identification approaches (polynomial libraries, radial basis functions (RBF), and neural network-based dictionary learning) is conducted. Accurate prediction of power consumption over entire driving cycles is demonstrated by incorporating power as a measurable output within the Koopman framework. The performance of each method is rigorously evaluated through simulations under various driving cycles and ambient conditions, highlighting their potential for real-time prediction and control in energy-efficient vehicle climate management. This study offers a scalable, data-driven methodology that can be extended to other complex nonlinear systems.

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arXiv2025

Modeling Driver Behavior in Speed Advisory Systems: Koopman-based Approach with Online Update

Accurate driver behavior modeling is essential for improving the interaction and cooperation of the human driver with the driver assistance system. This paper presents a novel approach for modeling the response of human drivers to visual cues provided by a speed advisory system using a Koopman-based method with online updates. The proposed method utilizes the Koopman operator to transform the nonlinear dynamics of driver-speed advisory system interactions into a linear framework, allowing for efficient real-time prediction. An online update mechanism based on Recursive Least Squares (RLS) is integrated into the Koopman-based model to ensure continuous adaptation to changes in driver behavior over time. The model is validated using data collected from a human-in-the-loop driving simulator, capturing diverse driver-specific trajectories. The results demonstrate that the offline learned Koopman-based model can closely predict driver behavior and its accuracy is further enhanced through an online update mechanism with the RLS method.

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arXiv2025

Communication-Based Distributed Control of Large-Scale District Heating Networks

This paper presents a non-cooperative distributed model predictive controller for the control of large-scale District Heating Networks. To enable the design of this controller a novel information passing scheme and feasibility restoration method are created, allowing the local controllers to achieve a global consensus while minimizing a local cost function. The effectiveness of this controller is demonstrated on an 18-user District Heating Network decomposed into six subsystems. The results show that the developed control scheme effectively uses flexibility to manage the buildings' heat demands reducing the total losses by 14% and the return temperature by 37%.

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arXiv2024

Data-Driven Personalized Energy Consumption Range Estimation for Plug-in Hybrid Electric Vehicles in Urban Traffic

In urban traffic environments, driver behaviors exhibit considerable diversity in vehicle operation, encompassing a range of acceleration and braking maneuvers as well as adherence to traffic regulations, such as speed limits. It is well-established that these intrinsic driving behaviors significantly influence vehicle energy consumption. Therefore, establishing a quantitative relationship between driver behavior and energy usage is essential for identifying energy-efficient driving practices and optimizing routes within urban traffic. This study introduces a data-driven approach to predict the equivalent fuel consumption of a plug-in hybrid electric vehicle (PHEV) based on an integrated model of driver behavior and vehicle energy consumption. Unlike traditional models that provide point predictions of fuel consumption, this approach uses Conformalized Quantile Regression (CQR) to offer prediction intervals that capture the variability and uncertainty in fuel consumption. These intervals reflect changes in fuel consumption, as well as variations in driver behavior, and vehicle and route conditions. To develop this model, driver-specific data were collected through a driver-in-the-loop simulator, which tested different human drivers responses. The CQR model was then trained and validated using the experimental data from the driver-in-the-loop simulator, augmented by the synthetic data generated from Monte Carlo simulations conducted using a calibrated microscopic driver behavior and vehicle energy model. The CQR model was evaluated by comparing its predictions of equivalent fuel consumption intervals with those of baseline prediction interval methods that rely solely on conformal prediction.

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arXiv2024

Novel Tour Construction Heuristic for Pick-Up and Delivery Routing Problems

In logistic applications that require the pickup and delivery of items, route optimization problems can be modeled as precedence constrained traveling salesperson problems. The combinatorial nature of this problem restricts the application of exact algorithms to small instances, and heuristics are largely preferred for tractability. However, due to precedence constraints that restrict the order in which locations can be visited, heuristics outside of the nearest neighbor algorithm have been neglected in literature. While the convex hull cheapest insertion heuristic is known to produce good solutions in the absence of precedence constraints, i.e., when locations can be visited in any order, it has not been adapted for pick-up and delivery considerations. This paper presents an adapted convex hull cheapest insertion heuristic that accounts for precedence constraints and compares its solutions with the nearest neighbor heuristic using the TSPLIB benchmark data set. The proposed algorithm is particularly suited to cases where pickups are located in the periphery and deliveries are centrally located, outperforming the Nearest Neighbor algorithm in every examined instance.

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arXiv2024

Using Flexibility Envelopes for the Demand-Side Hierarchical Optimization of District Heating Networks

The demand-side control of district heating networks is notoriously challenging due to the large number of connected users and the high number of states to be considered. To overcome these challenges, this paper presents a hierarchical optimization scheme using the flexibility in heating demand provided by the users to improve the performance of the network. This hierarchical scheme relies on a low level controller to calculate the costs for a subsystem over a given set of potential pressure drops for that subsystem. The high level controller then uses these calculated costs to determine the optimal set of pressure drops for every subgraph of the partitioned network. The proposed hierarchical optimization scheme is demonstrated on a representative 20 user district heating network, resulting in a 67\% reduction in bypass mass flow while ensuring all network users stay within 2 \degree C of their desired nominal temperatures.

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arXiv2024

Resilient Fleet Management for Energy-Aware Intra-Factory Logistics

This paper presents a novel fleet management strategy for battery-powered robot fleets tasked with intra-factory logistics in an autonomous manufacturing facility. In this environment, repetitive material handling operations are subject to real-world uncertainties such as blocked passages, and equipment or robot malfunctions. In such cases, centralized approaches enhance resilience by immediately adjusting the task allocation between the robots. To overcome the computational expense, a two-step methodology is proposed where the nominal problem is solved a priori using a Monte Carlo Tree Search algorithm for task allocation, resulting in a nominal search tree. When a disruption occurs, the nominal search tree is rapidly updated a posteriori with costs to the new problem while simultaneously generating feasible solutions. Computational experiments prove the real-time capability of the proposed algorithm for various scenarios and compare it with the case where the search tree is not used and the decentralized approach that does not attempt task reassignment.

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arXiv2024

LQ Control of Traffic Flow Models via Variable Speed Limits

In this paper, an extension of a linear control design for hyperbolic linear partial differential equations is presented for a first-order traffic flow model. Starting from the Lighthill-Whitham-Richards (LWR) model, variable speed limit control (VSL) is applied through a modification of Greenshield's equilibrium flow model. Then, an optimal linear quadratic (LQ) controller is designed on the linear LWR model. The LQ state feedback function is found via the solution of a Riccati differential equation. Unlike previous studies, the control input is the rate of change of the input, not the input itself. The proposed controller is then verified on both the linear and nonlinear models. In both cases, the controller is able to drive the system to a desired density profile. In the nonlinear application, a higher control gain is needed to achieve similar results as in the linear case.

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arXiv2023

Eco-Driving Control of Connected and Automated Vehicles using Neural Network based Rollout

Connected and autonomous vehicles have the potential to minimize energy consumption by optimizing the vehicle velocity and powertrain dynamics with Vehicle-to-Everything info en route. Existing deterministic and stochastic methods created to solve the eco-driving problem generally suffer from high computational and memory requirements, which makes online implementation challenging. This work proposes a hierarchical multi-horizon optimization framework implemented via a neural network. The neural network learns a full-route value function to account for the variability in route information and is then used to approximate the terminal cost in a receding horizon optimization. Simulations over real-world routes demonstrate that the proposed approach achieves comparable performance to a stochastic optimization solution obtained via reinforcement learning, while requiring no sophisticated training paradigm and negligible on-board memory.

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arXiv2023

A Graph-Based Technique for the Automated Control-Oriented Modeling of District Heating Networks

Advanced control strategies for delivering heat to users in a district heating network have the potential to improve performance and reduce wasted energy. To enable the design of such controllers, this paper proposes an automated plant modeling framework that captures the relevant system dynamics, while being adaptable to any network configuration. Starting from the network topology and system parameters, the developed algorithm generates a state-space model of the system, relying on a graph-based technique to facilitate the combination of component models into a full network model. The accuracy of the approach is validated against experimental data collected from a laboratory-scale district heating network. The verification shows an average normalized root mean square error of 0.39 in the mass flow rates delivered to the buildings, and 0.15 in the network return temperature. Furthermore, the ability of the proposed modeling technique to rapidly generate models characterizing different network configurations is demonstrated through its application to topology optimization. The optimal design, obtained via a branch and bound algorithm, reduces network heat losses by 15% as compared to the conventional length-minimized topology.

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