Practical solutions to multivariate feedback control performance assessment problem: reduced a priori knowledge of interactor matrices

Abstract The research on control loop performance monitoring and diagnostics has been and remains to be one of the most active research areas in process control community. Despite of numerous developments, it remains as a considerably challenging problem to obtain a minimum variance control benchmark from routine operating data for multivariable process since the solution relies on the interactor matrix (or inverse time delay matrix). Knowing the interactor matrix is tantamount to knowing a complete knowledge of process models that are either not available or not accurate enough for a meaningful calculation of the benchmark. However, the order of an interactor matrix (OIM) for a multivariable process, a scalar measure of multivariate time delay, is a relatively simple parameter to know or estimate a priori. This paper investigates the possibility to estimate a suboptimal multivariate control benchmark from routine operating data if the OIM is available. The relation between this suboptimal benchmark and the true multivariate minimum variance control benchmark is investigated. Analytical expressions for the lower and upper bounds of the true multivariate minimum variance are derived. Although not minimum variance control, this benchmark answers important practical questions like ''at least how much potential of the improvement does the control have by tuning or redesigning?'' It is further shown that the proposed suboptimal benchmark is achievable by a practical control provided that the system of interest is minimum phase. Simulation examples illustrate the feasibility of the proposed approach

Investigation of the nonlocal coherent-potential approximation

Recently the nonlocal coherent-potential approximation (NLCPA) has been introduced by Jarrell and Krishnamurthy for describing the electronic structure of substitutionally disordered systems. The NLCPA provides systematic corrections to the widely used coherent-potential approximation (CPA) whilst preserving the full symmetry of the underlying lattice. Here an analytical and systematic numerical study of the NLCPA is presented for a one-dimensional tight-binding model Hamiltonian, and comparisons with the embedded cluster method (ECM) and molecular coherent potential approximation (MCPA) are made.Comment: 18 pages, 5 figure

Utterance Selection Model of Language Change

We present a mathematical formulation of a theory of language change. The theory is evolutionary in nature and has close analogies with theories of population genetics. The mathematical structure we construct similarly has correspondences with the Fisher-Wright model of population genetics, but there are significant differences. The continuous time formulation of the model is expressed in terms of a Fokker-Planck equation. This equation is exactly soluble in the case of a single speaker and can be investigated analytically in the case of multiple speakers who communicate equally with all other speakers and give their utterances equal weight. Whilst the stationary properties of this system have much in common with the single-speaker case, time-dependent properties are richer. In the particular case where linguistic forms can become extinct, we find that the presence of many speakers causes a two-stage relaxation, the first being a common marginal distribution that persists for a long time as a consequence of ultimate extinction being due to rare fluctuations.Comment: 21 pages, 17 figure

Combining formal methods and functional strategies regarding the reverse engineering of interactive applications

Graphical user interfaces (GUIs) make software easy to use by providing the user with visual controls. Therefore, correctness of GUI’s code is essential to the correct execution of the overall software. Models can help in the evaluation of interactive applications by allowing designers to concentrate on its more important aspects. This paper describes our approach to reverse engineer an abstract model of a user interface directly from the GUI’s legacy code. We also present results from a case study. These results are encouraging and give evidence that the goal of reverse engineering user interfaces can be met with more work on this technique.Fundação para a Ciência e a Tecnologia (FCT) Fundo Europeu de Desenvolvimento Regional (FEDER

Finite-time behavior of inner systems

In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer function. The relation between nonminimum phase zeros and Hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance. The results are used to solve various tracking problems both on finite as well as on infinite time horizons. A typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller

The Korringa-Kohn-Rostoker nonlocal coherent-potential approximation : a new method for calculating the electronic structure of disordered metallic systems

The limitations of the current 'first-principles' effective medium approach to calculating the electronic structure of disordered systems are described. These limitations can be addressed by a cluster theory, and only very recently the first satisfactory cluster theory, the nonlocal coherent potential approximation, has been developed within a tight-binding framework. However an approach based on KKR multiple scattering is needed in order to treat the problem from first principles for ab-initio calculations. In this thesis, these ideas are reformulated in terms of multiple scattering theory and the Korringa-Kohn-Rostoker non-local coherent potential approximation (KKR-NLCPA) is introduced for describing the electronic structure of disordered systems. The KKR-NLCPA systematically provides a hierarchy of improvements upon the widely used local mean-field KKR-CPA approach and includes nonlocal correlations in the disorder configurations by means of a self-consistently embedded cluster. The KKR-NLCPA method satisfies all of the requirements for a successful cluster generalisation of the KKR-CPA; it determines a site-to-site translationally-invariant effective medium, it is herglotz analytic, becomes exact in the limit of large cluster sizes, reduces to the KKR-CPA for a single-site cluster, is straightforward to implement numerically, and enables the effects of short-range order upon the electronic structure to be investigated. In particular, it is suitable for combination with electronic density functional theory to give an ab-initio description of disordered systems. Future applications to charge correlation and lattice displacement effects in alloys and spin fluctuations in magnets amongst others are very promising. The method is illustrated by application to a simple one-dimensional model