Sufficient Conditions for Feasibility and Optimality of Real-Time Optimization Schemes - II. Implementation Issues

The idea of iterative process optimization based on collected output measurements, or "real-time optimization" (RTO), has gained much prominence in recent decades, with many RTO algorithms being proposed, researched, and developed. While the essential goal of these schemes is to drive the process to its true optimal conditions without violating any safety-critical, or "hard", constraints, no generalized, unified approach for guaranteeing this behavior exists. In this two-part paper, we propose an implementable set of conditions that can enforce these properties for any RTO algorithm. This second part examines the practical side of the sufficient conditions for feasibility and optimality (SCFO) proposed in the first and focuses on how they may be enforced in real application, where much of the knowledge required for the conceptual SCFO is unavailable. Methods for improving convergence speed are also considered.Comment: 56 pages, 15 figure

Sufficient Conditions for Feasibility and Optimality of Real-Time Optimization Schemes - I. Theoretical Foundations

The idea of iterative process optimization based on collected output measurements, or "real-time optimization" (RTO), has gained much prominence in recent decades, with many RTO algorithms being proposed, researched, and developed. While the essential goal of these schemes is to drive the process to its true optimal conditions without violating any safety-critical, or "hard", constraints, no generalized, unified approach for guaranteeing this behavior exists. In this two-part paper, we propose an implementable set of conditions that can enforce these properties for any RTO algorithm. The first part of the work is dedicated to the theory behind the sufficient conditions for feasibility and optimality (SCFO), together with their basic implementation strategy. RTO algorithms enforcing the SCFO are shown to perform as desired in several numerical examples - allowing for feasible-side convergence to the plant optimum where algorithms not enforcing the conditions would fail.Comment: Working paper; supplementary material available at: http://infoscience.epfl.ch/record/18807

Sociologie des pratiques familiales et des pratiques scolaires

François Bonvin, maître de conférences Enseignement suspendu durant l’année universitaire 2001-2002

Implementation techniques for the SCFO experimental optimization framework

The material presented in this document is intended as a comprehensive, implementation-oriented supplement to the experimental optimization framework presented in a companion document. The issues of physical degradation, unknown Lipschitz constants, measurement/estimation noise, gradient estimation, sufficient excitation, and the handling of soft constraints and/or a numerical cost function are all addressed, and a robust, implementable version of the sufficient conditions for feasible-side global convergence is proposed.Comment: supplementary document; 66 page

On linear and quadratic Lipschitz bounds for twice continuously differentiable functions

Lower and upper bounds for a given function are important in many mathematical and engineering contexts, where they often serve as a base for both analysis and application. In this short paper, we derive piecewise linear and quadratic bounds that are stated in terms of the Lipschitz constants of the function and the Lipschitz constants of its partial derivatives, and serve to bound the function's evolution over a compact set. While the results follow from basic mathematical principles and are certainly not new, we present them as they are, from our experience, very difficult to find explicitly either in the literature or in most analysis textbooks.Comment: 3 pages; supplementary documen

Design of multi-parametric NCO tracking controllers for linear dynamic systems

© 2016 The Authors.A methodology for combining multi-parametric programming and NCO tracking is presented in the case of linear dynamic systems. The resulting parametric controllers consist of (potentially nonlinear) feedback laws for tracking optimality conditions by exploiting the underlying optimal control switching structure. Compared to the classical multi-parametric MPC controller, this approach leads to a reduction in the number of critical regions. It calls for the solution of more difficult parametric optimization problems with linear differential equations embedded, whose critical regions are potentially nonconvex. Examples of constrained linear quadratic optimal control problems with parametric uncertainty are presented to illustrate the approach

Precise measurements of time delays in gravitationally lensed quasars for competitive and independent determination of the Hubble constant

During these last decades, by virtue of observations, the Standard Cosmological Model has emerged, providing a description of the Universe's evolution using a minimal set of independent constraints - the cosmological parameters. Among them is the expansion rate of the Universe, the so-called Hubble constant or H0, first measured by Lemaître in 1927. The century that followed this cornerstone measurement saw numerous attempts to refine the initial value, and for good reason: a precise and independent measurement of H0 will bring strong constraints on the cosmological models. It could notably help the astronomers to better understand the nature of dark energy, thus making it one of the most sought-after prizes in modern cosmology. My work at the Laboratory of Astrophysics of EPFL is embedded in this context. I am part of the COSMOGRAIL and H0LiCOW collaborations, aiming to measure the Hubble constant with the highest level of precision using time-delay cosmography, a method based on the theory of strong gravitational lensing. This effect occurs when an observer looks at a light source located behind a massive foreground galaxy. The mass of the galaxy acts similarly to an optical lens and focuses the light rays emitted by the source. As a consequence, multiple lensed images of the source appear around the lens galaxy. If the luminosity of the source changes over time, the variations will be seen in all the lensed images but with a temporal delay due to the different travel paths of the light rays. By carefully monitoring the luminosity variations of each lensed image, one can precisely measure the temporal delays between them. Combined to high-resolution observations of the foreground galaxy and its surroundings, it is possible to directly measure the Hubble constant upon the sole assumption that the General Relativity is correct. Since more than 13 years, COSMOGRAIL monitors dozens of lensed quasars to produce high-quality light curves and time-delay measurements. During these last four years, I took care of the monitoring schedule, continuous data reduction and time-delay measurements through the development of curve-shifting techniques. I produced light curves and measured time delays on a variety of lenses. After more than a decade of endeavours, COSMOGRAIL and H0LiCOW finally revealed their measurement of the expansion rate of the Universe from a blind analysis of three lensed sources. I had the privilege to be the lead author of the publication presenting our measurement of the Hubble constant, H0=71.9 -3.0+2.4 km/s/Mpc 3.8% precision in the Standard Cosmological Model. Such a precision allows a direct comparison with the results of the distance ladder technique in the local Universe and the Planck satellite Cosmic Microwave Background observations in the distant Universe, both of which being currently in a significant tension of unknown source

Use of Transient Measurements for the Optimization of Steady-State Performance via Modifier Adaptation

Real-time optimization (RTO) methods use measurements to offset the effect of uncertainty and drive the plant to optimality. RTO schemes differ in the way measurements are incorporated in the optimization framework. Explicit RTO schemes solve a static optimization problem repeatedly, with each iteration requiring transient operation of the plant to steady state. In contrast, implicit RTO methods use transient measurements to bring the plant to steady-state optimality in a single iteration, provided the set of active constraints is known. This paper considers the explicit RTO scheme "modifier adaptation" (MA) and proposes a framework that allows using transient measurements for the purpose of steady-state optimization. It is shown that convergence to the plant optimum can be achieved in a single transient operation provided the plant gradients can be estimated accurately. The approach is illustrated through the simulated example of a continuous stirred-tank reactor. The time needed for convergence is of the order of the plant settling time, while more than five iterations to steady state are required with conventional static MA. In other words, MA using transient information is able to compete in performance with RTO schemes based on gradient control, with the additional ability to handle plant constraints

Sociologie des pratiques familiales et des pratiques scolaires

François Bonvin, maître de conférencesavec Choukri Benayed, chargé d’enseignement à l’Université de Paris-V Socialisation familiale et scolaire en situation de rupture biographique Enseignement suspendu durant l’année universitaire 2000-2001