Nonlinear estimation and robust control by means of optimal interpolation and sliding manifold techniques

The theory of the optimal interpolation of bilinear systems is described. Its potential usefulness in a robust control system design is highlighted. The optimal interpolator is derived from a nonlinear system identification technique based on a Fock space framework. It has the ability of reducing the high dimensionality of the original bilinear system to the one defined by the number of test input-output pairs determined in a prior stage. This offline modeling technique is then used to generate estimates of the system states as well as upper bounds on their error estimates. Based on this, and through an adaptation of the sliding manifold theory, a robust control effort can be generated for the purpose of insuring the high tracking performance of a moving elastic structure subject to parametric uncertainties and induced disturbances