Numerical Optimization Design of Dynamic Quantizer via Matrix Uncertainty Approach

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1. Introduction

With the rapid network technology development, the networked control systems (NCSs) have been widely studied [1–10]. One of the challenges in NCSs is quantized control. In NCSs, the continuous-valued signals are compressed and quantized to the discrete-valued signals via the quantizer of the communication channel, and such quantization often degrades the control performance. Hence, a desirable quantizer minimizes the performance error between before and after the quantizer insertion.

Motivated by this, researchers [11–14] have provided optimal dynamic quantizers for the following problem formulation in the discrete-time domain. For a given plant P , synthesize a “dynamic” quantizer Q d such that the system Σ Q composed of P and Q d in Figure 1(a) “optimally” approximates the plant P in Figure 1(b) in the sense of the input-output relation. The obtained quantizer allows us to design various controllers for the plant P on the basis of the conventional control theories. Also, this framework is helpful in not only the NCS problem but also various control problems such as hybrid control, embedded system control, and on-off actuator control.

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When we consider controlling a mechanical system with an on-off actuator, first the controlled object and its uncertainties are usually modeled in the continuous-time domain. Second, the model and its uncertainties are discretized to apply the above dynamic quantizer. However, the discretization sometimes results in uncertainties more complicated than those in the original model and creates undesirable complexity in robust control. The continuous-time setting quantizer is more suitable for the robust control of the quantized system than discrete-time one. Thus, our previous works [15, 16] have considered the continuous-time setting, while a number of the discrete-time settings have been studied by others [11–14]. In these works, it is assumed that the switching process of discretizing the...