Self-Triggered Network Coordination Over Noisy Communication Channels

Abstract

This paper deals with the coordination problems over noisy communication channels. We consider a scenario where the communication between network nodes is corrupted by unknownbut-bounded noise. We introduce a novel coordination scheme which ensures: 1) boundedness of the state trajectories and 2) a linear map from the noise to the nodes disagreement value. The proposed scheme does not require any global information on the network parameters and/or the operating environment (the noise characteristics). Moreover, network nodes can sample at independent rates and in an aperiodic manner.

On the benefits of saturating information in consensus networks with noise

“…For constant thresholds, the method can achieve approximate consensus and make the system state converge within a set around the favourite interval in finite time. Compared with our previous result [22], the node disagreement in this paper is independent of the initial condition of the system. Moreover, with time-varying threshold and control magnitude, the algorithm can achieve asymptotic consensus in the noiseless case, while preserving state boundedness in the noisy case.…”

“…To the best of our knowledge, most of the works addressing the case of noise assume prior knowledge of the noise magnitude, see, e.g., [20]. The case of noise with unknown magnitude is considered in [22]. It employs an adaptive threshold which scales dynamically with the state absolute value.…”

“…Theorem 3. Consider a network of n dynamical systems as in (20), which are interconnected over the graph G. Let each local control input be generated in accordance with (21) and (22). If ε(t) and α(t) satisfy (23), then for all t ∈ R ≥0 ,…”

“…State boundedness and exact consensus are achieved in [21], but the result requires the restrictive assumption on the integral of the noise absolute value to be finite. Our previous work [22] has proposed an adaptive consensus algorithm to achieve practical consensus, a linear dependence of the disagreement on the noise magnitude and boundedness of the state, without assuming any a priori information on the noise, except its boundedness. In the noiseless case, the node disagreement normalized by the norm of the initial state can be arbitrarily reduced.…”

“…Our contribution. In this paper we propose a new method which, while still retaining the same properties of the algorithm in [22], also ensures a value of the disagreement that is independent of the norm of the initial conditions, thus guaranteeing a convergence result that is uniform over the system initial conditions.…”