Mohammad Hajiahmadi

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 dynamic route guidance: A model predictive approach using the macroscopic fundamental diagram

Since centralized control of urban networks with detailed modeling approaches is computationally complex and inefficient, hierarchical decentralized methods based on aggregate models are of great importance. In this paper, we use an aggregate modeling approach based on the macroscopic fundamental diagram (MFD), in order to find dynamic optimal routing strategies. An urban area can be divided into homogeneous regions each modeled by a (set of) macroscopic fundamental diagrams. Thus, the problem of route guidance can be solved in a regional fashion by using model predictive control and the novel high-level MFD-based model used for prediction of traffic states in the urban network. The optimal routing advices obtained from the high-level controller can be used as references (to track) for lower-level local controllers installed at the borders of the regions. Hence, the complexity of solving the routing problem will be decreased significantly. The performance of the proposed approach is evaluated using a multi-origin multi-destination grid network. Further, the obtained results show significant performance of the optimal dynamic route guidance over other static routing methods.

Stabilization and robust H ∞ control for sector-bounded switched nonlinear systems

This paper presents stability analysis and robust H ∞ control for a particular class of switched systems characterized by nonlinear functions that belong to sector sets with arbitrary boundaries. The sector boundaries can have positive and/or negative slopes, and therefore, we cover the most general case in our approach. Using the special structure of the system but without making additional assumptions (e.g. on the derivative of the nonlinear functions), and by proposing new multiple Lyapunov function candidates, we formulate stability conditions and a control design procedure in the form of matrix inequalities. The proposed Lyapunov functions are more general than the quadratic functions previously proposed in the literature, as they incorporate the nonlinearities of the system and hence, lead to less conservative stability conditions. The stabilizing switching controllers are designed through a bi-level optimization problem that can be efficiently solved using a combination of a convex optimization algorithm and a line search method. The proposed optimization problem is achieved using a special loop transformation to normalize the arbitrary sector bounds and by other linear matrix inequalities (LMI) techniques.

Integrated Predictive Control of Freeway Networks Using the Extended Link Transmission Model

In this paper, the recently developed link transmission model (LTM) is utilized in an online hybrid model-based predictive control (MPC) framework. The model is extended to include the effects of ramp metering and variable speed limits. Next, an integrated freeway traffic control based on the new model is presented in order to minimize the total time spent in the network. The integrated scheme has the capability of controlling large-scale freeway networks in real time as the model is computationally efficient, and it is yet accurate enough for our control purposes. In addition, the extended model is reformulated as a system of linear inequalities with mixed binary and real variables. The reformulated model along with the linearized total travel time objective function establish a mixed-integer linear optimization problem that is more tractable and even faster than the original optimization problem integrated in the MPC scheme. Finally, to investigate the performance of the proposed approaches (nonlinear MPC and the mixed-integer linear counterpart), a freeway network layout based on the Leuven Corridor in Belgium is selected. The extended LTM is calibrated for this network using microsimulation data and then is used for prediction and control of the large network. Microsimulation results show that the proposed methods are able to efficiently improve the total travel time.

Design of Stabilizing Switching Laws for Mixed Switched Affine Systems

This technical note presents stability analysis and stabilization for a general class of switched systems characterized by nonlinear functions. The proposed approach is composed of approximating the switched nonlinear system with a switched affine system that has a mixture of controlled and autonomous switching behavior. Utilizing a joint polyhedral partitioning approach, a stabilizing switching law based on quadratic Lyapunov functions and with considering the autonomous switching between polyhedral regions is proposed. To ensure the decrease of the overall Lyapunov function, two approaches are proposed: 1) guarantee continuity of the Lyapunov function over boundaries of polyhedral regions and 2) relax the continuity requirement by using additional matrix inequalities. The second approach is less conservative but with more variables and matrix inequalities than in the first method. With fixing one scalar variable, the stabilization conditions will have the form of linear matrix inequalities (LMIs). Further, the sufficient conditions for stabilizing the original switched nonlinear system using the proposed switching schemes are presented. Finally, through two examples, the performance of the proposed stabilization methods is demonstrated.

Distributed identification of the Cell Transmission traffic model: A case study

The problem of the distributed identification of a macroscopic first-order traffic model, viz. the Cell Transmission Model (CTM), is considered in the paper. The parameters to be identified characterize the dynamics of the density in different sections of the freeway (cells). We explore different distributed identification schemes. The purposes of the approach are mainly to obtain good prediction models through the minimization of the one-step ahead prediction error of the densities of the cells, and to reduce the computational time and the effort required to perform the identification. The methodology is validated relying on real-life data measured on a portion of the A12 freeway in The Netherlands. An evaluation of the performance of the identified model used as a set of virtual sensors in different scenarios is presented.

Variable speed limit control based on extended link transmission model

In this paper the link transmission model (LTM) is extended to include the effects of variable speed limit (VSL) and consequently to provide VSL control for traffic networks modeled by the LTM. The LTM was recently developed for route assignment, but in this study the LTM was modified to be used for control purposes. This modification achieved a model that provides a balanced trade-off between accuracy and computational complexity, and therefore the model is useful for online model-based traffic control. Nevertheless the extension of the model for ramp metering and speed limit control needed careful attention. Because the LTM lacks explicit velocity equations, the focus was on other potential sources that could imitate the influences of VSL. The delays inside the model were manipulated to achieve the mentioned goal. Moreover, different situations were taken into account that might occur in reality on the basis of changes in VSL and different traffic conditions. Finally, the total extensions were verified with simulation and real data. For that aim to be achieved, the VSL extension integrated in the LTM was verified with simulations for a benchmark case study (to show the performance of the extended LTM clearly). Next, the LTM was calibrated by real data collected from the A12 freeway in the Netherlands. The optimal parameters of the model were identified with a global optimization method. Comparison with real data from a period of time when VSL installed on the freeway was active showed the acceptable performance of the total extended and calibrated LTM.

Distributed model predictive control of freeway traffic networks: A serial partially cooperative approach

In this paper, a new distributed model predictive control (MPC) scheme for freeway traffic control is proposed. It is aimed at reducing the communication efforts and the computation times in a large network. This new algorithm can coordinate a large number of on-ramps throughout a freeway network in a partially cooperative scheme. The communication is performed between neighboring on-ramps in a special serial fashion and with three different proposed cooperative schemes. The computation time is much less than that of existing distributed MPC approaches in the literature, while achieving a performance close to the one of the centralized MPC method. To evaluate the performance of the proposed partially cooperative schemes, a freeway network case study is selected and the problem of coordination between several on-ramps is solved using different methods from a centralized approach to a fully decentralized one. The obtained results show a significant decrease in the total computation time with respect to the centralized and fully cooperative schemes, while maintaining a close distance to the optimal objective function obtained from the centralized case. Furthermore, the performance of the proposed partially cooperative MPC method is evaluated in the case of incidents in the network.

Robust H ∞ control for switched nonlinear systems with application to high-level urban traffic control

This paper presents robust switching control strategies for switched nonlinear systems with constraints on the control inputs. First, a model transformation is proposed in a way that the constraint on the continuous control inputs is relaxed. Next, the effect of disturbance is taken into account and the L2-gain analysis and H∞ control design problem for switched nonlinear systems are formulated and proved. Furthermore, the obtained control laws are utilized for urban traffic networks modeled on a high-level using macroscopic fundamental diagram representation. The flow transferred between urban regions along with the timing plans for each region are controlled using continuous and switching controllers. The control objective is translated into a stability and disturbance attenuation problem for the urban network represented as a switched nonlinear system. The uncertain trip demands are considered as norm-bounded disturbance inputs. One major advantage of the proposed scheme is that the parameters of the feedback switching law are obtained offline. Hence, real-time control is possible with this scheme. The achieved results show great performance of the proposed approach in handling uncertain demand profiles.

Robust H ∞ control of a class of switched nonlinear systems with application to macroscopic urban traffic control

This paper presents stability analysis and robust H∞ control for nonlinear switched systems bounded in sectors with arbitrary boundaries. By proposing new and more general multiple Lyapunov functions that incorporate nonlinearities in the system, we formulate the stability conditions under arbitrary switching in the form of linear matrix inequalities. Moreover, an optimization problem subject to bilinear matrix inequalities is established in order to determine the minimum L2-gain along with the optimal matrices for the Lyapunov functions and for the robust state feedback gains. Finally, the optimization problem is recast as a bi-level convex optimization problem using loop transformation and other linear matrix inequalities techniques. Furthermore, in order to illustrate the performance of the proposed switching control scheme, results for control of an urban network partitioned into sub-regions and modeled using a high-level hybrid model are presented.