Achieving an identifiable parametrization for direct adaptive control of multivariable plants

Identifiable parametrizations for direct adaptive control of linear multivariable plants, which assume exact knowledge of the systems observability indices and the full interactor, have been reported in the literature. The observability indices have no clear physical meaning, hence it is not obvious how they can be obtained in practical applications, Also, it is assumed that the interactor is known and is not very reasonable, since it, roughly speaking, describes the "high frequency" behaviour of the plant. We present an output re-ordering procedure, based on plant prior knowledge and data from simple experiments, which allows us to genetically obtain a unique parametrization for the interactor. A further contribution of our work is to show how, using practically sensible prior knowledge, one can restrict the controller parameters to insure uniqueness of the solution of the Diophantine equation.