Dynamic consensus and adaptive bias compensation for multi-agent linear systems over directed networks

Biased measurements in an inter- networked systems can have severe repercussions in closed-loop stability of the individual systems and decelerate dynamical consensus among the interacting agents. Bias in the measurement, even constant, cannot be dealt with ad hoc techniques of robust control, in the presence of additive perturbations, because the control gain amplifies the disturbance. One way to account for the effect of measurement bias is then to rely on adaptive control. This has been done in the literature in the context of individual systems, but to the best of our knowledge not for multi-agent systems, while ensuring consensus control. In this paper we provide a model-reference-adaptive-control scheme to ensure dynamic consensus of generic (stabilizable) linear systems interconnected over directed graphs and under the influence of constant bias measurements. Our controller ensures global asymptotic stability of the synchronization manifold and convergence of the bias estimates. Copyright (c) 2023 The Authors.