IEEE Trans Cybern. 2017 Oct;47(10):3124-3135. doi: 10.1109/TCYB.2016.2581220. Epub 2016 Jun 28.
This paper investigates the problem of stabilization of sampled-data neural-network-based systems with state quantization. Different with previous works, the communication limitation of state quantization is considered for the first time. More specifically, it is assumed that the sampled state measurements from sensor to the controller are quantized via a quantizer. To reduce conservativeness, a novel piecewise Lyapunov-Krasovskii functional (LKF) is constructed by introducing a line-integral type Lyapunov function and some useful terms that take full advantage of the available information about the actual sampling pattern. Based on the new LKF, much less conservative stabilization conditions are derived to obtain the maximal sampling period and the minimal guaranteed cost control performance. The desired quantized sampled-data three-layer fully connected feedforward neural-network-based controllers are designed by a linear matrix inequality approach. A search algorithm is given to find the optimal values of tuning parameters. The effectiveness and advantage of proposed method are demonstrated by the numerical simulation of an inverted pendulum.
本文研究了具有状态量化的采样数据神经网络系统的镇定问题。与以前的工作不同，首次考虑了状态量化的通信限制。更具体地说，假设传感器到控制器的采样状态测量通过量化器进行量化。为了减少保守性，通过引入线积分型 Lyapunov 函数和一些充分利用实际采样模式的可用信息的有用项，构建了一个新的分段 Lyapunov-Krasovskii 函数（LKF）。基于新的 LKF，导出了更不保守的镇定条件，以获得最大的采样周期和最小的保证成本控制性能。通过线性矩阵不等式方法设计了期望的量化采样数据三层全连接前馈神经网络控制器。给出了一个搜索算法来找到调整参数的最优值。通过倒立摆的数值仿真验证了所提出方法的有效性和优势。
