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摘要: 针对存在外部扰动的非线性不确定时滞分布参数多智能体系统一致性问题, 提出一种$H_{\infty}$模糊边界一致性控制方案. 首先, 通过T-S模糊偏微分方程对复杂分布参数多智能体系统进行精确描述. 之后, 基于该T-S模糊偏微分方程模型, 设计基于边界测量的$H_{\infty}$模糊边界一致性控制策略. 该策略仅需在空间域边界部署少量执行器和传感器, 可有效降低控制成本. 进一步, 通过运用不等式技术与Lyapunov直接法, 得到基于线性矩阵不等式的一致性充分条件, 以保证一致误差系统指数稳定且满足$H_{\infty}$性能. 最后, 通过仿真实验验证了该方法的有效性.
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关键词:
- 分布参数多智能体系统 /
- 边界控制 /
- H∞控制 /
- 模糊控制
Abstract: For the consensus control problem of nonlinear uncertain delayed distributed parameter multi-agent systems with external disturbances, an $H_{\infty}$ fuzzy boundary consensus control scheme is proposed. First, the complex distributed parameter multi-agent system is accurately described by T-S fuzzy partial differential equations. Then, based on this T-S fuzzy partial differential equation model, an $H_{\infty}$ fuzzy boundary consensus control strategy under boundary measurements is designed. This strategy only requires deploying a small number of actuators and sensors at the boundary of the spatial domain, which can effectively reduce the control cost. Further, by using inequality techniques and the Lyapunov direct method, sufficient conditions for consensus based on linear matrix inequalities are derived to ensure that the consensus error system is exponentially stable and satisfies the $H_{\infty}$ performance. Finally, the effectiveness of the proposed method is verified through simulation experiments.-
Key words:
- Distributed parameter multiagent systems /
- boundary control /
- H∞ control /
- fuzzy control
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图 2 控制输入$u_{i}(t)$, $i=1,\; 2,\; 3,\; 4$
Fig. 2 Control input $u_{i}(t)$, $i=1,\; 2,\; 3,\; 4$
图 3 误差系统状态$e_i(x,\; t)$, $i=1,\;2,\;3,\;4$的闭环演化轮廓
Fig. 3 Closed-loop evolution profiles of the states of the error systems $e_i(x,\; t)$, $i=1,\;2,\;3,\;4$
图 4 控制输入$u_{is}(t)$, $i=1,\;2,\;3,\;4$, $s=1,\;2$
Fig. 4 Control input $u_{is}(t)$, $i=1,\;2,\;3,\;4$, $s=1,\;2$
图 5 误差系统状态$e_{is}(x,\; t)$, $i=1,\;2,\;3,\;4$, $s=1,\;2$的闭环演化轮廓
Fig. 5 Closed-loop evolution profiles of the states of the error systems $e_{is}(x,\; t)$, $i=1,\;2,\;3,\;4$, $s=1,\;2$
表 1 系统参数及取值
Table 1 System parameters and values
参数 取值 $ \mu $ $ 1 $ $ r_0 $ $ 0.1 $ $ \xi $ $ 2 $ $ d_i(x,\; t) $ $ 5{\rm e}^{-t}{\rm cos}(2x) $ $ \phi_0(x,\; m) $ $ 0.5 $ $ \phi_1(x,\; m) $ $ 0.9{\rm cos}(\pi x/ l_2) $ $ \phi_2(x,\; m) $ $ 0.8{\rm cos}(\pi x/ l_2)+0.8 $ $ \phi_3(x,\; m) $ $ 0.2{\rm cos}(\pi x/ l_2)-0.2 $ $ \phi_4(x,\; m) $ $ 0.4{\rm cos}(\pi x/ l_2) $ 
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表 2 系统参数及取值
Table 2 System parameters and values
参数 取值 $ \omega $ $ 1 $ $ \eta $ $ 0.45 $ $ o $ $ 0.1 $ $ d_{i1}(x,\; t) $ $ 5{\rm e}^{-2t}{\rm cos}(2x) $ $ d_{i2}(x,\; t) $ $ 5{\rm e}^{-2t}{\rm cos}(2x) $ $ \phi_{01}(x,\; m) $ $ 0.5 $ $ \phi_{02}(x,\; m) $ $ 0.4 $ $ \phi_{11}(x,\; m) $ $ 0.9{\rm cos}(\pi x/ l_2) $ $ \phi_{12}(x,\; m) $ $ 0.5{\rm cos}(\pi x/ l_2)+0.4 $ $ \phi_{21}(x,\; m) $ $ 0.8{\rm cos}(\pi x/ l_2)+0.8 $ $ \phi_{22}(x,\; m) $ $ 0.6{\rm cos}(\pi x/ l_2)+0.2 $ $ \phi_{31}(x,\; m) $ $ 0.2{\rm cos}(\pi x/ l_2)-0.2 $ $ \phi_{32}(x,\; m) $ $ 0.5{\rm cos}(\pi x/ l_2)-0.1 $ $ \phi_{41}(x,\; m) $ $ 0.4{\rm cos}(\pi x/ l_2) $ $ \phi_{42}(x,\; m) $ $ 0.8{\rm cos}(\pi x/ l_2) $
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