98 research outputs found

    Robust controllers design for unknown error and exosystem: a hybid optimization and output regulation approach

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    This thesis addresses the problem of robustness in control in two main topics: linear output regulation when no knowledge is assumed of the modes of the exosystem, and hybrid gradient-free optimization. A framework is presented for the solution of the first problem, in which asymptotic regulation is achieved in case of a persistence of excitation condition. The stability properties of the closed-loop system are proved under a small-gain argument with no minimum phase assumption. The second part of the thesis addresses, and proposes, a solution to the gradientfree optimization problem, solved by a discrete-time direct search algorithm. The algorithm is shown to convergence to the set of minima of a particular class of non convex functions. It is, then, applied considering it coupled with a continuous-time dynamical system. A hybrid controller is developed in order to guarantee convergence to the set of minima and stability of the interconnection of the two systems. Almost global asymptotic is proven for the proposed hybrid controller. Shown to not be robust to any bounded measurement noise, a robust solution is also proposed. The aim of this thesis is to lay the ground for a solution of the output regulation problem in case the error is unknown, but a proxy optimization function is available. A controller embedding the characteristics of the two proposed approaches, as a main solution to the aforementioned problem, will be the focus of future studies

    Self-Similar Solutions to the Compressible Euler Equations and their Instabilities

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    This paper addresses the construction and the stability of self-similar solutions to the isentropic compressible Euler equations. These solutions model a gas that implodes isotropically, ending in a singularity formation in finite time. The existence of smooth solutions that vanish at infinity and do not have vacuum regions was recently proved and, in this paper, we provide the first construction of such smooth profiles, the first characterization of their spectrum of radial perturbations as well as some endpoints of unstable directions. One of these endpoints is a shock formation that happens before the singularity at the origin, showing that the implosion process is unstable.Comment: Main text: 24 pages, 13 figures. Appendices: 12 pages, 3 figures. v2: extended materia

    Renormalization group and critical properties of Long Range models

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    We study a Renormalization Group transformation that can be used also for models with quenched disorder, like spin glasses, for which a commonly accepted and predictive Renormalization Group does not exist. We validate our method by applying it to a particular long-range model, the hierarchical one (both the diluted ferromagnetic version and the spin glass version), finding results in agreement with Monte Carlo simulations. In the second part we deeply analyze the connection between long-range and short-range models that still has some unclear aspects even for the ferromagnet. A systematic analysis is very important to understand if the use of long range models is justified to study properties of short range systems like spin-glasses

    Resource-aware motion control:feedforward, learning, and feedback

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    Controllers with new sampling schemes improve motion systems’ performanc
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