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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. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of Nash equilibrium seeking of N -player games for high-order integrator dynamics with disturbances. Three features of our results are worth mentioning. First, our results apply to jointly strongly connected networks, which can be disconnected at every time instant. Second, our disturbances can be any bounded time function with the bound unknown, which include discontinuous disturbances that cannot be handled by the existing results. Third, in addition to two standard assumptions on the cost functions, the existing results also rely on the satisfaction of an inequality involving some Lipschitz constant of the pseudogradients of the cost functions and the smallest nonzero eigenvalue of the Laplacian of the communication graph. In contrast, our results hold without relying on the satisfaction of this inequality. To achieve our objective, we have developed an approach by integrating the distributed estimator, some nonlinear control technique, and adaptive control technique. Our design is illustrated by one example of force-actuated robots in sensor networks. [ABSTRACT FROM AUTHOR]

Recently, the distributed state estimation problem for continuous-time linear systems over jointly connected switching networks was solved. Due to the use of the generalized Barbalat's Lemma, it can only show that the estimation errors asymptotically converge to the origin. By a completely different approach, this paper further studies the distributed state estimation problem with two new features. First, the asymptotic convergence is strengthened to the exponential convergence. This strengthened result not only offers a guaranteed convergence rate, but also renders the error system total stability and thus the capability to withstand small disturbances. Second, the coupling gains of our local observers can be different from each other and thus offers greater design flexibility, while the coupling gains in the existing result were required to be identical. These two new features are achieved by establishing exponential stability for two classes of linear time-varying systems, which may have other applications. [ABSTRACT FROM AUTHOR]

A standard assumption on the existence of the distributed observer or adaptive distributed observer for a linear leader system over jointly connected switching networks is that none of the eigenvalues of the system matrix of the leader system have positive real parts. In this paper, after establishing a stability result for a class of linear periodic switched systems, we present sufficient conditions for the existence of both the distributed observer and the adaptive distributed observer for general linear leader systems over periodic jointly connected switching networks. As an application of the distributed observer, we solve the cooperative output regulation problem for linear multi-agent systems with general linear leader systems over periodic jointly connected switching networks. A numerical example is provided to illustrate our design. [ABSTRACT FROM AUTHOR]