Adaptive Output Regulation For Multivariable Nonlinear Systems Via Hybrid Identification Techniques

Output regulation refers to the class of control problems in which some outputs of the controlled system must be steered to some desired references, while maintaining closed-loop stability and in spite of the presence of unmeasured disturbances and model uncertainties. While for linear systems the problem has been elegantly solved in the 70s, output regulation for nonlinear systems is still a challenging research field, and 30 years of active research left open many fundamental problems. In particular, all the regulators proposed so far are limited to very specific classes of nonlinear systems and, even in those cases, they fail in extending in their full generality the celebrated properties of the linear regulator. The aim of this thesis is to make a decisive step towards the systematic extension of the output regulation theory to embrace more general multivariable problems. To this end, we touch here three fundamental pillars of regulation theory: the structure of regulators, the robustness issue, and the adaptation of the control system. Regarding the structural aspects, we pursue here a design paradigm that is complementary to canonical nonlinear regulators and that trades a conceptually more suitable structure with a strong internal intertwining between the different parts of the regulator. For what concerns robustness, we introduce a new framework to characterize robustness of regulators relative to steady-state properties more general than the usual requirement asking a zero asymptotic error. We characterize in this unifying terms a large part of the existing approaches, and we end conjecturing that general nonlinear regulation admits no robust solution. Regarding the evolution of regulators, we propose an adaptive regulation framework in which adaptation is used online to tune the internal models embedded in the control system. Adaptation is cast as a general system identification problem, allowing for different well-known algorithms to be used

The Chicken-Egg Dilemma and the Robustness Issue in Nonlinear Output Regulation with a Look Towards Adaptation and Universal Approximators

In this paper we review the problem of output regulation for nonlinear systems. We discuss how the robustness properties and the simple structure of the linear regulator are linear artefacts which do not extend in more general nonlinear cases. We talk about the intertwining that is necessarily present between the internal model and the stabilising parts of a nonlinear regulator, in which the role of the exosystem mixes up with those of the residual plant's dynamics. We discuss a general guideline to deal with such structural challenges, by looking at adaptation and universal approximators as a promising way to provide systematic design procedures for approximate regulators in a general nonlinear setting