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.@en

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.@en