Concepts and Algorithms for Non-Linear System Identifiability

Abstract: Recently, commutative algebra and differential algebra have come to use as mathematical tools for solving problems in automatic control. We will use these tools to answer questions regarding identifiability for models given as a set of differential polynomials. A constructive algorithm, Ritt's algorithm, has been modified for this specific situation. Furthermore, comparisons between Ritt's algorithm and Buchberger's algorithm, to answer the identifiability question when the model structures are given in state space form, are performed. The basic problem is that the computational complexity rapidly increases with the problem size. We examine various ways to simplify the computations in this respect, but it must also be stressed that the complexity increase is inherent in the problem.In identification from a deterministic point of view an algorithm is said to be robustly convergent if the true system is regained when the noise level tends to zero. In this thesis we introduce a concept close to this performance measure; robust global identifiability. A model structure, i.e., a smoothly parameterized set of models, is said to be robustly globally identifiable if there exist an identification algorithm such that the true parameters are regained when the noise level tends to zero. In this thesis we show that global identifiability implies robust global identifiability when the considered model structure is a characteristic set of differential polynomials. This means that any model structure with parameters, that can be uniquely estimated from data has this robustness property.Finally, a method for estirnation of residence time in continuous flow systems with varying dynamics is discussed. By resampling, i.e., choosing time instants different from the given sampling instants, and interpolation between measured data points, we obtain a continuous fl.ow system with constant residence time expressed in a new resampled time vector. We assume that the fiow patterns in the systems are invariant. The new data set is then used for identification of parameters in a chosen model structure. From the identified model, the residence time is readily calculated and a procedure for that is briefly described. The presented method is readily extended to enable use in recursive identification. In that case the modified recursive identification method is an improvement of the tracking ability compared to an ordinary recursive routine.