Quantized nonlinear control-a cyclic-small-gain approach

The problem of controlling systems through quantized communication channels has recently attracted a lot of attention from the controls community. The strong nonlinear characteristics of quantization such as discontinuity and saturation cause the major difficulties of quantized control. This paper reviews the results available in the literature of quantized control of linear and nonlinear systems, and specifically discusses the design techniques for quantized nonlinear control. With quantization considered as perturbation, robust control design ideas play an important role in quantized nonlinear control. We discuss how the quantized control problems are handled by modifying the robust nonlinear control techniques. In particular, it is shown that the notion of input-to-state stability (ISS) and its small-gain methods are quite powerful for quantized control of high-order nonlinear systems due to the capability of dealing with uncertainty, strong nonlinearity and interconnections. The paper ends with some future research directions of quantized nonlinear control. While many classical tools could be used for the future development, the ISS small-gain methods turn out to be fundamental in handling the complexity caused by quantization.