Trading Quantization Precision for Sampling Rates in Systems with Limited Communication in the Uplink Channel

There are many situations where distributed control applications have to exchange information through limited bandwidth communication channels. Examples may be found in areas ranging from the underwater robotics to the control of satellites clusters. Bandwidth limitations affect the behavior of these systems. For that reason, there is a strong need for developing methods that maximize the relevancy of the exchanged control information. In general, increasing control inputs update frequency improves the disturbance rejection abilities whereas increasing their quantization precision improves the steady state performance (set point tracking precision for example). However, when the bandwidth is limited, increasing the update frequency necessitates the reduction of the quantization precision and vice versa. Motivated by these observations, and focusing on the uplink bandwidth limitations, an approach for the dynamical on-line state-feedback assignment of control inputs quantization precision and update rate is proposed. This approach, which is based on the model predictive control (MPC) technique, enables to choose the update rate and the quantization levels of control signals from a predefined set, in order to optimize the control performance. A heuristic approach allowing an efficient choice of the elements of this set is proposed. Practical stability properties of the approach are then studied. Finally, the effectiveness of the proposed method is illustrated on a simulation example