Event-triggered Adaptive Critic Fault-tolerant Control for a Class of Discrete-time MIMO Systems
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摘要: 本文针对具有执行器故障的一类离散非线性多输入多输出(Multi-input multi-output, MIMO)系统, 提出了一种基于事件触发的自适应评判容错控制方案. 该控制方案包括评价和执行网络. 在评价网络里, 为了缓解现有的非光滑二值效用函数可能引起的执行网络跳变问题, 利用高斯函数构建了一个光滑的效用函数, 并采用评价网络近似最优性能指标函数. 在执行网络里, 通过变量替换将系统状态的将来信息转化成关于系统当前状态的函数, 并结合事件触发机制设计了最优跟踪控制器. 该控制器引入了动态补偿项, 不仅能够抑制执行器故障对系统性能的影响, 而且能够改善系统的控制性能. 稳定性分析表明所有信号最终一致有界且跟踪误差收敛于原点的有界小邻域内. 数值系统和实际系统的仿真结果验证了该方案的有效性.Abstract: In this paper, an event-triggered adaptive critic fault-tolerant control scheme is proposed for a class of discretetime multi-input multi-output (MIMO) nonlinear systems with actuator fault. The proposed control scheme includes the critic and action neural networks (NNs). In the critic NN, a smooth utility function is constructed based on the Gaussian function, which avoids the possible chattering problem caused by the existing non-smooth utility function. Subsequently, the critic NN is used to approximate the optimal strategic utility function. In the action NN, the future system state is expressed by the functions of present system states by using the variable substitution method. By the combination of event-triggered mechanism, this paper designs the optimal tracking controller. An dynamic auxiliary signal is introduced in the developed controller, thereby eliminating the effect of the actuator fault and improving the control performance. Stability analysis indicates that all signals in the control-loop are ultimately uniformly bounded, and the tracking error converges to a small neighborhood of the origin. Finally, simulations of a numerical system and a practical system are performed to demonstrate the effectiveness of the proposed scheme.
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表 1 仿真实验对比1
Table 1 Comparison of simulation results
触发次数 MAE ABO (bit/s) 无执行器补偿,非光滑效用函数 921 $ z_{1,1} $ 0.0201 5894.4 $ z_{2,1} $ 0.0335 有执行器补偿,非光滑效用函数 907 $ z_{1,1} $ 0.0185 5804.8 $ z_{2,1} $ 0.0229 有执行器补偿,光滑效用函数 843 $ z_{1,1} $ 0.0130 5395.2 $ z_{2,1} $ 0.0147 注: “无执行器补偿” 表示$\omega_j(k) = \hat{ {\boldsymbol{W} } }^{\rm T}_j(k){\boldsymbol{\varphi}}_j({\boldsymbol{Z} }_j(k_t))$; “有执行器补偿” 表示$\omega_j(k) = \hat{ {\boldsymbol{W} } }^{\rm T}_j(k){\boldsymbol{\varphi}}_j({\boldsymbol{Z} }_j(k_t))+\hat{\mu}_j(k)$; “非光滑效用函数” 表示若$ |z_{j,1}(k)| $大于一个给定的正常数, 则$ q_j(k) = 1 $. 否则, $ q_j(k) = 0 $; “光滑效用函数” 表示$q_j(k) = 1 - {\rm{e}}^{-z_{j, 1}^{2}(k)/\eta_j}$. 
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表 2 仿真实验对比2
Table 2 Comparison of simulation results
触发条件 触发次数 MAE ABO (bit/s) CPU耗时(s) SETC 843 $ z_{1,1} $ 0.0130 5395.2 0.6875 $ z_{2,1} $ 0.0147 DETC 801 $ z_{1,1} $ 0.0129 5126.4 0.8125 $ z_{2,1} $ 0.0144
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