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Verwertbare Ergebnisse
The principal topic of the research project was the study of non-parametric control and identification algorithms. The theoretical developments were concentrated along the following axes:
1. Development of a general methodology of non-parametric adaptive control. This part is a result of the collaboration between IRISA, Rennes (and INRIA Rhône-Alpes since 1997) and the Institute of Control Sciences, Moscow. The following results are obtained: optimum adaptive control algorithms are derived for both linear and non-linear (non-parametric) adaptive control problem of a discrete stochastic dynamical system. Those algorithms are based on a well-known certainty equivalence principle and on related optimal identification procedures for closed loop systems as well. In order to prove the optimality a new technique for deriving information inequalities for adaptive control problems has been developed and generalised Van-Trees-Gill-Levit information lower bound of a Bayes type proved.
2. Study of the properties of non-linear continuous models relevant to the development of identification algorithms.
3. The study of mixing properties of non-linear dynamic systems constitutes an important part of the theoretical analysis of estimation algorithms. In the work participant A. Veretennikov established the polynomial bounds for the mixing coefficients of discrete dynamic systems. These polynomial bounds have been applied to check a "Castellana-Leadbetter condition" in the problem of nonparametric estimation of an unknown invariant density for an ergodic diffusion.
4. Development of efficient estimation procedures for complex non-linear model. The result is a new estimation approach which uses efficient optimisation methods and which can be seen as a stable modification of neural net modelling. We used extensively the help of Arkadi Nemirovski from Technion, Haifa, Israel when developing this part of the project.
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