Robust sensor location optimization in distributed parameter systems using functional observers

TL;DR: Advection-diffusion equations with constant coefficients on infinite 1-D and 2-D spatial domains are considered and suitable sensor and/or actuator locations are determined for which high-gain and low-gain proportional feedback can effectively reduce the influence of a disturbance at a point of interest.

TL;DR: A new basis for the design vector is created via Proper Orthogonal Decomposition (POD) using the trajectories of initial optimisation paths as a “training set” and parametrisation is shown to make the optimisation more robust with respect to the initial design, and facilitate an automated variable selection methodology.

TL;DR: In this article , the observer design problem for a class of one-dimensional multi-species transport-reaction systems satisfying sector bounded nonlinearities is considered and a design method is proposed based on a reduced-order model and a Lyapunov function, which provides sufficient conditions in terms of standard linear matrix inequalities (LMIs) to ensure the exponential convergence of the estimation error with a prescribed decay rate.

TL;DR: This book presents Semigroup Theory, a treatment of systems theory concepts in finite dimensions with a focus on Hankel Operators and the Nehari Problem.

TL;DR: This new text is a substantially enlarged and revised version of Professor Chen's earlier book on linear systems, which is a balanced and comprehensive treatment of all the useful concepts from both state space and frequency domain approaches for the analysis and design of linear control systems.

Abstract: These six volumes - the result of a ten year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the Methoden der mathematischen Physik by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which together with given boundary data and, if the phenomenon is evolving in time, initial data, defines the system. The advent of high-speed computers has made it possible for the first time to caluclate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every fact of technical and industrial activity has been affected by these developments. Modeling by distributed systems now also supports work in many areas of physics (plasmas, new materials, astrophysics, geophysics), chemistry and mechanics and is finding increasing use in the life sciences. Volumes 5 and 6 cover problems of Transport and Evolution.

TL;DR: In this article, the idea of continuous designs for moving sensors is proposed to optimize sensor trajectories based on the optimal experimental design problem in the presence of correlated observations and maximizing an Observability Measure.