Complexity has many facets as does any general concept. The relationship between "infinitely" complex reality and restricted complexity of the artificial world of models is addressed. Particularly, the paper tries to clarify the meaning of Bayesian identification under mismodelling by answering the question, "What is the outcome of the Bayesian identification without supposing the model set considered contains the "true" system model?" The answer relates known asympotic results to the "natural" finite-time domain of Bayesian paradigm. It serves as an interpretation "smoother" of those Bayesian identification results that quietly ignore the mismodelling present. Keywords: decision-making, model selection, Bayesian identification, approximation 1 Introduction System identification can be understood as the set of procedures which model an investigated part of reality (called object, process, plant or system) using data measured on it [8]. Modelling of the reality, often informal, is a n...

Ústav teorie informace a automatizace, v.v.i.

The problem of model structure determination of an examined process is usually necessary prerequsite for successful prediction and/or control of the process. In particular, dynamic, discrete-in-time, input-output, stochastic, parametrized, linear-in-parameters, with normal white noise, models have been used to describe the process. Due to the incompleteness of the available information about it, a certain number of hypotheses about the model structure is formulated and the best (optimal, true) one corresponding to the true model structure (which is supposed to be among them) is searched for. Bayesian statistics proved to be a useful tool for theoretical solution of the presented problem. However, the number of competitive hypotheses appeared to be very large to find between them the best one. Thus, the special algorithm was developed which searches only a "reasonable" subset of all the hypotheses and tries to find the true model structure of the examined process.

This paper represents only the first step in the indicated direction. It deals only with identification of a single traffic flow (it detects only the traffic state in a specific position of a single road). The further development will aim to the identification of some more complex situation (crossroads and area of crossroads) and finally to the control of traffic areas. 19 8 Appendix I. Selection of initial conditions

This paper presents experiments with tracking time--varying parameters of a dynamic system applied to parameter estimation and smoothing of piecewise continuous function. The smoothing algorithm is based on bayesian computation of the probability distribution over the set of alternative hypotheses describing a set of alternative models of expected (possible) parameter development. The sequence of optimal hypotheses can be interpreted as a solution of the continuity fault detection problem. The properties of the algorithm are illustrated on the simulated and real range data. 1 Introduction Extended Kalman filter is generally used for simultaneous parameter tracking and state estimation in time--varying systems. I our case the augmented state of the system consists of parameter state vector only. To achieve the parameter tracking ability in the case of time-- varying parameters, some form of obsolete information forgetting must be incorporated into the identification algorithm. The forg...

Abstract Growing interest in applications of distributed systems, such as multi-agent systems, increases demands on identification of distributed systems from partial information sources collected by local agents. We are concerned with fully distributed scenario where system is identified by multiple agents, which do not estimate state of the whole system but only its local ‘state’. The resulting estimate is obtained by merging of marginal and conditional posterior probability density functions (pdf) on such local states. We investigate the use of recently proposed non-parametric log-normal merging of such ‘fragmental ’ pdfs for this task. We derive a projection of the optimal merger to the class of weighted empirical pdfs and mixtures of Gaussian pdfs. We illustrate the use of this technique on distributed identification of a controlled autoregressive model.

Decentralized adaptive control is based on the use of many local controllers in parallel, each of them estimating its own local model and pursuing local aims. When each controller designs its strategy using only its model, the resulting control will be suboptimal since its local model is not predicting consequences of actions of the neighbors. We propose to improve this by exchange multistep predictors on common data between the neighboring controllers and their subsequent use in the design of control strategy. Care is taken to assure that the resulting design procedure is of the same complexity as the one without the exchange. Performance of the approach is illustrated on a simple example. 1

Ústav teorie informace a automatizace, v.v.i.

Ústav teorie informace a automatizace, v.v.i.

Abstract – Particle filtering has evolved into wide range of techniques giving rise to many implementations and specialized algorithms. In theory, all these techniques are closely related, however this fact is usually ignored in software implementations. In this paper, particle filtering is studied together with marginalized particle filtering and a generic software scheme unifying these two areas is proposed. It is presented in general terms of object-oriented programming so that it may be implemented in existing Bayesian filtering toolboxes that are briefly reviewed. The power of the approach is illustrated on a new variant of the marginalized particle filter. A range of new variants of the filter is obtained by plugging this class into the proposed software structure. The framework and the illustrative example is implemented in the BDM library.