Modeling

This paper describes an adaptive control approach to improve urban mobility and relieve congestion. The basic idea consists in monitoring and controlling aggregate vehicular accumulations at the neighborhood level. To do this, physical models of the gridlock phenomenon are presented both for single neighborhoods and for systems of inter-connected neighborhoods. The models are dynamic, aggregate and only require observable inputs. The latter can be obtained in real-time if the neighborhoods are properly instrumented. Therefore, the models can be used for adaptive control. Experiments should...

This book focuses on control problems for conservation laws, i.e., equations of the type: ∂tu+∂xf(u)=0ut+(f(u))x=0,$$\displaystyle \partial _t\, u + \partial _x\, f(u) = 0 \qquad u_t+(f(u))_x=0, $$where u:ℝ+×ℝ→ℝn$$u:\mathbb {R}^+\times \mathbb {R} \to \mathbb {R}^n$$is the vector of conserved quantities and f:ℝn→ℝn$$f:\mathbb {R}^n\to \mathbb {R}^n$$is the flux. Most results will be given for the scalar case (n = 1), but we will present few results valid in the general case.

This chapter focuses on control of systems of conservation laws with boundary data. Problems with one or two boundaries are considered and, in particular, we focus on cases where shocks may be developed by the solution. However, for completeness we briefly discuss in Sect. 2.2 other existing results where singularities are prevented via suitable feedback controls such as in [32].

The first-order degenerate parabolic traffic flow dynamics are the simplest extension of the Lighthill, Whitham, and Richards (LWR) model which aim at correcting the discrepancies between the LWR model and the observation collected from real data. In addition, the nonlinearity and degeneracy of these models are designed to address the fundamental criticism of linear diffusivelycorrected kinematic-wave models. While several first-order methods have been proposed in the literature, the predictive capabilities of these models has not been sufficiently studied with respect to real data. The...