含未知系数的非严格反馈系统的自适应控制

Adaptive Control of Non-Strict Feedback Systems with Unknown Coefficients

针对一类单输入单输出非严格反馈系统的自适应模糊控制问题,该受控系统含有未知的虚拟控制系数,提出了一种基于观测器的自适应模糊控制方案。采用凸组合的方法,设计了一个鲁棒观测器来估计未知的系统状态变量,同时运用Young不等式及变量分离方法,解决非严格反馈结构带来控制设计上的困难,并结合模糊自适应控制方法和Backstepping技术,构造出理想的控制器。根据Lyapunov稳定性理论,证明所提出的自适应模糊控制器能保证跟踪误差收敛到原点的一个小领域内,且自适应闭环系统的所有信号都是有界的,以一个仿真算例验证了方案的有效性。说明含未知系数的非严格反馈系统,最终可以转化成稳定性良好的系统。该研究具有广阔的应用前景。

For the problem of adaptive fuzzy control for a class of single-input and single-output non-strict feedback system, in which the controlled system contains unknown virtual control coefficients, an observer-based adaptive fuzzy control scheme is proposed. Using the convex combination method, a robust observer is designed to estimate unknown system state variables, at the same time the Young′s inequality and variable separation method are used to overcome the difficulty caused by the non-strict feedback structure in control design, combined with the fuzzy adaptive control method and Backstepping technology to construct the ideal controller. According to the Lyapunov stability theory, the proposed adaptive fuzzy controller can ensure that the tracking error converges to a small area of the origin, and all signals of the adaptive closed-loop system are bounded. A simulation example is used to verify the effectiveness of the scheme. This shows that a non-strict feedback system with unknown coefficients can eventually be transformed into a system with good stability. The research has broad application prospects.