不确定非线性系统高精度自适应模糊控制

Adaptive Fuzzy Control with High Accuracy for Uncertain Nonlinear Systems

针对一类未知边界函数的不确定仿射非线性系统,提出一种高跟踪精度特性的自适应模糊控制器。基于变论域模糊系统理论证明了最优逼近误差在特定条件下具有局部收敛特性。通过以跟踪误差作为输入并选择适当的自适应参数,设计出逼近误差局部收敛的自适应模糊控制器。以最优逼近误差存在未知上确界为主要假设,证明了闭环系统在所有信号一致有界意义下的稳定性和跟踪误差收敛性。该控制器无需附加补偿器即可在理论上消除逼近误差对跟踪误差的影响,从而实现平滑控制输入下的高精度跟踪性能。单力臂机械手控制的仿真结果表明了该方法的有效性。

For a class of uncertain affine nonlinear systems with unknown boundary functions,an adaptive fuzzy controller（AFC） with the characteristic of high tracking accuracy is proposed in this paper.Based on the theory of variable universe fuzzy system,it is proved that the optimal fuzzy approximation error（FAE） has local convergence property under certain conditions.By using the tracking errors as inputs and selecting suitable adaptive parameters,an AFC with optimal FAE local convergence is developed.Under the key assumption that the optimal FAE is bounded,it is proved that the closed-loop system is stable in the sense that all involving variables are bounded and the tracking errors converge to zero.This approach can theoretically eliminate the effect of the FAE on the tracking errors without additional compensator,thus it can achieve high tracking accuracy with smooth control input.Simulated application of a single-link manipulator demonstrates the effectiveness of this approach.