35 research outputs found
Mean-square Exponential Stabilization of Mixed-autonomy Traffic PDE System
Control of mixed-autonomy traffic where Human-driven Vehicles (HVs) and
Autonomous Vehicles (AVs) coexist on the road have gained increasing attention
over the recent decades. This paper addresses the boundary stabilization
problem for mixed traffic on freeways. The traffic dynamics are described by
uncertain coupled hyperbolic partial differential equations (PDEs) with Markov
jumping parameters, which aim to address the distinctive driving strategies
between AVs and HVs. Considering the spacing policies of AVs vary in the mixed
traffic, the stochastic impact area of AVs is governed by a continuous Markov
chain. The interactions between HVs and AVs such as overtaking or lane changing
are mainly induced by the impact areas. Using backstepping design, we develop a
full-state feedback boundary control law to stabilize the deterministic system
(nominal system). Applying Lyapunov analysis, we demonstrate that the nominal
backstepping control law is able to stabilize the traffic system with Markov
jumping parameters, provided the nominal parameters are sufficiently close to
the stochastic ones on average. The mean-square exponential stability
conditions are derived, and the results are validated by numerical simulations
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal