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摘要: 研究了一类非线性离散系统的量化反馈控制.对于一类满足齐次性质的非线性系统,针对有界的初始状态,我们设计了具有可数个固定控制输入的控制方式,实现了用"可数"去镇定"不可数"这一控制问题.值得指出的是,我们的结论可以直接应用到线性的情形,并与已有的关于线性系统的结论保持一致.同时,给出了例子验证了结论的有效性.Abstract: This paper deals with a class of nonlinear systems which satisfy the homogeneous property and considers quantized feedback control for these nonlinear systems. On the assumption that the initial condition is bounded, a countable fixed control input is designed to stabilize these nonlinear systems, which makes it possible to stabilize "uncountable" by "countable". Moreover, it is worthy to point out that the result can be applied to the linear case directly, which is consistent with the existing result. Meanwhile, an example is given to illustrate the result.
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Key words:
- Nonlinear systems /
- quantized feedback /
- stabilization /
- countable
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图 1 $\phi(x)$ 与 $x$ 同号时,控制输入在 $x\in(\rho c,c]$ 的图形
Fig. 1 The input for $x\in(\rho c,c]$ when $\phi(x) x>0$ ( $x\neq0$ )
图 2 非线性系统的量化控制器下的闭环响应
Fig. 2 Response of the closed-loop nonlinear system with the quantized controller
图 3 非线性系统的量化控制器下的输入
Fig. 3 Input of the closed-loop nonlinear system with the quantized controller
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