Petr Nedoma

Initial Description of Multi-Modal Dynamic Models

Multiple models, neural networks, cluster analysis and probabilistic mixtures are prominent examples of situations when complex multi-modal models [1] are built using vast amount of data. Complexity and non-unicity of modified situation imply that resulting description depends heavily on the initial phase of search. The safest repetitive purely random search is mostly inhibited by computational complexity of the addressed task. For this reasons, various techniques have been designed. None of them, to our best knowledge, suits to cases when dynamic models are constructed. The paper describes a novel technique that fills this gap in a promising way. Essentially, the trial description is gradually split whenever there is possibility that a unimodal sub-model hides more modes.

CROSS-VALIDATION OF CONTROLLED DYNAMIC MODELS: BAYESIAN APPROACH

Abstract The best test of quality of an estimated model is its implementation in real application. However, the use of a bad model is typically too costly. Therefore, model validation is considered as an obligatory step in model learning, and extensive theory has been developed within statistical community. However, the available rules deal almost exclusively with independent data samples. Consequently, they are substantially disqualified for validation of dynamic models. This paper approaches the problem using Bayesian formulation and solution. An algorithm for validation of models estimated within practically important exponential family is presented. Performance of the algorithms is illustrated on simulated example.

Factorized EM Algorithm for Mixture Estimation

A classical version of the EM algorithm is considered in the paper. Its numerical properties are improved using factorized algorithms for maximization in M step of the algorithm. The results are illustrated on simulated examples.

Software Tools for Use of Prior Knowledge in Design of LQG Adaptive Controllers

Abstract A systematic probabilistic approach to off-line design of LQG adaptive controllers can be supported by use of prior information in each design step. The prior information processing and its use is a relative new topic. The article contributes to understanding of the prior knowledge importance by a simulation case study. A toolbox ABET for MATLAB (MathWorks) is presented that makes it possible to carry out each step of design of adaptive controller with use of prior knowledge.

APPROXIMATE ARX MODEL ESTIMATION FOR JACKETING ADAPTIVE SYSTEMS

Abstract Recently, a substantial progress has been achieved in attempts to merge systematically various pieces of information of different precision, compatibility and origin. The developed technique provides a new tool needed for jacketing adaptive predictors/controllers based on LQG the paradigm. When applied to the autoregressive model with exogenous variables (ARX) the method contributes to the solution of the following tasks: - incorporation of prior knowledge into initial conditions of the recursive least squares; - Instruction of a reference for an advanced forgetting technique; - improvement of Bayesian structure estimation algorithm. Here, a practical experience with the procedure will be reported using realistic simulation results.

ESTIMATION OF APPROXIMATE MARKOV CHAINS

Abstract Controlled Markov chains represent important universal class of models distinguished by their ability to describe non-linear stochastic dynamic systems. However, their use is restricted: the demands on the amount of data as well as on computer power required for the estimation blow up exponentially with the dimension of their state. Recently proposed Bayesian infonnation pooling has been recognized as a promising tool for approaching the dimensionality problem. Essentially, Markov chains with low-dimensional states are estimated independently and pooled into a global description of the system. The partial models are naturally approximate and this fact should be taken into account by the estimation procedure used which has to be adaptive. Within the Bayesian framework, an analogy of exponential and/or restricted forgetting can be used. In this paper, an attempt to improve the estimation of the approximate Markov chain is presented. It is based on the same pooling idea, now applied to a single model understood as a collection of models labelled by the measured states.

Solving control engineering problems with MATLAB

This book was designed to help engineering students as well as practising engineers to use MATLAB (MathWorks) to solve classical control engineering problems and to present the results of control systems analysis in graphical form. The book successfully fills a gap that exists in the control engineering literature-there are excellent texts treating theory as well as outstanding software tools. but little has been done to connect them and to outline possible software solutions. The MATLAB background required of the book is not limiting, since most CADCS (CAD of control systems) packages facilitate problem solving in a similar way. MATLAB is one of the most popular CADCS packages, and offers an excellent collection of commands and functions that are immediately applicable to solving control engineering problems. The author presupposes that the reader has access to at least the student edition of MATLAB. namely to the routines to compute and display: step responses; root-locus plots; frequency-response plots (both Bode and Nyquist plots); transformation between state-space and transfer-function models: eigenvalues and eigenvectors of square matrices; conversion from continuous-time models to discrete-time models; design of linear quadratic regulators. This selection of functions shows that the book is orientated towards classical methods for linear. timeinvariant and deterministic control systems-both continuousand discrete-time. The reader should have a background in linear control at the level of at least a university introductory control course. Each topic treated in the book begins with a clear summary of the problem formulation and solution. and a broad selection of examples is given. The examples constitute the main contribution of the book; the selection is excellent and is based on the author’s broad experience in teaching the subject and on his previous publications. We shall now briefly summarize the book’s contents. The first two chapters represent an introduction to MATLAB, and discuss the background material concerning matrix operations, the computation of eigenvalues and eigenvectors and functions that work with polynomials. The function ‘plot’ is discussed in detail, since it forms the basic tool for presentation of results throughout the book. These chapters