基于贝叶斯回归LS-SVM的非线性系统观测

摘要

Based on least squares regressive support vector machine (LS-SVM), a new design method of observer is proposed for a class of single-input single output (SISO) uncertain nonlinear control system.The key assumptions are that the norm of the difference (between optimal approximation parameter vector and nominal parameter vector) and the approximation errors are bounded, and the bounds are unknown.The problem of how to get the ultimate solution of the LS-SVM can be transformed to a quadratic programming problem with linear restriction, and the local minimum can be avoided.Considering the effect of LS-SVM's parameters, a parameter selection and soft modelling method is presented within Bayesian evidence framework and the method can improve LS-SVM's approximation ability.The theory research and simulation example demonstrates the feasibility and effect of the proposed approach.%基于回归最小均方支持向量机(LS-SVM),针对一类单输入单输出不确定非线性控制系统,提出了一种新的观测器的设计方法.在这个算法中,主要假设LS-SVM的最优逼近参数向量和标称参数向量之差的范数和逼近误差的界限是未知的.LS-SVM的最终解可以化为一个具有线性约束的二次规划问题,不存在局部极小;考虑到LS-SVM本身参数对LS-SVM性能的影响,文中利用贝叶斯证据框架对LS-SVM的参数进行优化和软测量建模,从而提高LS-SVM的逼近能力.理论研究和仿真例子证实了所提方法的可行性和有效性.