Bound-based methods for constructing and testing models of dynamical systems

The main requirement of any procedure for validating models is that it should test whether the assumptions built into the model are justified by the observations and compatible with experience. Statistical model-structure selection formalizes such tests into hypothesis tests, whereas informal validation consists of repeatedly asking whether one believes a feature of the model´s behaviour. A procedure intermediate between the two extremes, permitting the use of numerical but nonstatistical background information for testing, has an obvious appeal. Such a procedure is provided by bound-based methods, which represent uncertainty in the model by specifying only that the parameters lie within certain bounds, rather than estimating the parameters and calculating the covariance of the estimates. The parameter bounds are computed from input-output observations, given assumed bounds on the model-output error. They can also embody bounds on any other aspects of the model´s behaviour which can be related to its parameter values. The method, and its use in control system design are described