一类非仿射非线性系统的自适应模糊控制

Adaptive fuzzy control for a class of non-affine nonlinear systems

为了讨论一类非仿射非线性系统自适应模糊控制问题,利用有关隐函数定理和泰勒公式,将系统由非仿射型转变为仿射型,基于滑模控制原理,并运用模糊逻辑系统对未知函数进行在线逼近,提出了一种具有监督器的自适应模糊控制方法。该方法在考虑到外界干扰的情况下,通过监督控制器保证闭环系统所有信号有界,通过引入最优逼近误差的自适应补偿项来消除建模误差的影响。通过Lyapunov方法,证明了跟踪误差收敛到零,仿真结果表明了该方法的有效性。

The problem of adaptive fuzzy control for a class of non-affine nonlinear systems is discussed. Using some implicit function principles and Taylor＇ s polynomial, the form of the non-affine nonlinear systems is transformed to the form of affine nonlinear systems, firstly. Then, based on the principle of sliding mode control, a novel adaptive fuzzy control with supervisory controller is designed for the transformed nonlinear system. With the help of a supervisory controller, the resulting closed-loop system is globally stable in the sense that all signals involved are uniformly bounded in the presence of the external disturbance. Furthermore, the adaptive compensation term of the optimal approximation errors is adopted to minimize the effects of modeling errors. By theoretical analysis, it is shown that tracking errors converge to zero. Simulation results demonstrate the effectiveness of the approach.