# Institute of Information Engineering, Automation, and Mathematics

Alexander Szucs will give a seminar on "Algorithms for Process Modelling and Fast Model Predictive Control" on Thursday, July 10, 2014 at 13:00 in room no. 641.

In the first part of the seminar 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.

Second part of the presentation 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 part of the talk 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.