Jack Haddad

Optimal Perimeter Control for Two Urban Regions With Macroscopic Fundamental Diagrams: A Model Predictive Approach

Recent analysis of empirical data from cities showed that a macroscopic fundamental diagram (MFD) of urban traffic provides for homogenous network regions a unimodal low-scatter relationship between network vehicle density and network space-mean flow. In this paper, the optimal perimeter control for two-region urban cities is formulated with the use of MFDs. The controllers operate on the border between the two regions and manipulate the percentages of flows that transfer between the two regions such that the number of trips that reach their destinations is maximized. The optimal perimeter control problem is solved by model predictive control, where the prediction model and the plant (reality) are formulated by MFDs. Examples are presented for different levels of congestion in the regions of the city and the robustness of the controller is tested for different sizes of error in the MFDs and different levels of noise in the traffic demand. Moreover, two methods for smoothing the control sequences are presented. Comparison results show that the performances of the model predictive control are significantly better than a “greedy” feedback control. The results in this paper can be extended to develop efficient hierarchical control strategies for heterogeneously congested cities.

Optimal Hybrid Perimeter and Switching Plans Control for Urban Traffic Networks

Since centralized control of urban networks with detailed modeling approaches is computationally complex, developing efficient hierarchical control strategies based on aggregate modeling is of great importance. The dynamics of a heterogeneous large-scale urban network is modeled as R homogeneous regions with the macroscopic fundamental diagrams (MFDs) representation. The MFD provides for homogeneous network regions a unimodal, low-scatter relationship between network vehicle density and network space-mean flow. In this paper, the optimal hybrid control problem for an R-region MFD network is formulated as a mixed-integer nonlinear optimization problem, where two types of controllers are introduced: 1) perimeter controllers and 2) switching signal timing plans controllers. The perimeter controllers are located on the border between the regions, as they manipulate the transfer flows between them, while the switching controllers influence the dynamics of the urban regions, as they define the shape of the MFDs and as a result affect the internal flows within each region. Moreover, to decrease the computational complexity due to the nonlinear and nonconvex nature of the optimization problem, we reformulate the problem as a mixed-integer linear programming (MILP) problem utilizing piecewise affine approximation techniques. Two different approaches for transformation of the original model and building up MILP problems are presented, and the performances of the approximated methods along with the original problem formulation are evaluated and compared for different traffic scenarios of a two-region urban case study.

Optimal Steady-State Control for Isolated Traffic Intersections

A simplified isolated controlled vehicular traffic intersection with two movements is considered. A discrete-event max-plus model is proposed to formulate an optimization problem for the green-red switching sequence. In the case when the criterion is a strictly increasing, linear function of the queue lengths, the problem becomes a linear programming problem. Also, in this case, the steady-state control problem can be solved analytically. A sufficient and necessary condition for steady-state control is derived, and the structure of optimal steady-state traffic control is revealed. Our condition is the same as the necessary condition in for both queue lengths to be non-increasing at an isolated intersection.

Optimal Steady-State Traffic Control for Isolated Intersections

Abstract In this paper a simplified isolated controlled intersection is introduced. A discrete-event max-plus model is proposed to formulate the optimization problem for the switching sequences. The formulated max-plus problem is converted to be solved by linear programming (LP). In the special case when the criterion is a strictly increasing and linear function of the queue lengths, the steady-state control problem can be solved analytically. In addition, necessary condition for the steady-state control is derived.

Steady-state and N-stages control for isolated controlled intersections

In this paper a simplified isolated controlled intersection is introduced. Discrete-event piecewise affine (PWA) and discrete-event max-plus models are proposed to formulate the optimization problem for the switching sequences. Two control problems are considered: steady-state control and N-stages control. The formulated discrete-event PWA and maxplus problems are converted to be solved by linear programming (LP), mixed-integer programming (MIP), and mixed-integer linear programming (MILP). In the special case when the criterion is a strictly monotonous and linear function of the queue lengths, the steady-state control problem is solved analytically.

Offset effects on the capacity of paired signalised intersections during oversaturated conditions

Paired signalised intersections (PSI) are two closely signalised intersections with short distance between them as queue spillbacks and upstream intersection blockages occur. Due to queue spillbacks, the PSI have their own consideration regarding operational characteristics that are different from isolated intersections or coordinated networks. This paper explores the effects of timing plans offset on the movement capacity that passes through both intersections under several cases and situations. For this purpose, an analytical model is chosen to evaluate the movement capacities. The model has been coded and integrated into INBAR software, then it has been validated with results from the micro simulation software Vissim for various tests. A comparison of the two sets of results shows only minor deviations. The importance of offset is demonstrated through sensitivity analyses for different timing plan variables and parameters.

Design of optimal traffic flow control at intersection with regard for queue length constraints

Consideration was given to a well-known problem of traffic control at an individual intersection with minimal total delay. The constraints on control (duration of green light in the main direction) and phase variables (queue lengths along each direction) were taken into account. A continuous traffic model and the methods of the optimal control theory were used. An analytical solution was established in the form of feedback control design. The solutions obtained were compared with the results acquired in the 1960s and 1970s.

Robust control design for a perimeter traffic flow controller at an urban region

Recent works have introduced perimeter feedback-control strategies for a homogenous urban region and multiple urban regions with the help of the macroscopic fundamental diagram (MFD) representation, that relates average flow and density (or accumulation) across the network. The perimeter controller is located on the region border, and manipulates the transfer flows across the border, while aiming at regulating around (nearby) the critical densities or accumulations, whereby the system throughput is maximized. While in the one urban region system the desired state is known in advance (given the MFD shape), for the system with multiple urban regions the desired accumulation points are not well known. Moreover, in some traffic scenarios the controller cannot regulate around the critical accumulations, e.g. because of high demand. In this paper, a robust perimeter controller for an urban region is designed. The controller aims at satisfying the control specifications and having a good performance for the whole accumulation set, uncongested and congested accumulations, and not necessary for a value range nearby the critical accumulation set-point. Moreover, unlike previous works, the robust controller is also designed to handle the control constraint within the design level in a systematic way, where the constraints are explicitly integrated utilizing the so-called describing function. Comparison results show that the performances of the robust controller are significantly better than a “standard” feedback controller, for different traffic scenarios.

Macroscopic Traffic Control of a Mixed Urban and Freeway Network

Abstract In this paper, the macroscopic traffic control of a large-scale mixed transportation network consisting of freeway and urban network is tackled. The urban network is partitioned in two regions, each one with a well-defined macroscopic fundamental diagram (MFD), i.e. a unimodal and low-scatter relationship between network density and outflow. The freeway is regarded as one alternative commuting route which has one on-ramp and one off-ramp within each urban region. The urban and freeway flow dynamics are formulated with the tool of MFD and asymmetric cell transmission models, respectively. Four controllers are considered to control the flow distribution between urban regions and freeway: (i) two on the border of urban regions operating to manipulate the perimeter interflow rates between the two regions, and (ii) two other controllers on the on-ramps for ramp metering to control the flow rates from urban roads to the freeway. The optimal traffic control problem for the mixed network is solved by a receding horizon approach in order to maximize the number of trips that reach their destinations. The results of this paper can be extended to develop efficient control strategies for large-scale mixed traffic networks.

Tracking with asymptotic sliding mode and adaptive input delay effect compensation of nonlinearly perturbed delayed systems applied to traffic feedback control

ABSTRACT Asymptotical sliding mode-model reference adaptive control design for a class of systems with parametric uncertainty, unknown nonlinear perturbation and external disturbance, and with known input and state delays is proposed. To overcome the difficulty to directly predict the plant state under uncertainties, a control design is based on a developed decomposition procedure, where a ‘generalised error’ in conjunction with auxiliary linear dynamic blocks with adjustable gains is introduced and the sliding variable is formed on the basis of this error. The effect of such a decomposition is to pull the input delay out of first step of the design procedure. As a result, similarly to the classical Smith predictor, the adaptive control architecture based only on the lumped-delays, i.e. without conventional in such cases difficult-implemented distributed-delay blocks. Two new adaptive control schemes are proposed. A linearisation-based control design is constructed for feedback control of an urban traffic region model with uncertain dynamics. Simulation results demonstrate the effectiveness of the developed adaptive control method.