Anders Stenman

Just in time models for dynamical systems

The concept of just in time models is introduced for models that are not estimated until they are really needed. The idea is to store all observations of the process in a database, and then estimate a local model at the current working point. The variance/bias tradeoff is optimized locally by adapting the number of data and their relative weighting. This is in contrast to general nonlinear black-box models, like neural networks, where the performance is optimized globally.

Model-free predictive control

Model predictive control, MPC, is a model-based control philosophy that select control actions by online optimization of objective functions. Design methods based on MPC have found wide acceptance in industrial process control applications, and have been thoroughly studied by the academia. Most of the work so far have relied on linear models of different sophistication because of their advantage of providing simple and straightforward implementations. However, when turning to the nonlinear domain, problems often arise as a consequence of the difficulties in obtaining good nonlinear models, and the computational burden associated with the control optimization. In this paper we present a new approach to the nonlinear MPC problem using the recently proposed concept of model-on-demand. The idea is to estimate the process dynamics locally and online using process data stored in a database. By treating the local model obtained at each sample time as a local linearization, it is thus possible to reuse tools and concepts from the linear MPC framework. Three different variants of the idea, based on local linearization, linearization along a trajectory and nonlinear optimization respectively, are studied. They are all illustrated in numerical simulations.

Asymptotic Properties of Just-in-Time Models

The concept of Just-in-Time models has been introduced for models that are not estimated until they are really needed. The prediction is taken as a weighted average of neighboring points in the regressor space, such that an optimal bias/variance trade-off is achieved. The asymptotic properties of the method are investigated, and are compared to the corresponding properties of related statistical non-parametric kernel methods. It is shown that the rate of convergence for Just-in-Time models at least is in the same order as traditional kernel estimators, and that better rates probably can be achieved.

A NONPARAMETRIC APPROACH TO MODEL ERROR MODELING

To validate an estimated model and evaluate its reliability is an important part of the system identification process. Recent work on model validation has shown that the use of explicit model error models provide a better way of visualizing the possible deficiencies of the nominal model. Previous contributions have mainly focused on parametric black-box models for estimating the error model. However, this requires that a correct model order for the error model has to be selected. Here we suggest an adaptive and nonparametric frequency-domain method that estimates the frequency response of the model error by an automatic procedure. A benefit with this approach is that the tuning can be done locally, i.e., that different resolutions can be used in different frequency bands. The ideas are based on local polynomial regression and utilize a statistical criterion for selecting the optimal resolution.

On adaptive smoothing of empirical transfer function estimates

Abstract The determination of the right resolution parameter when estimating frequency functions for linear systems is a trade-off between bias and variance. Traditional approaches, like “window-closing” employ a global resolution parameter - the window width - that is tuned by ad hoc methods, usually visual inspection of the results. Here we suggest an adaptive method that tunes such parameters by an automatic procedure. A further benefit is that the tuning can be done locally, i.e., different resolutions can be used in different frequency bands. The ideas are based on local polynomial regression and the “just-in-time”-model concept. The advantages of the method are illustrated in numerical examples.

On Model Structure Selection for Nonparametric Prediction Methods

In this paper we continue to explore identification of nonlinear systems using the previously proposed concept of model-on-demand. The idea is to estimate the process dynamics locally and on-line using process data stored in a database, and has in earlier contributions proven to be capable to produce results comparable to (or better than) other nonlinear black-box approaches. The modeling part of the method is based on local polynomial modeling ideas. This has several implications on the choice of model structure, which is discussed at length in the paper. It is concluded that the NARX structure should be considered as the default choice in the local polynomial context. Furthermore, it is shown that the predictions in some situations can be enhanced by tuning other parameters that are special for the nonparametric case. The usefulness of the method is illustrated in numerical simulations. For the chosen application it is shown that the prediction errors are in order of magnitude directly comparable to more established modeling tools such as artificial neural nets.

FuzzyCAT-towards a mathematical analysis of fuzzy controllers

The aim of this paper is to show that, contrary to what is commonly believed, it is possible to get rather simple analytic expressions for a class of fuzzy controllers. The authors describe a Maple package called FuzzyCAT that supports analysis and simulation of fuzzy controllers. The restrictions made in the program concern the shape of the membership functions, the defuzzification methods available and the number of input and output variables.<<ETX>>