Input Redundancy under Input and State Constraints (Extended version of the submission accepted to Automatica)

For a given unconstrained dynamical system, input redundancy has been recently redefined as the existence of distinct inputs producing identical output for the same initial state. By directly referring to signals, this definition readily applies to any input-to-output mapping. As an illustration of this potentiality, this paper tackles the case where input and state constraints are imposed on the system. This context is indeed of foremost importance since input redundancy has been historically regarded as a way to deal with input saturations. An example illustrating how constraints can challenge redundancy is offered right at the outset. A more complex phenomenology is highlighted. This motivates the enrichment of the existing framework on redundancy. Then, a sufficient condition for redundancy to be preserved when imposing constraints is offered in the most general context of arbitrary constraints. It is shown that redundancy can be destroyed only when input and state trajectories lie on the border of the set of constraints almost all the time. Finally, those results are specialized and expanded under the assumption that input and state constraints are linear

A Geometric Point of View on Parallel Interconnection of Buck Converters

International audienceThis paper tackles the current sharing problem for interconnected power converters. Specifically, it considers a single load, fed by buck converters via a common DC bus. In such a case, it has been recently shown that dynamics related to (i) voltage regulation and (ii) current distribution can be completely separated without resorting to frequency separation argument, which inevitably lowers achievable performance. In this paper, the origin of this separation is investigated. A comprehensive analysis is provided by relying on geometric techniques. Controller design example exploiting the new structure is also proposed. Numerical simulations promote the decomposition benefit and illustrate the geometric notions