Advanced modeling and control of complex systems

The latest engineering developments oriented towards the control of robotic systems encompass a diverse range of strategies and approaches in order to achieve this result. This is particularly valid for systems that show high complexity: from a single, but very complex agent (for example a humanoid robot, a multicopter drone, an industrial process, ...) to a huge number of systems, interconnected in possibly complex ways (an ecosystem, a social network, multiple robots that need coordination in order to successfully accomplish a task). All of these scenarios, together with all the combinations of systems in between, fall into the complex system category. In this manuscript, we then address the modeling problem by extending what in literature is called the planar hexarotor, that is a multirotor drone with the propellers all spinning on the same plane, by tilting these propellers by fixed angles, and studying what is possible to achieve with this change. This is done in two steps, i.e. with two different tilting angles: the first already adds noticeable properties, while the second turns out to be way more interesting from the view of practical utility, turning out to be extremely use-case specific, and making considerations on its employment more delicate. After the entire modeling of these hexarotors, the control part enters the scene: with a good model of such platforms, is it possible to exploit it in order to create controllers that are tailored for it? An entire chapter of this thesis is dedicated to this problem, showing two novel control schemes. Later on, the focus moves away from the control of only hexarotors, and shifts towards controllers that can be more general, and can possibly be applied to a wide variety of dynamical systems. This is where Contraction Theory is used, having already proved to be robust in literature. The state of the art about it, though, presents only very few examples of practical applications, due to various reasons: first, the calculations to find controllers that make the system contractive can be very tedious, if not impossible. Secondly, even if calculations are computationally affordable, sometimes the assumptions can turn out to be too restrictive. This is why in this manuscript we build upon methods that do not require integration at run-time, and we extend them with a double contribution first, an adaptive-control layer is added to said controller, and later on the original state-feedback controller is enhanced to an output-feedback controller. The adaptive control layer is added because the controller we build upon, like many others, heavily depend on the model: if an uncertainty that is not negligible arises, various control methods fail to even achieve boundedness of the controlled system. This is greatly reduced by the fact that a contractive system is very likely to provide error bounds, and not diverge, if the uncertainty is bounded. In order to strengthen the convergence even these scenarios though, an adaptive control layer is proved to work remarkably well, combining robustness of the contractive controller with the adaptation, jointly achieving convergence under structured uncertainty. The problem of output feedback instead finds immediate usefulness in the simple fact that most of the time, not all the state is observable, and usually resorting to observers leads to instabilities that mine the overall effectiveness of the controller. We expand the existing controller, showing how it is possible to achieve output-feedback as well, at the cost of higher computational complexity and stricter assumptions.