Non-affine minimum variance controller design by inverse modeling procedure

The minimum variance lower bound (MVLB) represents the best achievable controller capability in the variance sense. Realization of MVLB for nonlinear systems confronts some difficulties. To realize the MVLB, in this paper, a nonlinear non-affine generalized minimum variance controller is designed. The situations in which the model is not in hand, accurate, or invertible are addressed. Moreover, in order to design minimum variance controller for nonlinear structures, inverse of the system is modeled; then, the controller parameters are tuned by a recursive optimization algorithm. The most classical recursive algorithms are gradient-based. In this paper, a relationship between gradient of the controller with that of the system model is derived by inverse lemma. Therefore, the recursive algorithm is free of any need for the gradient of the system model. Finally, an experimental test on four-tank benchmark processes is used to clarify the effectiveness of the proposed control scheme.