64 research outputs found
Exact boundary controllability for 1-D quasilinear hyperbolic systems with a vanishing characteristic speed
The general theory on exact boundary controllability for general first order
quasilinear hyperbolic systems requires that the characteristic speeds of
system do not vanish. This paper deals with exact boundary controllability,
when this is not the case. Some important models are also shown as applications
of the main result. The strategy uses the return method, which allows in
certain situations to recover non zero characteristic speeds.Comment: 20 page
Analysis and control of a scalar conservation law modeling a highly re-entrant manufacturing system
In this paper, we study a scalar conservation law that models a highly
re-entrant manufacturing system as encountered in semi-conductor production. As
a generalization of \cite{CKWang}, the velocity function possesses both the
local and nonlocal character. We prove the existence and uniqueness of the weak
solution to the Cauchy problem with initial and boundary data in .
We also obtain the stability (continuous dependence) of both the solution and
the out-flux with respect to the initial and boundary data. Finally, we prove
the existence of an optimal control that minimizes, in the -sense with
, the difference between the actual out-flux and a forecast
demand over a fixed time period.Comment: 32 pages, 12 figure
On the global controllability of scalar conservation laws with boundary and source controls
We provide global and semi-global controllability results for hyperbolic
conservation laws on a bounded domain, with a general (not necessarily
convex)flux and a time-dependent source term acting as a control. The results
are achieved for, possibly critical, both continuously differentiable states
and BV states. The proofs are based on a combination of the return method and
on the analysis of the Riccati equaiton for the space derivative of the
solution.Comment: 22 pages, 5 figure
Exact Boundary Controllability for Free Traffic Flow with Lipschitz Continuous State
We consider traffic flow governed by the LWR model. We show that a Lipschitz continuous initial density with free-flow and sufficiently small Lipschitz constant can be controlled exactly to an arbitrary constant free-flow density in finite time by a piecewise linear boundary control function that controls the density at the inflow boundary if the outflow boundary is absorbing. Moreover, this can be done in such a way that the generated state is Lipschitz continuous. Since the target states need not be close to the initial state, our result is a global exact controllability result. The Lipschitz constant of the generated state can be made arbitrarily small if the Lipschitz constant of the initial density is sufficiently small and the control time is sufficiently long. This is motivated by the idea that finite or even small Lipschitz constants are desirable in traffic flow since they might help to decrease the speed variation and lead to safer traffic
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