Design of adaptive pole-placement controllers for plants of unknown order

By an indirect control approach, an adaptive pole-placement control problem is considered for a scalar discrete-time linear plant assuming the knowledge of an upper bound of the plant order. A class of models that can be regarded IO be input-output equivalent to the plant is first constructed based on the parrrneter estimate generated by a least-squares-type identification scheme. A minimization problem is then derived that enables one to determine the model’s coefficients and the pole-placing feedback gains so that the desired closed-loop poles are assigned in a limit.