Jean-François TRÉGOUËT will defend his HDR on July 9th, 2025 at 10:15AM at the INSA de Lyon, Amphitheater Émilie de Châtelet, Library Marie Curie.
Title :
Hierarchical control and input redundancy
Jury :
Rapporteurs :
Dr Jean Jacques LOISEAU, Directeur de recherches, LS2N
Pr. Andrea SERRANI, Professore ordinario, Università di Bologna
Dr Luca ZACCARIAN, Directeur de recherches, LAAS
Examinateurs :
Pr. Éric BIDEAUX, Professeur des Universités, INSA de Lyon
Dr. Antoneta Iuliana BRATCU, Maître de Conférences HdR, Grenoble INP - UGA
Pr. Jamal DAAFOUZ, Professeur des Universités, ENSEM - Université de Lorraine
Pr. Bernhard MASCHKE, Professeur des Universités, Université Lyon I
Pr. Sorin OLARU, Professeur des Universités, CentraleSupélec
Abstract :
Replacing a single high-capacity actuator with several ones operating in concert is an increasingly popular technological trend.
The aim is to increase not only the overall capacity of the actuation subsystem, but also its systemic robustness against the failure of one of its components.
The control specifications for such a system are naturally ordered, since component preferences must only be taken into account if their overall contribution to the control effort is preserved.
Strict compliance with this hierarchy is closely related to the notion of Input Redundancy (IR). This property is redefined as the existence of distinct input trajectories giving rise to the same output trajectory. In other words, IR is the opposite of left-invertibility. In the case of linear systems associated with linear input and state spaces, IR is equivalent to the existence of an annihilator, whose output can be injected at the system input without modifying its output trajectory. Under the same assumptions, it is possible to isolate the part of the input that influences the output. These three points of view (inversion, annihilator, input decomposition) are illustrated by considering the case of the 3-phases star-connected inverter, then generalized to general static and affine systems subject to input constraints.
In the case of dynamic systems, the structure of the control law is traditionally based on control allocation. This strategy formulates the overall actuation effort distribution as an optimization problem, which is solved quasi-continuously, on-line. An in-depth analysis of the literature dedicated to this approach is proposed, adopting a historical point of view and illustrating the techniques presented on a single academic example.
This analysis naturally opens on the extension to dynamic systems of the discussion adopting the three previous points of view. IR is formally defined for this class of systems. Taking the state trajectory into account gives rise to a taxonomy of input-redundant systems, in the linear case. Under the latter assumption, characterizations of IR and its taxonomy are proposed. The existence, construction and implementation of an annihilator are also discussed, as well as the impact of input and state constraints on IR.
The central problem of output regulation is also re-examined through the lens of IR. The inadequacy of the regulator equations to take advantage of the degrees of freedom offered by IR is highlighted. On the contrary, equipping the trajectories generator with an annihilator specifically designed for this purpose enables exhaustive parameterization of acceptable steady-state. This in turn offers the possibility of making an optimal choice of permanent regime, on-line. In so doing, the notion of IR is weakened, then shaped into a version specifically adapted to output control: the bounded and persistent weak IR. The resulting framework enables an in-depth comparison of existing definitions of IR, which are also linked to several notions of left-invertibility.
The problem of output regulation of a parallel interconnection of buck converters is addressed. In addition to its relevance to power electronics research, this problem is inspiring for control theory. It allows us to concretize and enrich the discussions on the three previous points of view, in the case of dynamic systems. The analysis carried out within a general framework is also made deeper on the closed-loop robustness.
Finally, three perspectives are outlined. The first aims to build a universal framework for the control of modular power electronics converters. In this sense, it extends the results obtained on parallel buck converters and the 3-phases inverter. The challenges identified justify a series of research directions around IR and its exploitation in control, aimed at completing and extending the results of this manuscript. Finally, the expected benefits of co-designing the system, its control and the specifications are highlighted. To this end, the importance of inversion in the context of constrained dynamic systems is emphasized.
Publications :