Robust control strategies for unstable systems with input/output delays

Los sistemas con retardo temporal aparecen con frecuencia en el ámbito de la ingeniería, por ejemplo en transmisiones hidráulicas o mecánicas, procesos metalúrgicos o sistemas de control en red. Los retardos temporales han despertado el interés de los investigadores en el ámbito del control desde finales de los años 50. Se ha desarrollado una amplia gama de herramientas para el análisis de su estabilidad y prestaciones, especialmente durante las dos últimas décadas. Esta tesis se centra en la estabilización de sistemas afectados por retardos temporales en la actuación y/o la medida. Concretamente, las contribuciones que aquí se incluyen tienen por objetivo mejorar las prestaciones de los controladores existentes en presencia de perturbaciones. Los retardos temporales degradan, inevitablemente, el desempeño de un bucle de control. No es de extrañar que el rechazo de perturbaciones haya sido motivo de estudio desde que emergieron los primeros controladores predictivos para sistemas con retardo. Las estrategias presentadas en esta tesis se basan en la combinación de controladores predictivos y observadores de perturbaciones. Estos últimos han sido aplicados con éxito para mejorar el rechazo de perturbaciones de controladores convencionales. Sin embargo, la aplicación de esta metodología a sistemas con retardo es poco frecuente en la literatura, la cual se investiga exhaustivamente en esta tesis. Otro inconveniente de los controladores predictivos está relacionado con su implementación, que puede llevar a la inestabilidad si no se realiza cuidadosamente. Este fenómeno está relacionado con el hecho de que las leyes de control predictivas se expresan mediante una ecuación integral. En esta tesis se presenta una estructura de control alternativa que evita este problema, la cual utiliza un observador de dimensión infinita, gobernado por una ecuación en derivadas parciales de tipo hiperbólico.Time-delay systems are ubiquitous in many engineering applications, such as mechanical or fluid transmissions, metallurgical processes or networked control systems. Time-delay systems have attracted the interest of control researchers since the late 50's. A wide variety of tools for stability and performance analysis has been developed, specially over the past two decades. This thesis is focused on the problem of stabilizing systems that are affected by delays on the actuator and/or sensing paths. More specifically, the contributions herein reported aim at improving the performance of existing controllers in the presence of external disturbances. Time delays unavoidably degrade the control loop performance. Disturbance rejection has been a matter of concern since the first predictive controllers for time-delay systems emerged. The key idea of the strategies presented in this thesis is the combination of predictive controllers and disturbance observers. The latter have been successfully applied to improve the disturbance rejection capabilities of conventional controllers. However, the application of this methodology to time-delay systems is rarely found in the literature. This combination is extensively investigated in this thesis. Another handicap of predictive controllers has to do with their implementation, which can induce instability if not done carefully. This issue is related to the fact that predictive control laws take the form of integral equations. An alternative control structure that avoids this problem is also reported in this thesis, which employs an infinite-dimensional observer, governed by a hyperbolic partial differential equation.Sanz Díaz, R. (2018). Robust control strategies for unstable systems with input/output delays [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/111830TESI

Learning and Control of Dynamical Systems

Despite the remarkable success of machine learning in various domains in recent years, our understanding of its fundamental limitations remains incomplete. This knowledge gap poses a grand challenge when deploying machine learning methods in critical decision-making tasks, where incorrect decisions can have catastrophic consequences. To effectively utilize these learning-based methods in such contexts, it is crucial to explicitly characterize their performance. Over the years, significant research efforts have been dedicated to learning and control of dynamical systems where the underlying dynamics are unknown or only partially known a priori, and must be inferred from collected data. However, much of these classical results have focused on asymptotic guarantees, providing limited insights into the amount of data required to achieve desired control performance while satisfying operational constraints such as safety and stability, especially in the presence of statistical noise. In this thesis, we study the statistical complexity of learning and control of unknown dynamical systems. By utilizing recent advances in statistical learning theory, high-dimensional statistics, and control theoretic tools, we aim to establish a fundamental understanding of the number of samples required to achieve desired (i) accuracy in learning the unknown dynamics, (ii) performance in the control of the underlying system, and (iii) satisfaction of the operational constraints such as safety and stability. We provide finite-sample guarantees for these objectives and propose efficient learning and control algorithms that achieve the desired performance at these statistical limits in various dynamical systems. Our investigation covers a broad range of dynamical systems, starting from fully observable linear dynamical systems to partially observable linear dynamical systems, and ultimately, nonlinear systems. We deploy our learning and control algorithms in various adaptive control tasks in real-world control systems and demonstrate their strong empirical performance along with their learning, robustness, and stability guarantees. In particular, we implement one of our proposed methods, Fourier Adaptive Learning and Control (FALCON), on an experimental aerodynamic testbed under extreme turbulent flow dynamics in a wind tunnel. The results show that FALCON achieves state-of-the-art stabilization performance and consistently outperforms conventional and other learning-based methods by at least 37%, despite using 8 times less data. The superior performance of FALCON arises from its physically and theoretically accurate modeling of the underlying nonlinear turbulent dynamics, which yields rigorous finite-sample learning and performance guarantees. These findings underscore the importance of characterizing the statistical complexity of learning and control of unknown dynamical systems.</p