Set Membership Parameter Estimation for Nonlinear Systems Using Isomap

This paper proposes a novel set membership parameter estimation method for nonlinear systems. According to the theory of geometry and topology, the boundary of the feasible parameter set (FPS) is homeomorphic to an n-1-sphere (n is the number of parameters). From the viewpoint of manifold learning, the proposed method constructs a mapping which can approximate the homeomorphism between the FPS boundary and the n-1-sphere. Once this mapping is established, it can be used to map the n-1-sphere into an approximation of the FPS boundary. The following technologies are used to build the mapping. First, a data set consisting of vectors uniformly sampled from the FPS boundary is mapped into a data set contained by the n-1-sphere. This is achieved by Isomap followed by the data normalization. Then, a non-parametric method based on the two data sets is used to build a mapping which approximates the homeomorphism between the FPS boundary and the n-1-sphere. The simulation results show that the proposed method exhibits superior accuracy compared with the support vector machine method.