421 research outputs found
Internal rapid stabilization of a 1-D linear transport equation with a scalar feedback
We use the backstepping method to study the stabilization of a 1-D linear
transport equation on the interval (0, L), by controlling the scalar amplitude
of a piecewise regular function of the space variable in the source term. We
prove that if the system is controllable in a periodic Sobolev space of order
greater than 1, then the system can be stabilized exponentially in that space
and, for any given decay rate, we give an explicit feedback law that achieves
that decay rate
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
Minimum time control of heterodirectional linear coupled hyperbolic PDEs
We solve the problem of stabilization of a class of linear first-order
hyperbolic systems featuring n rightward convecting transport PDEs and m
leftward convecting transport PDEs. Using the backstepping approach yields
solutions to stabilization in minimal time and observer based output feedback
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