There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Introduction to linear and nonlinear programming

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

Introduction. Cellular Growth Reactions. Analysis of Reaction Rates. Modelling of Reaction Kinetics. Morphologically Structured Models. Population Balances Based on Cell Number. Mass Transfer. Ideal Bioreactors. Bioreactor Modelling. Index.

Bioreaction Engineering Principles

Nonlinear observer design using Lyapunov's auxiliary theorem

This paper studies the design of feedback controllers for trajectory tracking in single-input/ single-output nonlinear systems x = f(x) + g(x) u, y = h(x). A nonlinear transformation of the form v = k(x) + λ(x) u that transforms this nonlinear input/output system into a linear system is first constructed. On the basis of this transformation, an approach for designing control laws for trajectory tracking is presented. The control law is robust in the sense that small changes in it do not produce large steady state errors or loss of stability. The theory provides a unified framework for treating control problems arising in nonlinear chemical processes; this is illustrated by a batch reactor control example.

/pdf/nonlinear-state-feedback-synthesis-by-global-input-output-5bh6jgtd7h.pdf

Nonlinear state feedback synthesis by global input/output linearization

Identification of spatially varying parameters in distributed parameter systems from noisy data is an ill-posed problem. The concept of regularization, widely used in solving linear Fredholm integral equations, is developed for the identification of parameters in distributed parameter systems. A general regularization identification theory is first presented and then applied to the identification of parabolic systems. The performance of the regularization identification method is evaluated by numerical experiments on the identification of a spatially varying diffusivity in the diffusion equation.

/pdf/identification-of-parameters-in-distributed-parameter-56wnj3078r.pdf

Identification of Parameters in Distributed Parameter Systems by Regularization

The work proposes an approach to the nonlinear observer design problem. Based on the early ideas that influenced the development of the linear Luenberger observer theory, the proposed approach develops a nonlinear analogue. The formulation of the observer design problem is realized via a system of first-order linear singular PDEs, and a rather general set of necessary and sufficient conditions for solvability is derived by using Lyapunov's auxiliary theorem. The solution to the above system of PDEs is locally analytic and this enables the development of a series solution method, that is easily programmable with the aid of a symbolic software package. Within the proposed design framework, both full-order and reduced-order observers are studied.

We review the mathematical and systems theory background, including linear results, tools from differential geometry, nonlinear inversion, and zero dynamics. The concept of feedback linearization of nonlinear systems is introduced at the end

Costas Kravaris

Papers

Nonlinear observer design using Lyapunov's auxiliary theorem

Nonlinear state feedback synthesis by global input/output linearization

Identification of Parameters in Distributed Parameter Systems by Regularization

Nonlinear observer design using Lyapunov's auxiliary theorem

Geometric methods for nonlinear process control. 1. Background