ON THE HAMILTONIAN TECHNIQUES FOR DESIGNING NONLINEAR OBSERVERS UNDER SET-MEMBERSHIP UNCERTAINTY

摘要

This paper deals with the problem of constructing observers for nonlinear systems subjected to unknown but bounded disturbances. The problem is therefore treated within the framework of the so-called guaranteed (set membership) approach. The solutions are thus given in set-theoretic terms as "information sets" consistent with the model, the measurements and the given constraints on the uncertain items. The novelty in the approach is the application of Hamiltonian techniques which allow to treat nonlinear systems. The observation process is described by an HJB (Hamilton - Jacobi - Bellman) equation for a certain value function (the "information state") whose level sets are the set-valued estimates. Presented here are two types of HJB equation with some comparison theorems which allow to replace the rather complicated solutions to these equations by their upper and lower estimates, which are simpler to calculate. The application of information states in input design for guaranteed parameter identification is finally considered.