Set‐based gain‐scheduled control via quasi‐convex difference inclusions

A nonlinear system with sector-bounded nonlinearities may be expressed as a quasiLPV system (convex combination of linear models), being this a well-known fact. The convex difference inclusion (CDI) modelling framework proposed by M. Fiacchini and coworkers in several of their works generalises the quasi-LPV modelling procedure and proposes robust controllers enlarging polytopic domain of attraction estimates. This works further generalises the CDI approach to a gain-scheduled case including, also, some quasi-convex cases. Controller design is based on convexity properties of two set valued maps describing (with some uncertainty) the state evolution and the state-dependent set where scheduling variables take values. As most set-based approaches, the proposal is tractable in low-dimensional cases. The presented results encompass prior quasi-LPV and CDI models as particular cases

Contributions to nonlinear system modelling and controller synthesis via convex structures

Esta tesis discute diferentes metodologías de modelado para extraer mejores prestaciones o resultados de estabilidad que aquéllas que el modelado convencional basado en sector no-lineal de sistemas Takagi-Sugeno (también denominados cuasi-LPV) es capaz de producir. En efecto, incluso si las LMIs pueden probar distintas cotas de prestaciones o márgenes de estabilidad (tasa de decaimiento, $\mathcal H_\infty$, etc.) para sistemas politópicos, es bien conocido que las prestaciones probadas dependen del modelo elegido y, dado un sistema no-lineal, dicho modelo politópico no es único. Por tanto, se presentan exploraciones hacia cómo obtener el modelo que es menos perjudicial para la medida de prestaciones elegida. Como una última contribución, mejores resultados son obtenidos mediante la extensión del modelado politópico Takagi-Sugeno a un marco de inclusiones en diferencias cuasi-convexas con planificación de ganancia. En efecto, una versión sin planificación de ganancia fue propuesta por un equipo de investigadores de la Universidad de Sevilla (Fiaccini, Álamo, Camacho) para generalizar el modelado politópico, y esta tesis propone una version aún más general de algunos de dichos resultados que incorpora planificación de ganancia.This thesis discusses different modelling methodologies to eke out best performance/stability results than conventional sector-nonlinearity Takagi-Sugeno (also known as quasi-LPV) systems modelling techniques are able to yield. Indeed, even if LMIs can prove various performance and stability bounds (decay rate, $\mathcal H_\infty$, etc.) for polytopic systems, it is well known that the proven performance depends on the chosen model and, given a nonlinear dynamic systems, the polytopic embeddings available for it are not unique. Thus, explorations on how to obtain the model which is less deletereous for performance are presented. As a last contribution, extending the polytopic Takagi-Sugeno setup to a gain-scheduled quasi-convex difference inclusion framework allows to improve the results over the polytopic models. Indeed, the non-scheduled convex difference inclusion framework was proposed by a research team in University of Seville (Fiacchini, Alamo, Camacho) as a generalised modelling methodology which included the polytopic one; this thesis poses a further generalised gain-scheduled version of some of these results.Aquesta tesi discuteix diferents metodologies de modelatge per extreure millors prestacions o resultats d'estabilitat que aquelles que el modelatge convencional basat en sector no-lineal de sistemes Takagi-Sugeno (també anomenats quasi-LPV) és capaç de produir. En efecte, fins i tot si les LMIs poden provar diferents cotes de prestacions o marges d'estabilitat (taxa de decaïment, $\mathcal H_\infty$, etc.) per a sistemes politòpics, és ben conegut que les prestacions provades depenen del model triat i, donat un sistema no-lineal, el dit model politòpic no és únic. Per tant, es presenten exploracions cap a com obtenir el model que és menys perjudicial per a la mesura de prestacions triada. Com una darrera contribució, millors resultats són obtinguts mitjançant l'extensió del modelatge politòpic Takagi-Sugeno a un marc d'inclusions en diferències quasi-convexes amb planificació de guany. En efecte, una versió sense planificació de guany va ser proposada per un equip d'investigadors de la Universitat de Sevilla (Fiaccini, Álamo, Camacho) per a generalitzar el modelatge politòpic, i aquesta tesi proposa una versió més general d'alguns d'aquests resultats que incorpora planificació de guany.Robles Ruiz, R. (2018). Contributions to nonlinear system modelling and controller synthesis via convex structures [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/100848TESI

Coordinate-Descent Augmented Lagrangian Methods for Interpretative and Adaptive Model Predictive Control

Model predictive control (MPC) of nonlinear systems suffers a trade-off between model accuracy and real-time compu- tational burden. This thesis presents an interpretative and adaptive MPC (IA-MPC) framework for nonlinear systems, which is related to the widely used approximation method based on successive linearization MPC and Extended Kalman Filtering (SL-MPC-EKF). First, we introduce a solution algo- rithm for linear MPC that is based on the combination of Co- ordinate Descent and Augmented Lagrangian (CDAL) ideas. The CDAL algorithm enjoys three features: (i) it is construction-free, in that it avoids explicitly constructing the quadratic pro-gramming (QP) problem associated with MPC; (ii) is matrix-free, as it avoids multiplications and factorizations of matri-ces; and (iii) is library-free, as it can be simply coded without any library dependency, 90-lines of C-code in our implemen-tation. We specialize the algorithm for both state-space for-mulations of MPC and formulations based on AutoRegres-sive with eXogenous terms models (CDAL-ARX). The thesis also presents a rapid-prototype MPC tool based on the gPROMS platform, in which the qpOASES and CDAL algorithm was integrated. In addition, based on an equivalence between SS-based and ARX-based MPC problems we show,we investigate the relation between the proposed IA-MPC and the classical SL-MPC-EKF method. Finally, we test and show the effectiveness of the proposed IA-MPC frameworkon four typical nonlinear MPC benchmark examples

Robust and Multi-Objective Model Predictive Control Design for Nonlinear Systems

The multi-objective trade-off paradigm has become a very valuable design tool in engineering problems that have conflicting objectives. Recently, many control designers have worked on the design methods which satisfy multiple design specifications called multi-objective control design. However,the main challenge posed for the MPC design lies in the high computation load preventing its application to the fast dynamic system control in real-time. To meet this challenge, this thesis has proposed several methods covering nonlinear system modeling, on-line MPC design and multi-objective optimization. First, the thesis has proposed a robust MPC to control the shimmy vibration of the landing gear with probabilistic uncertainty. Then, an on-line MPC method has been proposed for image-based visual servoing control of a 6 DOF Denso robot. Finally, a multi-objective MPC has been introduced to allow the designers consider multiple objectives in MPC design. In this thesis, Tensor Product (TP) model transformation as a powerful tool in the modeling of the complex nonlinear systems is used to find the linear parameter-varying (LPV) models of the nonlinear systems. Higher-order singular value decomposition (HOSVD) technique is used to obtain a minimal order of the model tensor. Furthermore, to design a robust MPC for nonlinear systems in the presence of uncertainties which degrades the system performance and can lead to instability, we consider the parameters of the nonlinear systems with probabilistic uncertainties in the modeling using TP transformation. In this thesis, a computationally efficient methods for MPC design of image-based visual servoing, i.e. a fast dynamic system has been proposed. The controller is designed considering the robotic visual servoing system's input and output constraints, such as robot physical limitations and visibility constraints. The main contributions of this thesis are: (i) design MPC for nonlinear systems with probabilistic uncertainties that guarantees robust stability and performance of the systems; (ii) develop a real-time MPC method for a fast dynamical system; (iii) to propose a new multi-objective MPC for nonlinear systems using game theory. A diverse range of systems with nonlinearities and uncertainties including landing gear system, 6 DOF Denso robot are studied in this thesis. The simulation and real-time experimental results are presented and discussed in this thesis to verify the effectiveness of the proposed methods