Robust Distributed Average Tracking With Disturbance Observer Control

This paper is concerned with the study of robust distributed average tracking (DAT) algorithms for networked control systems in the presence of external disturbances or false data injection attacks (FDIAs). To eliminate the impacts of external disturbances and FDIAs, the technologies of disturbance-observer-based control (DOBC) and active disturbance rejection control (ADRC) are introduced into the context of DAT problems. First, for a class of external disturbances with known dynamics, we propose an anti-disturbance DAT (AD-DAT) algorithm, where a stand-alone disturbance observer based on the idea of DOBC is employed to estimate the disturbance and then to compensate it in the design of control inputs. The proposed AD-DAT algorithm can track the average of multiple time-varying reference signals with zero steady-state error and the accurate tracking is robust with respect to initialization constraints. Furthermore, for another class of FDIAs with unknown dynamics, we design an anti-attack DAT (AA-DAT) algorithm where the control input is based on the estimates of states instead of original states, and construct an extended state observer including a state observer and an FDIAs observer based on the idea of ADRC. The extended state observer plays a key role in estimating and eliminating the impact of FDIAs without compromising the accurate tracking performance. In addition, sufficient conditions are derived for the proposed two algorithms from a theoretical point of view to guarantee accurate average tracking. Finally, some numerical examples are given to illustrate the validity and effectiveness of the proposed algorithms. Note to Practitioners —This paper is motivated by the problem of robust distributed average tracking (DAT) for the time-varying centroid of the formation of a group of autonomous vehicles. The problem arises in the scenario where two groups of unmanned ground vehicles (UGVs) and unmanned aerial vehicles (UAVs) perform a combined surveillance-reconnaissance mission (where the UAVs aim to provide aerial coverage and early warning against threats for the UGVs, as shown in Fig. 1) in an uncertain environment where the external disturbances might exist or the FDIAs might be launched by adversaries. Obviously, the tracking accuracy of the target signal will be compromised in the presence of external disturbances or FDIAs. However, most existing works for disturbance rejection mainly focused on the static average consensus rather than the dynamic one even though a few works mentioned the DAT problem with only considering the case of external disturbances. Based on this, we propose an AD-DAT algorithm and an AA-DAT algorithm for the DAT problem based on the ideas of DOBC and ADRC, respectively. Numerical examples show that the proposed algorithms are able to estimate and eliminate the impacts of the external disturbances and the FDIAs, which implies that the algorithms can be implemented in practical scenarios. In future research, we will extend the results to more general scenarios in the presence of external disturbances and FDIAs.