2 research outputs found
Adaptive unit-vector control of an uncertain heat diffusion process
This paper deals with the distributed tracking control of a heat process having uncertain diffusivity and subject to a distributed disturbance whose L2 norm is bounded by a constant which is not known a priori. Under certain regularity assumptions on the disturbance and on the chosen reference profile, a distributed unit-vector control, with an adaptive magnitude, is designed which provides the asymptotic tracking of the reference. The logic governing the gain adaptation is gradient-based and monodirectional, i.e. the gain cannot decrease over time. Lyapunov arguments are invoked to support the convergence properties of the proposed scheme, whose performance are also investigated by means of computer simulation
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