Guaranteed Cost Control of Networked Control Systems With Bounded Packet Loss Based on Quantization Dependent Lyapunov Function
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摘要: 研究了一类具有有界丢包的网络控制系统（Networked control systems，NCSs）的保成本控制问题，提出了一种包含量化反馈的网络控制系统数学模型，该模型将系统的镇定问题转化为镇定一系列子系统的鲁棒控制问题.在对网络控制系统的分析中，区别于常用的二次型Lyapunov函数，本文采用了一种新的且能够降低保守性的量化依赖Lyapunov函数方法.基于本文的Lyapunov函数，得到了充分考虑丢包过程的保成本控制器的设计方法.仿真算例验证了所给出方法的有效性.
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关键词:
- 网络控制系统 /
- 保成本控制 /
- 量化反馈 /
- Lyapunov函数
Abstract: This paper investigates modeling and guaranteed cost control of quantized feedback systems over networks with bounded packet loss. The model of the networked control systems, which appropriately incorporates quantized feedback, is established in terms of robust control which transforms the problem of stabilization of networked control systems with packet loss into the problem of robust stabilization of a class of subsystems. Unlike the quadratic Lyapunov function which is normally used in analyzing networked control systems, this paper presents a new approach that can significantly reduce conservativeness by taking the quantization dependent Lyapunov function. Based on the provided Lyapunov function, a guaranteed cost state feedback controller is derived, which explicitly considers the packet loss process. A numerical example illustrates the effectiveness of the proposed method. -
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图 3 单输入系统状态响应及控制输入
Fig. 3 The state responses and control input of the single-input system
图 4 多输入系统状态响应及控制输入
Fig. 4 The state responses and control input of the multiple-input system
表 1 两种Lyapunov函数方法下的反馈增益$K$及性能指标$J$对比
Table 1 Comparison of feedback gain $K$ and performance index $J$ values using two Lyapunov function methods
系统 量化密度$\rho$值 方法 反馈增益$K$值 性能指标$J$值 单输入 $\rho=0.1754$ 量化依赖Lyapunov方法 $\left[\begin{array}{ccc} -0.5888 & -1.6344 \end{array}\right]$ $0.0022$ [25]中二次型Lyapunov方法 不可行 不可行 $\rho=0.3404$ 量化依赖Lyapunov方法 $\left[\begin{array}{ccc}-0.6563 & -1.5303\end{array}\right]$ $0.0020$ [25]中二次型Lyapunov方法 $\left[\begin{array}{ccc}-0.4870 & -1.0089\end{array}\right]$ $0.0022$ $\rho=0.3918$ 量化依赖Lyapunov方法 $\left[\begin{array}{ccc}-0.6691 & -1.5135\end{array}\right]$ $0.0018$ [25]中二次型Lyapunov方法 $\left[\begin{array}{ccc}-0.5079 & -1.0487\end{array}\right]$ $0.0020$ $\rho=0.4286$ 量化依赖Lyapunov方法 $\left[\begin{array}{ccc}-0.6764 & -1.5042\end{array}\right]$ $0.0019$ [25]中二次型Lyapunov方法 $\left[\begin{array}{ccc}-0.5214 & -1.0764\end{array}\right]$ $0.0020$ $\rho=0.6015$ 量化依赖Lyapunov方法 $\left[\begin{array}{ccc}-0.7054 & -1.4931\end{array}\right]$ $0.0034$ [25]中二次型Lyapunov方法 $\left[\begin{array}{ccc}-0.5835 & -1.2062\end{array}\right]$ $0.0035$ 多输入 $\rho=0.1754$ 量化依赖Lyapunov方法 $\left[\begin{array}{ccc} -0.0642 & -0.0508\\ 0.0173 & -0.0746 \end{array}\right]$ $0.0016$ [25]中二次型Lyapunov方法 不可行 不可行 $\rho=0.4286$ 量化依赖Lyapunov方法 $\left[\begin{array}{ccc} -0.1380 & -0.0674\\ 0.0035 & -0.1285\end{array}\right]$ $0.0007$ [25]中二次型Lyapunov方法 $\left[\begin{array}{ccc}-0.0717 & -0.0274\\0.0122 & -0.1371\end{array}\right]$ $0.0012$ $\rho=0.6794$ 量化依赖Lyapunov方法 $\left[\begin{array}{ccc} -0.1286 & -0.0582\\ 0.1125 & -0.0763\end{array}\right]$ $0.0005$ [25]中二次型Lyapunov方法 $\left[\begin{array}{ccc}-0.1085 & -0.0579\\0.0833 & -0.0777\end{array}\right]$ $0.0007$ $\rho=0.9625$ 量化依赖Lyapunov方法 $\left[\begin{array}{ccc} -0.2041 & -0.0577\\ 0.1914 & -0.1517\end{array}\right]$ $0.0003$ [25]中二次型Lyapunov方法 $\left[\begin{array}{ccc}-0.1455 & -0.0601\\0.1445 & -0.0785\end{array}\right]$ $0.0004$ 
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