Measurement bias estimation and dynamic consensus of controllable systems over directed graphs
Résumé
Dynamic consensus pertains to the case in which a group of interconnected systems adopt a consensual dynamic behaviour; this covers in particular the more common consensus problem in which case all the systems admit a stable common equilibrium point. In this article we tackle the problem of dynamic consensus for systems under measurement bias. The latter may result, e.g., from sensor faults or attacks, but it is assumed that bias is constant. Under this condition we design a nonlinear adaptive estimator that successfully estimates the bias, so the controller ensures dynamic consensus. Our results are designed for linear controllable systems, but the class of systems that we consider is broader than in the available literature since, in particular, it covers systems with singular matrices ( e.g., chains of integrators). The only assumption on the graph topology is that it is directed and contains a spanning tree. For illustration purpose, we address a case-study of formation control of a group of satellites, whose orbital relative motion is modelled as per Clohessy-Wiltshire equations, under the assumption that the measurements are biased.
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