Output regulation and adaptive control of uncertain linear systems: an overview and an adaptive passification approach

In the current literature of control systems design, there are numerous techniques and approaches have been developed to achieve regulation and tracking, with prescribed requirements of stability, performance and robustness. On the one hand, the problem of Output Regulation (OR) refers to the design of a control system able to achieve asymptotic tracking of prescribed trajectories and asymptotic rejection of disturbances, in a robust way, both generated by an autonomous system called exosystem. On the other hand, Model Reference Adaptive Control (MRAC) is one of the main design approaches in adaptive control, where the goal is that of tracking time-varying bounded references under parametric model uncertainties. In this respect, one of the aims of this work is to compare the two frameworks, highlighting the differences and the common points. The peculiarity of the MRAC approach is that is possible to give a particular interpretation, that is useful in order to compare the two approaches and show the similar structure. In order to study in depth the two frameworks, two particular cases will be taken into account. First, the classic OR problem is considered with a non-autonomous exosystem, in which a geometric approach is used to conclude regulation of the error to zero. Then, MRAC is considered in case the classic bounded and measurable reference signal is now generated by a known autonomous exosystem. In the MRAC approach, it is also shown how the useful tool of passivity plays a fundamental role in the analysis and design of adaptive systems. The passivity property can be used also in the OR case, where is useful in order to design an adaptive law for the stabilizer. In the considered case of linear systems, the passivity property is shown to be strictly related to the incremental passivity. The study of the passivity is done considering the classic OR framework, with a stabilizer and a well defined internal model unit. It is shown how the interconnection and the properties on the single subsystems make the close-loop system incrementally passive, and how asymptotic regulation is achieved. In presence of model uncertainties, an adaptive law can be employed to solve the problem by recovering the static feedback control law asymptotically. Finally, a numerical example will be presented to validate the results of the thesis.