79 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
Boundary control and observation of coupled parabolic PDEs
Reaction-diffusion equations are parabolic Partial Differential Equations (PDEs) which
often occur in practice, e.g., to model the concentration of one or more substances, distributed
in space, under the in
uence of different phenomena such as local chemical reactions,
in which the substances are transformed into each other, and diffusion, which causes
the substances to spread out over a surface in space. Certainly, reaction-diffusion PDEs
are not confined to chemical applications but they also describe dynamical processes of
non-chemical nature, with examples being found in thermodynamics, biology, geology,
physics, ecology, etc.
Problems such as parabolic Partial Differential Equations (PDEs) and many others
require the user to have a considerable background in PDEs and functional analysis before
one can study the control design methods for these systems, particularly boundary control
design.
Control and observation of coupled parabolic PDEs comes in roughly two settingsdepending
on where the actuators and sensors are located \in domain" control, where
the actuation penetrates inside the domain of the PDE system or is evenly distributed
everywhere in the domain and \boundary" control, where the actuation and sensing are
applied only through the boundary conditions.
Boundary control is generally considered to be physically more realistic because actuation
and sensing are nonintrusive but is also generally considered to be the harder problem,
because the \input operator" and the "output operator" are unbounded operators.
The method that this thesis develops for control of PDEs is the so-called backstepping
control method. Backstepping is a particular approach to stabilization of dynamic
systems and is particularly successful in the area of nonlinear control. The backstepping
method achieves Lyapunov stabilization, which is often achieved by collectively shifting
all the eigenvalues in a favorable direction in the complex plane, rather than by assigning
individual eigenvalues. As the reader will soon learn, this task can be achieved in a rather
elegant way, where the control gains are easy to compute symbolically, numerically, and
in some cases even explicitly.
In addition to presenting the methods for boundary control design, we present the dual
methods for observer design using boundary sensing. Virtually every one of our control
designs for full state stabilization has an observer counterpart. The observer gains are
easy to compute symbolically or even explicitly in some cases. They are designed in
such a way that the observer error system is exponentially stabilized. As in the case of
finite-dimensional observer-based control, a separation principle holds in the sense that a
closed-loop system remains stable after a full state stabilizing feedback is replaced by a
feedback that employs the observer state instead of the plant state
Aeronautical engineering: A continuing bibliography with indexes (supplement 289)
This bibliography lists 792 reports, articles, and other documents introduced into the NASA scientific and technical information system in Mar. 1993. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics
Aeronautical Engineering: A continuing bibliography with indexes
This bibliography lists 529 reports, articles, and other documents introduced into the NASA Scientific and Technical Information System in May 1980
Goddard Visiting Scientist Program for the Space and Earth Sciences Directorate
A visiting scientist program was conducted in the space and earth sciences at GSFC. Research was performed in the following areas: astronomical observations; broadband x-ray spectral variability; ground-based spectroscopic and photometric studies; Seyfert galaxies; active galactic nuclei (AGN); massive stellar black holes; the differential microwave radiometer (DMR) onboard the cosmic background explorer (COBE); atmospheric models; and airborne and ground based radar observations. The specific research efforts are detailed by tasks
Aeronautical engineering: A continuing bibliography with indexes (supplement 284)
This bibliography lists 974 reports, articles, and other documents introduced into the NASA scientific and technical information system in Oct. 1992. The coverage includes documents on design, construction, evaluation, testing, operation, and performance of aircraft (including aircraft engines) and associated components, equipment, and systems. It also includes research and development in aerodynamics, aeronautics, and ground support equipment for aeronautical vehicles
Aeronautical engineering: A continuing bibliography with indexes (supplement 216)
This bibliography lists 505 reports, articles and other documents introduced into the NASA scientific and technical information system in July, 1987
Aeronautical Engineering: A cumulative index to the 1980 issue
This bibliography is a cumulative index to reports, articles, and other documents introduced into the NASA scientific and technical information system. Abstracts for the entries cited appeared in issues 119 through 130 of Aeronautical Engineering: A Continuing Bibliography (NASA SP-7037). Subject, personal author, corporate author, contract number, and report/accession number indexes are provided
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