基于等距映射的非线性系统集员参数估计

给出一种新的非线性系统集员参数估计方法。该方法从流形学习的角度出发，视可行集边界与n维空间中的单位球面（n-1-sphere）为同胚，构造二者之间的同胚映射的近似。该映射可以将n-1-sphere映射为可行集近似边界。构造映射首先将等距映射与数据归一化结合，把在可行集边界上均匀采样得到的数据集映射为包含于n-1-sphere的数据集；然后，基于非参数方法得到可行集边界与n-1-sphere的同胚映射的近似。仿真结果表明，该方法比支持向量机方法具有更高的可行集边界逼近精度。

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.