Adaptive robust bearing-based formation control for multi-agent systems

The problem of bearing-based formation control with disturbance rejection has been studied by quite a few papers under various assumptions on the disturbances such as constant disturbances, trigonometric polynomial disturbances or bounded uniformly continuous disturbances with known bounds. In this paper, we further study the same problem with the disturbances being bounded piecewise continuous time functions. We first consider the case where the bounds of the disturbances are known. We show that the problem can be solved by a distributed static state feedback control law. Then we further consider the case where the bounds of the disturbances are unknown. We manage to solve this problem by introducing the adaptive control technique to deal with the unknown bounds of the disturbances. Our results include all the existing results on the bearing-based formation control with disturbance rejection as special cases. Moreover, we present a sufficient condition on the initial values of the closed-loop system for each case that prevents the collision.