Achieving an Identi able Parametrization for Direct Adaptive Control of Multivariable Plants

Identiiable 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 recently. The observability indices have no clear physical meaning, hence it is not obvious how they can be obtained in practical applications. Also, assuming the interactor is known is not very reasonable , since it, roughly speaking, describes the \high frequency" behaviour of the plant. In this brief note we present an output reordering procedure, based on plant prior knowledge and data from simple experiments, which allows us to {generically{ 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.