Data

Using least-squares with an l1-norm penalty is well-known to encourage sparse solutions. In this article, we propose an algorithm that performs online least-squares estimation of a time varying system with a l1-norm penalty on the variations of the state estimate, leading to state estimates that exhibit few “jumps” over time. The algorithm analytically computes a path to update the state estimate as a new observation becomes available. The algorithm performs computationally efficient and numerically robust state estimation for time varying systems in which the dynamics are slow compared to...

In this article, a new analytical traffic flow model is proposed for traffic dynamics at signalized intersections. During each cycle, both the arrival and the departure traffic are approximated by three distinct traffic streams with uniform density. Because of the similar representation of the arrival and the departure traffic, results from a single intersection can easily be extended to a series of intersections. With this model, the number of parameters of the model is tractable, leading to analytical solutions of the problem. It also is proved that the total delay of one-way...

In arterial networks, traffic flow dynamics are driven by the presence of traffic signals, for which precise signal timing is difficult to obtain in arbitrary networks or might change over time. A comprehensive model of arterial traffic flow dynamics is necessary to capture its specific features in order to provide accurate traffic estimation approaches. From hydrodynamic theory, arterial traffic dynamics are modeled under specific assumptions standard in transportation engineering. This flow model is used to develop a statistical model of arterial traffic. The statistical approach...

We consider the initial-boundary value problem governed by systems of linear hyperbolic partial differential equations in the canonical diagonal form and study conditions for exponential stability when the system discontinuously switches between a finite set of modes. The switching system is fairly general in that the system matrix functions as well as the boundary conditions may switch in time. We show how the stability mechanism developed for classical solutions of hyperbolic initial boundary value problems can be generalized to the case in which weaker solutions become necessary due to...