PDE-Based Feedback Control of Freeway Traffic Flow via Time-Gap Manipulation of ACC-Equipped Vehicles

Bekiaris-Liberis, Nikolaos; Delis, A. I.

doi:10.1109/tcst.2020.2974148

Cited by 24 publications

(24 citation statements)

References 60 publications

(116 reference statements)

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“…We consider the ARZ traffic model introduced in [4] but we add an input delay which acts on adaptive cruise controlequipped (ACC-equipped) vehicles. The state variables of the model are the traffic density ρ(x, t) and the traffic speed v(x, t), both defined in domain (x, t) ∈ [0, L] × R + where t is time, x is the spatial variable and the constant L > 0 is the length of the concerned freeway stretch.…”

Section: Model Description a Arz Traffic Model With Mixed Vehiclesmentioning

confidence: 99%

“…Consider the same equilibria of system (1)-(4) as in [4], dictated by a constant inflow q in and a constant, steady-state time gap hacc for ACC-equipped vehicles, which results in the following steady-state traffic speed and density:…”

Section: B Linearization Of the Arz Modelmentioning

confidence: 99%

“…We apply the control law (47) directly on the nonlinear model ( 1)-( 4). The parameters utilized in the simulation are shown in Table I, for which we choose the same values as those in [4]. We also choose hm = 1s, see, e.g., [4], that is, slightly lower than 1.2s, which is the reported average value for the time gap, see, e.g., [20], [27], to reflect evidence that drivers may follow a preceding vehicle at smaller time gaps in congested traffic, compared to the case of light traffic conditions.…”

Section: Simulationmentioning

confidence: 99%

“…The stop-and-go oscillation in traffic flow leads to poorer driving experience, higher fuel consumption and a high accident risk. One promising way to reduce the oscillation in the congested regime is to develop control design tools that exploit the capabilities of automated and connected vehicles, such as manipulation of the time gap setting of ACC-equipped and connected vehicles [11], [4].…”

Section: Introductionmentioning

confidence: 99%

“…In order to eliminate the stop-and-go waves, a distributed actuation using the timegap of the ACC-equipped vehicles is employed for control. If the actuator delay is present and sufficiently large, the state feedback control proposed in [4] may become destabilizing.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Delay-Compensated Distributed PDE Control of Traffic with Connected/Automated Vehicles

Qi,

Mo,

Krstic

2021

Preprint

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We develop an input delay-compensating design for stabilization of an Aw-Rascle-Zhang (ARZ) traffic model in congested regime which is governed by a 2 × 2 first-order hyperbolic nonlinear PDE. The traffic flow consists of both adaptive cruise control-equipped (ACC-equipped) and manually-driven vehicles. The control input is the time gap of ACC-equipped and connected vehicles, which is subject to delays resulting from communication lag. For the linearized system, a novel three-branch bakcstepping transformation with explicit kernel functions is introduced to compensate the input delay. The transformation is proved aeto be bounded, continuous and invertible, with explicit inverse transformation derived. Based on the transformation, we obtain the explicit predictor-feedback controller. We prove exponential stability of the closed-loop system with the delay compensator in L2 norm. The performance improvement of the closed-loop system under the proposed controller is illustrated in simulation.

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Section: Model Description a Arz Traffic Model With Mixed Vehiclesmentioning

confidence: 99%

Section: B Linearization Of the Arz Modelmentioning

confidence: 99%

Section: Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Delay-Compensated Distributed PDE Control of Traffic with Connected/Automated Vehicles

Qi,

Mo,

Krstic

2021

Preprint

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Proximal policy optimization learning based control of congested freeway traffic

Mo,

Wu,

et al. 2023

Optim Control Appl Methods

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In this paper, a delay compensation feedback controller based on reinforcement learning is proposed to adjust the time interval of the adaptive cruise control (ACC) vehicle agents in the traffic congestion by introducing the proximal policy optimization (PPO) scheme. The high‐speed traffic flow is characterized by a two‐by‐two Aw Rasle Zhang nonlinear first‐order partial differential equations (PDEs). Unlike the backstepping delay compensation control,23 the PPO controller proposed in this paper consists of the current traffic flow velocity, the current traffic flow density and the previous one step control input. Since the system dynamics of the traffic flow are difficult to be expressed mathematically, the control gains of the three feedback can be determined via learning from the interaction between the PPO and the digital simulator of the traffic system. The performance of Lyapunov control, backstepping control and PPO control are compared with numerical simulation. The results demonstrate that PPO control is superior to Lyapunov control in terms of the convergence rate and control efforts for the traffic system without delay. As for the traffic system with unstable input delay value, the performance of PPO controller is also equivalent to that of backstepping controller. Besides, PPO is more robust than backstepping controller when the parameter is sensitive to Gaussian noise.

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Traffic flow control on cascaded roads by event‐triggered output feedback

Espitia

Auriol

et al. 2022

Intl J Robust & Nonlinear

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In this article, we propose an event‐triggered output‐feedback controller that guarantees the simultaneous stabilization of traffic flow on two connected roads. The density and velocity traffic dynamics are described with the linearized Aw‐Rascle‐Zhang macroscopic traffic partial differential equation model, which results in a coupled hyperbolic system. The control objective is to simultaneously stabilize the upstream and downstream traffic to a given spatially uniform constant steady‐state that is in the congested regime. To suppress stop‐and‐go traffic oscillations on the cascaded roads, we consider a ramp metering strategy that regulates the traffic flow rate entering from the on‐ramp to the mainline freeway. The ramp metering is located at the outlet with only boundary measurements of flow rate and velocity. Under the event‐triggered scheme, the control signal is only updated when an event triggering condition is satisfied. Compared with the continuous input signal, the event‐triggered boundary output control presents a more realistic setting to implement by ramp metering on a digital platform. The event‐triggered control design relies on the emulation of the backstepping boundary output feedback and on a dynamic event‐triggered strategy to determine the time instants at which the control value must be updated. We prove that there is a uniform minimal dwell‐time (independent of initial conditions), thus avoiding the Zeno phenomenon. We guarantee the exponential convergence of the closed‐loop system under the proposed event‐triggered control. A numerical example illustrates the results.

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PDE-Based Feedback Control of Freeway Traffic Flow via Time-Gap Manipulation of ACC-Equipped Vehicles

Cited by 24 publications

References 60 publications

Delay-Compensated Distributed PDE Control of Traffic with Connected/Automated Vehicles

Delay-Compensated Distributed PDE Control of Traffic with Connected/Automated Vehicles

Proximal policy optimization learning based control of congested freeway traffic

Traffic flow control on cascaded roads by event‐triggered output feedback

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