3,529 research outputs found
Control of Homodirectional and General Heterodirectional Linear Coupled Hyperbolic PDEs
Research on stabilization of coupled hyperbolic PDEs has been dominated by
the focus on pairs of counter-convecting ("heterodirectional") transport PDEs
with distributed local coupling and with controls at one or both boundaries. A
recent extension allows stabilization using only one control for a system
containing an arbitrary number of coupled transport PDEs that convect at
different speeds against the direction of the PDE whose boundary is actuated.
In this paper we present a solution to the fully general case, in which the
number of PDEs in either direction is arbitrary, and where actuation is applied
on only one boundary (to all the PDEs that convect downstream from that
boundary). To solve this general problem, we solve, as a special case, the
problem of control of coupled "homodirectional" hyperbolic linear PDEs, where
multiple transport PDEs convect in the same direction with arbitrary local
coupling. Our approach is based on PDE backstepping and yields solutions to
stabilization, by both full-state and observer-based output feedback,
trajectory planning, and trajectory tracking problems
Kinetic layers and coupling conditions for macroscopic equations on networks I: the wave equation
We consider kinetic and associated macroscopic equations on networks. The
general approach will be explained in this paper for a linear kinetic BGK model
and the corresponding limit for small Knudsen number, which is the wave
equation. Coupling conditions for the macroscopic equations are derived from
the kinetic conditions via an asymptotic analysis near the nodes of the
network. This analysis leads to the consideration of a fixpoint problem
involving the coupled solutions of kinetic half-space problems. A new
approximate method for the solution of kinetic half-space problems is derived
and used for the determination of the coupling conditions. Numerical
comparisons between the solutions of the macroscopic equation with different
coupling conditions and the kinetic solution are presented for the case of
tripod and more complicated networks
A Polynomial Spectral Calculus for Analysis of DG Spectral Element Methods
We introduce a polynomial spectral calculus that follows from the summation
by parts property of the Legendre-Gauss-Lobatto quadrature. We use the calculus
to simplify the analysis of two multidimensional discontinuous Galerkin
spectral element approximations
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