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| Adaptive critic design of nonlinear system with unknown control direction |
| CUI Li-li, ZHANG Hua-guang, LUO Yan-hong |
| School of Information Science and Engineering, Northeastern University, Shenyang 110819, China |
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Abstract A novel fuzzy wavelet network based robust adaptive critic design was proposed for a class of non-affine nonlinear system with unknown control direction. The mean value theorem and Nussbaum function were used to handle with the problem of the nonlinear functions being implicitly functions with respect to the control input and the control direction being unknown. Two fuzzy wavelet networks (FWNs) with the same fuzzy basis functions were employed to implement the control element and the critic element, the weights, dilation and translation parameters of which were tuned online. In order to attenuate FWNs approximation errors, a robust term was designed by adaptive bounding technique. No a prior knowledge of the control direction and bound of uncertainty is needed. Moreover, the semi-globally uniformly ultimate boundedness of the closed-loop system was proved by Lyapunov theory. Simulation results demonstrate the effectiveness of the proposed design．
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Published: 01 May 2012
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控制方向未知的非线性系统的自适应评价设计
针对一类具有未知控制方向的非仿射非线性系统,提出一种新型的基于模糊小波神经网络的鲁棒自适应评价设计.利用中值定理和Nussbaum函数处理非线性函数隐含控制输入及控制方向未知问题.采用2个具有相同模糊基函数的模糊小波神经网络(fuzzy wavelet networks, FWNs)分别实现控制单元和评价单元,FWNs的权值、扩张参数及平移参数均在线调节.为了抑制FWNs近似误差,利用自适应界化技术设计一个鲁棒项.该设计不需要控制方向及不确定项上界的先验知识.通过 Lyapunov 理论严格证明闭环系统的半全局一致最终有界稳定性.仿真结果验证所提出设计的有效性.
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