Consensus Disturbance Rejection with Delay and Parameter Adaptive Estimation

This paper deals with the consensus disturbance rejection problem for systems subject to delay and unknown parameter. Three main problems are considered. The first problem is how to deal with input delay. Due to the communication condition, the delays could be large or small, so it is difficult to use the robust technique to deal with. The second problem is the disturbance rejection. The disturbance under consideration are unknown constant disturbances or sinusoidal functions with unknown amplitudes and phases. Third, we consider the unknown graph algebraic connectivity case. This assumption is useful since fully distributed controller can only be designed without this global information. Predictor feedback method and predictor observer design method are both used to deal with the delay. Disturbance observer-based control (DOBC) strategy is used to estimate the disturbance and adaptive technique is applied to estimate the graph algebraic connectivity. Finally, consensus disturbance rejection controllers are designed for all the agents and the consensus can be achieved with certain condition derived from the Lyapunov analysis.