Theory and applications of fuzzy Volterra integral equations

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations. The investigation is restricted to Volterra type equations with mildly restrictive conditions, but the methods are capable of extensive generalization to other types and more general assumptions. The results are illustrated by integral equations relating to control models with fuzzy uncertainties.

Control of chaotic motion in a dual-spin spacecraft with nutational damping

Control of chaotic vibrations in a dual-spin spacecraft with an axial nutational damper is achieved using two techniques. The control methods are implemented on two realistic spacecraft parameter configurations that have been found to exhibit chaotic instability when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitudes and frequencies. Such a torque, in practice, may arise under malfunction of the control system or from an unbalanced rotor. Chaotic instabilities arising from these torques could introduce uncertainties and irregularities into a spacecraft's attitude motion and, consequently, could have disastrous effects on its operation. The two control methods, recursive proportional feedback and continuous delayed feedback, are recently developed techniques for control of chaotic motion in dynamic systems. Each technique is outlined and the effectiveness on this model compared and contrasted. Numerical simulations are performed, and the results are studied by means of time history, phase space, Poincare map, Lyapunov characteristic exponents, and bifurcation diagrams.

Review and future directions in the modelling and control of continuous drum granulation

Many granulation plants operate well below design capacity, suffering from high recycle rates and even periodic instabilities. This behaviour cannot be fully predicted using the present models. The main objective of the paper is to provide an overview of the current status of model development for granulation processes and suggest future directions for research and development. The end-use of the models is focused on the optimal design and control of granulation plants using the improved predictions of process dynamics. The development of novel models involving mechanistically based structural switching methods is proposed in the paper. A number of guidelines are proposed for the selection of control relevant model structures. (C) 2002 Published by Elsevier Science B.V.

Evaluating plant breeding strategies by simulating gene action and dryland environment effects

Functional genomics is the systematic study of genome-wide effects of gene expression on organism growth and development with the ultimate aim of understanding how networks of genes influence traits. Here, we use a dynamic biophysical cropping systems model (APSIM-Sorg) to generate a state space of genotype performance based on 15 genes controlling four adaptive traits and then search this spice using a quantitative genetics model of a plant breeding program (QU-GENE) to simulate recurrent selection. Complex epistatic and gene X environment effects were generated for yield even though gene action at the trait level had been defined as simple additive effects. Given alternative breeding strategies that restricted either the cultivar maturity type or the drought environment type, the positive (+) alleles for 15 genes associated with the four adaptive traits were accumulated at different rates over cycles of selection. While early maturing genotypes were favored in the Severe-Terminal drought environment type, late genotypes were favored in the Mild-Terminal and Midseason drought environment types. In the Severe-Terminal environment, there was an interaction of the stay-green (SG) trait with other traits: Selection for + alleles of the SG genes was delayed until + alleles for genes associated with the transpiration efficiency and osmotic adjustment traits had been fixed. Given limitations in our current understanding of trait interaction and genetic control, the results are not conclusive. However, they demonstrate how the per se complexity of gene X gene X environment interactions will challenge the application of genomics and marker-assisted selection in crop improvement for dryland adaptation.

Prediction of multilayer adsorption and capillary condensation phenomena in cylindrical mesopores

MCM-41 periodic mesoporous silicates with a high degree of structural ordering are synthesized and used as model adsorbents to study the isotherm prediction of nitrogen adsorption. The nitrogen adsorption isotherm at 77 K for a macroporous silica is measured and used in high-resolution alpha(s)-plot comparative analysis to determine the external surface area, total surface area and primary mesopore volume of the MCM-41 materials. Adsorption equilibrium data of nitrogen on the different pore size MCM-41 samples (pore diameters from 2.40 to 4.92 nm) are also obtained. Based on the Broekhoff and de Boer' thermodynamic analysis, the nitrogen adsorption isotherms for the different pore size MCM-41 samples are interpreted using a novel strategy, in which the parameters of an empirical expression, used to represent the potential of interaction between the adsorbate and adsorbent, are obtained by fitting only the multilayer region prior to capillary condensation for C-16 MCM-41. Subsequently the entire isotherm, including the phase transition, is predicted for all the different pore size MCM-41 samples without any fitting. The results show that the prediction of multilayer adsorption and total adsorbed amount are in good agreement with the experimental isotherms. The predictions of the relative pressure corresponding to capillary equilibrium (coexistence) transition agree remarkably with experimental data on the adsorption branch even for hysteretic isotherms, confirming that this is the branch appropriate for pore size distribution analysis. The impact of pore radius on the adsorption film thickness and capillary coexistence pressure is also investigated, and found to agree with the experimental data. (C) 2003 Elsevier Inc. All rights reserved.

Robust multivariable control of complex biological processes

This paper addresses advanced control of a biological nutrient removal (BNR) activated sludge process. Based on a previously validated distributed parameter model of the BNR activated sludge process, we present robust multivariable controller designs for the process, involving loop shaping of plant model, robust stability and performance analyses. Results from three design case studies showed that a multivariable controller with stability margins of 0.163, 0.492 and 1.062 measured by the normalised coprime factor, multiplicative and additive uncertainties respectively give the best results for meeting performance robustness specifications. The controller robustly stabilises effluent nutrients in the presence of uncertainties with the behaviour of phosphorus accumulating organisms as well as to effectively attenuate major disturbances introduced as step changes. This study also shows that, performance of the multivariable robust controller is superior to multi-loops SISO PI controllers for regulating the BNR activated sludge process in terms of robust stability and performance and controlling the process using inlet feed flowrate is infeasible. (C) 2003 Elsevier Ltd. All rights reserved.

Trait physiology and crop modelling as a framework to link phenotypic complexity to underlying genetic systems

New tools derived from advances in molecular biology have not been widely adopted in plant breeding for complex traits because of the inability to connect information at gene level to the phenotype in a manner that is useful for selection. In this study, we explored whether physiological dissection and integrative modelling of complex traits could link phenotype complexity to underlying genetic systems in a way that enhanced the power of molecular breeding strategies. A crop and breeding system simulation study on sorghum, which involved variation in 4 key adaptive traits-phenology, osmotic adjustment, transpiration efficiency, stay-green-and a broad range of production environments in north-eastern Australia, was used. The full matrix of simulated phenotypes, which consisted of 547 location-season combinations and 4235 genotypic expression states, was analysed for genetic and environmental effects. The analysis was conducted in stages assuming gradually increased understanding of gene-to-phenotype relationships, which would arise from physiological dissection and modelling. It was found that environmental characterisation and physiological knowledge helped to explain and unravel gene and environment context dependencies in the data. Based on the analyses of gene effects, a range of marker-assisted selection breeding strategies was simulated. It was shown that the inclusion of knowledge resulting from trait physiology and modelling generated an enhanced rate of yield advance over cycles of selection. This occurred because the knowledge associated with component trait physiology and extrapolation to the target population of environments by modelling removed confounding effects associated with environment and gene context dependencies for the markers used. Developing and implementing this gene-to-phenotype capability in crop improvement requires enhanced attention to phenotyping, ecophysiological modelling, and validation studies to test the stability of candidate genetic regions.

Identification of MIMO Hammerstein systems using cardinal spline functions

A new approach to identify multivariable Hammerstein systems is proposed in this paper. By using cardinal cubic spline functions to model the static nonlinearities, the proposed method is effective in modelling processes with hard and/or coupled nonlinearities. With an appropriate transformation, the nonlinear models are parameterized such that the nonlinear identification problem is converted into a linear one. The persistently exciting condition for the transformed input is derived to ensure the estimates are consistent with the true system. A simulation study is performed to demonstrate the effectiveness of the proposed method compared with the existing approaches based on polynomials. (C) 2006 Elsevier Ltd. All rights reserved.

Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, sub-Riemannian, and Finslerian manifolds. These results generalize the results of [Nielsen, Dowling, Gu, and Doherty, Science 311, 1133 (2006)], which showed that the gate complexity can be related to distances on a Riemannian manifold.

The role of software tools in influencing creative problem solving in engineering design and education

Creativity is increasingly recognised as an essential component of engineering design. This paper describes an exploratory study into the nature and importance of creativity in engineering design problem solving in relation to the possible impact of software design tools. The first stage of the study involved an empirical investigation in the form of a case study of the use of standard CAD tool sets and the development of a systems engineering software support tool. It was found that there were several ways in which CAD influenced the creative process, including enhancing visualisation and communication, premature fixation, circumscribed thinking and bounded ideation. The tool development experience uncovered the difficulty in supporting creative processes from the developer's perspective. The issues were the necessity of making assumptions, achieving a balance between structure and flexibility, and the pitfalls of satisfying user wants and needs. The second part of the study involved the development of a model of the creative problem solving process in engineering design. This provided a possible explanation for why purpose designed engineering software tools might encourage an analytical problem solving approach and discourage a more creative approach.