Entropic Regularization Approach for Mathematical Programs with Equilibrium Constraints

A new smoothing approach based on entropic perturbationis proposed for solving mathematical programs withequilibrium constraints. Some of the desirableproperties of the smoothing function are shown. Theviability of the proposed approach is supported by acomputationalstudy on a set of well-known test problems.mathematical programs with equilibrium constraints;entropic regularization;smoothing approach

Entropic Regularization Approach for Mathematical Programs with Equilibrium Constraints

A new smoothing approach based on entropic perturbation is proposed for solving mathematical programs with equilibrium constraints. Some of the desirable properties of the smoothing function are shown. The viability of the proposed approach is supported by a computationalstudy on a set of well-known test problems

Learning Non-Parametric Models with Guarantees: A Smooth Lipschitz Interpolation Approach

We propose a non-parametric regression method that does not rely on the structure of the ground-truth, but only on its regularity properties. The methodology can be readily used for learning surrogate models of nonlinear dynamical systems from data, while providing bounds on the prediction error. In contrast with the well known Set Membership and Kinky Inference techniques that yield non-differentiable functions, the approach presented herein produces a smooth regressor. Consequently, it is more suitable to optimization-based controllers that heavily rely on gradient computations. A numerical example is provided to show the effectiveness of the method we call Smooth Lipschitz Interpolation (SLI) when compared to the aforementioned alternatives in a Model Predictive Control problem

Full Stability In Optimization

The dissertation concerns a systematic study of full stability in general optimization models including its conventional Lipschitzian version as well as the new Holderian one. We derive various characterizations of both Lipschitzian and Holderian full stability in nonsmooth optimization, which are new in finite-dimensional and infinite-dimensional frameworks. The characterizations obtained are given in terms of second-order growth conditions and also via second-order generalized differential constructions of variational analysis. We develop effective applications of our general characterizations of full stability to parametric variational systems including the well-known generalized equations and variational inequalities. Many relationships of full stability with the conventional notions of strong regularity and strong stability are established for a large class of problems of constrained optimization with twice continuously differentiable data. Other applications of full stability to nonlinear programming, to semidefinite programming, and to optimal control problems governed by semilinear elliptic PDEs are also studied

Learning-based Nonlinear Model Predictive Control

© 2017 This paper presents stabilizing Model Predictive Controllers (MPC) in which prediction models are inferred from experimental data of the inputs and outputs of the plant. Using a nonparametric machine learning technique called LACKI, the estimated (possibly nonlinear) model function together with an estimation of Holder constant is provided. Based on these, a number of predictive controllers with stability guaranteed by design are proposed. Firstly, the case when the prediction model is estimated offline is considered and robust stability and recursive feasibility is ensured by using tightened constraints in the optimisation problem. This controller has been extended to the more interesting and complex case: the online learning of the model, where the new data collected from feedback is added to enhance the prediction model. An on-line learning MPC based on a double sequence of predictions is proposed.Spanish MINECO Grant PRX15-00300 and projects DPI2013-48243-C2-2-R and DPI2016-76493-C3-1-R. UK Engineering and Physical Research Council, grant no.EP/J012300/1

Learning-based Nonlinear Model Predictive Control

© 2017 This paper presents stabilizing Model Predictive Controllers (MPC) in which prediction models are inferred from experimental data of the inputs and outputs of the plant. Using a nonparametric machine learning technique called LACKI, the estimated (possibly nonlinear) model function together with an estimation of Holder constant is provided. Based on these, a number of predictive controllers with stability guaranteed by design are proposed. Firstly, the case when the prediction model is estimated offline is considered and robust stability and recursive feasibility is ensured by using tightened constraints in the optimisation problem. This controller has been extended to the more interesting and complex case: the online learning of the model, where the new data collected from feedback is added to enhance the prediction model. An on-line learning MPC based on a double sequence of predictions is proposed.Spanish MINECO Grant PRX15-00300 and projects DPI2013-48243-C2-2-R and DPI2016-76493-C3-1-R. UK Engineering and Physical Research Council, grant no.EP/J012300/1

Design of Experiments for Nonlinear System Identification

L'abstract è presente nell'allegato / the abstract is in the attachmen

Learning-based model predictive control for constrained nonlinear systems

Esta tesis está dedicada al control de sistemas, bajo la hipótesis de que no se conoce nada sobre la dinámica del sistema a controlar. En vez de eso, solamente las entradas y salidas son accesibles, y por tanto se puede tener acceso a un histórico de datos. El objetivo principal es el control de la planta en condiciones eficientes y seguras usando únicamente dichas medidas. Con este fin, se usará un conjunto de métodos de aprendizaje automático conocido como link inferencia, para modelar sistemas no lineales desconocidos, usando controladores predictivos basados en modelo. Por ello, esta tesis presenta contribuciones en dos campos distintos. En primer lugar, se extenderán las técnicas de link inferencia, proponiendo métodos con dos objetivos: reducir tanto el tiempo de cálculo de los algoritmos como el error de predicción cometido por ellos. En segundo lugar, se desarrollarán controladores predictivos robustos y con la habilidad de aprender basándose en datos. Estos controladores serán estables por diseño, capaces de satisfacer restricciones robustamente y de mejorar su actuación beneficiándose de nuevas medidas recogidas en línea

Robust and Multi-objective Portfolio Selection

In this thesis, robust and multi-objective portfolio selection problem will be studied. New models and computational algorithms will be developed to solve the proposed models. In particularly, we have studied multi-objective portfolio selection with inexact information on investment return and covariance matrix. The problems have been transformed into easily solvable problems through theoretical analysis. Numerical experiments are presented to validate the methods