| annote | = | {This work aims to contribute to modelling and fast predictive control
of processes. It can be divided into several topics.
Process modelling is investigated and an effective approximation
technique is described. It can be used to approximate an original
non-linear process model as a hybrid system with piecewise affine
dynamics. We discuss three different cases, how one can
obtain the approximation of an arbitrary nonlinear function. The most
trivial case assumes that the analytic form of the nonlinear term is
already known. On the other hand, if only some set of input-output
measurements are given, we employ a two-stage procedure to obtain the
final approximation. This method aims to select the appropriate subset
of basis functions and consecutively finding a proper linear
combination of them. Once we possess the analytic formula of our
approximated function, we can obtain the final PWA approximation by
solving standard nonlinear programs. We show, that under mild
assumptions, the task can be transformed into a series of
one-dimensional problems. Finally, we demonstrate the efficiency of
our technique on an illustrative example, involving a highly nonlinear
reactor.
The second part of the work deals with fast model predictive control.
We investigate the problem of reduction of the amount of memory needed
to describe explicit MPC solutions. The main idea of explicit MPC
stems from pre-computation of the optimal control action for all
possible initial conditions and subsequently storing them in a form of
a look-up table. On one hand, this concept allows faster
implementation, but on the other, requirements for memory storage
increase too. In order to eliminate this drawback, we continue with
a description of an effective, three-layer compression technique,
allowing fast implementation on low-cost hardware platforms. This
three-layer procedure first identifies similarities between polytopic
regions in form of an affine transformation. If such a mapping exists,
certain regions can be represented using less data. The second layer
then applies data de-duplication to identify and remove repeating
sequences of data. Regions are then described by integer pointers to
such a unique set. Finally Huffman encoding is applied to compress
such integer pointers using prefix-free variable-length bit
encoding. The chapter ends with efficiency evaluation of the proposed
technique on several, randomly generated feedback law examples.
The final chapter is devoted to the so-called operator splitting methods,
by means of one can solve convex optimisation problems very efficiently
by simply decomposing the original possibly complex problem into a
series of simple operations well known from linear algebra.
Several algorithms and their range of applicability are presented.}, |