Trading Quantization Precision for Sampling Rates in Networked Systems with Limited Communication

In many situations, control applications have to exchange a significant amount of information through limited bandwidth communication channels. This occurs in areas ranging from the underwater robotics to the control of satellites clusters. Bandwidth limitations impose constraints on information exchange. Consequently, there is a strong need for developing methods that maximize the relevancy of the exchanged control information. In general, increasing the sampling frequency improves the disturbance rejection abilities whereas increasing the quantization precision improves the steady state precision. However, when the bandwidth is limited, increasing the sampling frequency necessitates the reduction of the quantization precision. In the opposite, augmenting the quantization precision requires the lowering of the sampling frequency. Motivated by these observations, an approach for the dynamical on-line assignment of sampling frequencies and control inputs quantization is proposed. This approach, which is based on the model predictive control (MPC) technique, enables to choose the sampling frequency and the quantization levels of control signals from a predefined set, in order to optimize the control performance. The effectiveness of this approach is illustrated on a simulation example