Design of Neural Network Quantizers for Networked Control Systems

Nowadays, networked control systems (NCSs) are being widely implemented in many applications. However, several problems negatively affect and compromise the design of practical NCSs. One of them is the performance degradation of the system due to quantization. This paper aims to develop dynamic quantizers for NCSs and their design methods that alleviate the effects of the quantization problem. In this paper, we propose a type of dynamic quantizers implemented with neural networks and memories, which can be tuned by a time series data of the plant inputs and outputs. Since the proposed quantizer can be designed without the model information of the system, the quantizer could be applied to any system with uncertainty or nonlinearity. This paper gives two types of quantizers, and they differ from each other in the neural networks structure. The effectiveness of these quantizers and their design method are verified using numerical examples. Besides, their performances are compared among each other using statistical analysis tools.

The quantization for in-homogeneous self-similar measures with in-homogeneous open set condition

Let [Formula: see text] be a family of contractive similitudes satisfying the open set condition. Let ν be a self-similar measure associated with [Formula: see text]. We study the quantization problem for the in-homogeneous self-similar measure μ associated with a condensation system [Formula: see text]. Assuming a version of in-homogeneous open set condition for this system, we prove the existence of the quantization dimension for μ of order r ∈ (0, ∞) and determine its exact value ξr. The finiteness and positivity of the ξr-dimensional upper and lower quantization coefficient are also explored.