Parameter set estimation for non-linear systems

Abstract

Models of dynamical systems are instrumental for many purposes: prediction, control, simulation, tracking and so on. In this paper, we will show how parameter set estimation (PSE) can be applied to non-linear systems. Parameter set estimation identifies a set of estimates which are feasible with respect to the measured data and a priori information. This set of parameters, feasible for the given model structure, can then be used for system tracking or robust control designs. For application to robust control, it is important that the size of this set be as small as possible. In order to apply parameter set estimation techniques to a non-linear system, the system function is expressed in a tensor parameterization which is linear in the parameters (LP). Then it is shown how an optimum volume ellipsoid strategy for linear time invariant systems can be extended to this tensor parameterization of a non-linear system. The methodology is illustrated on two examples, the second of which uses data obtained from an operating glass furnace.