A novel zonotope-based set-membership identification approach for uncertain system
As a Minkowski summation of several linear segments in the real space, zonotopes have been widely used in set-membership identification (SMI) for uncertain system because of its advantages, such as higher accuracy, compactness of representation and less complexity. A new SMI approach is proposed in this paper to develop a control oriented model based on zonotope, with which complex mathematical calculation of feasible system set (FSS) can be avoided. The main contributions of this work are that we obtain a zonotope-based uncertainty model in an iterative form, via minimizing a new criterion representing the accuracy of the nominal model and the size of uncertainty. To circumvent the problem that the order of identified zonotope increases persistently during iteration and to reduce the computational effort, a novel approach is proposed to keep the order of zonotope constant without losing optimality, which is a contrast to the conventional approach that reduces the order after performing the optimization. The proposed zonotope-based SMI approach can be directly extended for multi-input multi-output (MIMO) system identification using decomposition-composition rule. The effectiveness of the proposed approach is demonstrated by two illustrative examples.