最小二乘小波支持向量机在非线性控制中的应用

摘要

结合小波技术和支持向量机,提出了一种基于多维允许小波核的最小二乘小波支持向量机,其小波核函数具有近似正交和适用于信号局部分析的特点.同时,给出了一种有效求解最小二乘小波支持向量机的Cholesky分解算法. 将最小二乘小波支持向量机应用在非线性系统的自适应控制上,仿真结果表明,与最小二乘支持向量机、多层前向神经网络或模糊逻辑系统相比, 最小二乘小波支持向量机均能给出较好的性能,显示出快速而稳定的学习速度,而且在相同条件下,最小二乘小波支持向量机比最小二乘支持向量机的逼近精确度提高了一个数量级.所提出的用于非线性动态系统自适应控制的最小二乘小波支持向量机方法具有效性和实用性.%A form of least squares wavelet support vector machines(LS-WSVM) using multi-dimensional admissible wavelet kernel was proposed, which combined the wavelet techniques with support vector machines(SVM). The wavelet kernel was characterized by its local analysis and approximate orthogonality. Simultaneously, an efficient implementation algorithm via Cholesky factorisation for LS-WSVM was also given. The LS-WSVM was then applied to adaptive control of nonlinear dynamical systems. Simulation results reveal that the modeling and adaptive control scheme suggested based on LS-WSVM gives considerably better performance and shows faster and stable learning in comparison with neural networks or fuzzy logic systems. Furthermore the approximation accuracy of the LS-WSVM one order of magnitude increases over the LS-SVM under the same conditions. The proposed LS-WSVM method for the adaptive control of nonlinear dynamical systems shows the effectiveness and applicability.