Vehicle Merging Control Design for an Automated Highway System

The merging process in an automated highway system (AHS) is divided into a speed adjustment stage and a lane merging stage. Three important parameters, namely acceptability, availability and pursuability, are analyzed to characterize the AHS lane gap features for the ideal, smooth and safe merging of the ramp vehicles. Three control guidance laws, namely linear, optimal and parabolic speed profiles, are developed to describe the desired behaviors of the merging vehicle based on the merging quality and safety. The desired states of the merging vehicle are generated through the outer loop by specified control guidance law. The tracking errors compared with desired states are eliminated by the proper design of controllers in the inner loop. Both longitudinal and lateral controllers are designed using sliding mode control theory that can handle the nonlinear and model uncertainties of the vehicle dynamics. The simulation results show encouraging results

Peakon, pseudo-peakon, and cuspon solutions for two generalized Camassa- Holm equations

In this paper, we study peakon, cuspon, and pseudo-peakon solutions for two generalized Camassa-Holm equations. Based on the method of dynamical systems, the two generalized Camassa-Holm equations are shown to have the parametric representations of the solitary wave solutions such as peakon, cuspon, pseudo-peakons, and periodic cusp solutions. In particular, the pseudo-peakon solution is for the first time proposed in our paper. Moreover, when a traveling system has a singular straight line and a heteroclinic loop, under some parameter conditions, there must be peaked solitary wave solutions appearing

Bifurcations of traveling wave solutions for an integrable equation

This paper deals with the following equation mt= 1/2 1/mk xxx− 1/2 1/mk x, which is proposed by Z. J. Qiao J. Math. Phys. 48, 082701 2007 and Qiao and Liu Chaos, Solitons Fractals 41, 587 2009. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the cases of k=−2,−1 2 , 1 2 ,2, and parametric representations of all possible bounded traveling wave solutions are given in the different c,g -parameter regions