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Control Problems for Hamilton-Jacobi Equations Co-authored by Alexander Keimer

Bayen, Alexandre
Monache, Maria Laura Delle
Garavello, Mauro
Goatin, Paola
Piccoli, Benedetto
2022

In this chapter, we introduce Hamilton-Jacobi PDEs. These PDEs are related to conservation laws and their solutions are the anti-derivative (in space) of the Entropy solutions of the corresponding conservation law, given that some assumptions are satisfied.

Control Problems for Hamilton-Jacobi Equations Co-authored by Alexander Keimer

Bayen, Alexandre
Monache, Maria Laura Delle
Garavello, Mauro
Goatin, Paola
Piccoli, Benedetto
2022

In this chapter, we introduce Hamilton-Jacobi PDEs. These PDEs are related to conservation laws and their solutions are the anti-derivative (in space) of the Entropy solutions of the corresponding conservation law, given that some assumptions are satisfied.

Decentralized Control of Conservation Laws on Graphs

Bayen, Alexandre
Monache, Maria Laura Delle
Garavello, Mauro
Goatin, Paola
Piccoli, Benedetto
2022

Conservation and/or balance laws on networks in the recent years have been the subject of intense study, since a wide range of different applications in real life can be covered by such a research.

Decentralized Control of Conservation Laws on Graphs

Bayen, Alexandre
Monache, Maria Laura Delle
Garavello, Mauro
Goatin, Paola
Piccoli, Benedetto
2022

Conservation and/or balance laws on networks in the recent years have been the subject of intense study, since a wide range of different applications in real life can be covered by such a research.

Distributed Control for Conservation Laws

Bayen, Alexandre
Monache, Maria Laura Delle
Garavello, Mauro
Goatin, Paola
Piccoli, Benedetto
2022

This chapter focuses on control of systems of conservation laws with distributed parameters. Problem with different parameterized fluxes is addressed: in particular, we deal with cases where the control is the maximal speed and look for continuous dependence of the solution on parameters.

Introduction

Bayen, Alexandre
Monache, Maria Laura Delle
Garavello, Mauro
Goatin, Paola
Piccoli, Benedetto
Bayen, Alexandre
2022

This book focuses on control problems for conservation laws, i.e., equations of the type: ∂tu+∂xf(u)=0ut+(f(u))x=0,$$\displaystyle \partial _t\, u + \partial _x\, f(u) = 0 \qquad u_t+(f(u))_x=0, $$where u:ℝ+×ℝ→ℝn$$u:\mathbb {R}^+\times \mathbb {R} \to \mathbb {R}^n$$is the vector of conserved quantities and f:ℝn→ℝn$$f:\mathbb {R}^n\to \mathbb {R}^n$$is the flux. Most results will be given for the scalar case (n = 1), but we will present few results valid in the general case.

Lagrangian Control of Conservation Laws and Mixed Models

Bayen, Alexandre
Monache, Maria Laura Delle
Garavello, Mauro
Goatin, Paola
Piccoli, Benedetto
2022

A vehicle with different (eventually controlled) dynamics from general traffic along a street may reduce the road capacity, thus generating a moving bottleneck, and can be used to act on the traffic flow. The interaction between the controlled vehicle and the surrounding traffic, and the consequent flow reduction at the bottleneck position, can be described either by a conservation law with space dependent flux function [200], or by a strongly coupled PDE-ODE system proposed in [112, 208].

A Holistic Approach to the Energy-Efficient Smoothing of Traffic via Autonomous Vehicles

Hayat, Amaury
Gong, Xiaoqian
Lee, Jonathan
Truong, Sydney
McQuade, Sean T.
Bayen, Alexandre
2022

The technological advancements in terms of vehicle on-board sensors and actuators, as well as for infrastructures, open an unprecedented scenario for the management of vehicular traffic. We focus on the problem of smoothing traffic by controlling a small number of autonomous vehicles immersed in the bulk traffic stream. Specifically, we aim at dissipating stop-and-go waves, which are ubiquitous and proven to increase fuel consumption tremendously and reduce. Our approach is holistic, as it is based on a large collaborative effort, which ranges from mathematical models for traffic and...

Medium-Scale to Large-Scale Implementation of Cyber-Physical Human Experiments in Live Traffic

McQuade, Sean T.
Denaro, Christopher
Mahmood, Malaika
Lee, Jonathan W.
Gumm, Gracie
Bayen, Alexandre M.
2022

Autonomous Vehicles (AVs) such as cars and trucks are being developed and tested as Cyber-Physical Human systems while the technology improves. Before these systems can achieve full autonomy, some serve as tools in the form of adaptive cruise control. The CIRCLES Consortium investigates the potential for AVs to increase fuel efficiency of highway traffic by smoothing “stop-and-go” traffic waves that result from normal human driving behavior in congestion. We have performed an experiment to evaluate the real world effects of implementing this strategy. A medium-scale experiment was...

The Lord of the Ring Road: A Review and Evaluation of Autonomous Control Policies for Traffic in a Ring Road

Chou, Fang-Chieh
Bagabaldo, Alben Rome
Bayen, Alexandre
2022

This study focuses on the comprehensive investigation of stop-and-go waves appearing in closed-circuit ring road traffic wherein we evaluate various longitudinal dynamical models for vehicles. It is known that the behavior of human-driven vehicles, with other traffic elements such as density held constant, could stimulate stop-and-go waves, which do not dissipate on the circuit ring road. Stop-and-go waves can be dissipated by adding automated vehicles (AVs) to the ring. Thorough investigations of the performance of AV longitudinal control algorithms were carried out in Flow, which is an...