Event-triggered Tracking Control for a Class of Nonlinear Systems With Observer and Prescribed Performance
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摘要: 针对一类具有外部扰动的非线性系统, 提出了一种自适应模糊跟踪控制方法. 首先, 利用模糊逻辑系统逼近系统未知的非线性函数, 并设计了一个模糊状态观测器来估计系统的不可测状态. 其次, 通过指定性能函数, 使系统的跟踪误差能够约束在指定范围内. 然后, 利用Backsteping方法结合包含对数函数的Lyapunov泛函, 设计了一个基于事件触发条件的自适应模糊控制器. 基于Lyapunov稳定性理论和$\tanh$函数的性质证明了所提出的控制策略能够保证闭环系统中所有信号是半全局一致最终有界的. 最后, 通过一个数值仿真例子验证了所提出方法的有效性.Abstract: This paper investigates an adaptive fuzzy tracking control method for a class of nonlinear systems with external disturbances. Firstly, fuzzy logic systems and the fuzzy state observer are implemented to approximate unknown nonlinear functions and estimate the unmeasured states of systems, respectively. Then, the tracking error can be constrained within the specified range by means of the performance function. Furthermore, an event-triggered adaptive fuzzy controller is designed by employing the Backstepping method and Lyapunov functional with logarithm function. The proposed control strategy can ensure that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded based on the Lyapunov stability theory and the properties of $\tanh$function. Finally, a numerical simulation example is provided to verify the effectiveness of proposed method.
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Key words:
- Adaptive control /
- prescribed performance /
- event-triggered /
- fuzzy logic system /
- fuzzy observer
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图 2 不同方法下的系统跟踪误差$\bar{s}_{1}$
Fig. 2 System tracking errors$\bar{s}_{1}$under different methods
图 3 参考信号${y}_{d}$和不同方法下的系统状态$z_{1}$
Fig. 3 Reference signal${y}_{d}$and system states$z_{1}$ under different methods
图 4 参考信号${\dot{y}}_{d}$和不同方法下的系统状态$z_{2}$
Fig. 4 Reference signal${\dot{y}}_{d}$and system states$z_{2}$underdifferent methods
图 5 系统输出$y = z_{1}$和观测状态$\hat{z}_{1}$
Fig. 5 System output$y = z_{1}$and observed state$\hat{z}_{1}$
图 6 系统状态$z_{2}$和观测状态$\hat{z}_{2}$
Fig. 6 System state$z_{2}$and observed state$\hat{z}_{2}$
图 7 自适应律$\|{{\boldsymbol{ \vartheta}}}_{1}\|$和$\|{{\boldsymbol{ \vartheta}}}_{2}\|$
Fig. 7 Adaptive laws$\|{{\boldsymbol{ \vartheta}}}_{1}\|$and$\|{{\boldsymbol{ \vartheta}}}_{2}\|$
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