Declan G. Bates

Clearance of Nonlinear Flight Control Laws Using Hybrid Evolutionary Optimization

The application of two evolutionary optimization methods, namely, differential evolution and genetic algorithms, to the clearance of nonlinear flight control laws for highly augmented aircraft is described. The algorithms are applied to the problem of evaluating a nonlinear handling quality clearance criterion for a simulation model of a high-performance aircraft with a delta canard configuration and a full-authority flight control law. Hybrid versions of both algorithms, incorporating local gradient-based optimization, are also developed and evaluated. Statistical comparisons of computational cost and global convergence properties reveal the benefits of hybridization for both algorithms. The differential evolution approach in particular, when appropriately augmented with local optimization methods, is shown to have significant potential for improving both the reliability and efficiency of the current industrial flight clearance process

New Tools for Computing Tight Bounds on the Real Structured Singular Value

New tools are presented for the computation of tight lower bounds on the structured singular value π, for highorder plants subject to purely real parametric uncertainty. The e rst approach uses the π-sensitivity function to systematically reduce the order of the real uncertainty matrix, so that exponential time lower bound algorithms can be applied. The second approach formulates the search for a worst-case real destabilizing perturbation as a constrained nonlinearoptimization problem.Both approachesareapplied to theproblem ofanalyzing thestability robustness properties of an integrated e ight and propulsion control system for an experimental vertical/short takeoff and landing aircraft cone guration. Currently available software tools for calculating lower bounds on real π fail for this problem, whereas both new approaches deliver tight bounds over the frequency range of interest.

Feedback control in systems biology

Introduction What is feedback control? Feedback control in biological systems Application of control theory to biological systems: a historical perspective References Linear systems Introduction State-space models Linear time-invariant systems and the frequency response Fourier analysis Transfer functions and the Laplace transform Stability Change of state variables and canonical representations Characterising system dynamics in the time domain Characterising system dynamics in the frequency domain Block diagram representations of interconnected systems Case Study I: Characterising the frequency dependence of osmo-adaptation in Saccharomyces cerevisiae Case Study II: Characterising the dynamics of the Dictyostelium external signal receptor network References Nonlinear systems Introduction Equilibrium points Linearisation around equilibrium points Stability and regions of attractions Optimisation methods for nonlinear systems Case study III: Stability analysis of tumor dormancy equilibrium Case study IV: Global optimisation of a model of the tryptophan control system against multiple experiment data References Negative feedback systems Introduction Stability of negative feedback systems Performance of negative feedback systems Fundamental tradeoffs with negative feedback Case Study V: Analysis of stability and oscillations in the p53-Mdm2 feedback system Case Study VI: Perfect adaptation via integral feedback control in bacterial chemotaxis References Positive feedback systems Introduction Bifurcations, bistability and limit cycles Monotone systems Chemical reaction network theory Case Study VII: Positive feedback leads to multistability, bifurcations and hysteresis in a MAPK cascade Case Study VIII: Coupled positive and negative feedback loops in the yeast galactose pathway References Model validation using robustness analysis Introduction Robustness analysis tools for model validation New robustness analysis tools for biological systems Case Study IX: Validating models of cAMP oscillations in aggregating Dictyostelium cells Case Study X: Validating models of the p53-Mdm2 System References Reverse engineering biomolecular networks Introduction Inferring network interactions using linear models Least squares Exploiting prior knowledge Dealing with measurement noise Exploiting time-varying models Case Study XI: Inferring regulatory interactions in the innate immune system from noisy measurements Case Study XII: Reverse engineering a cell cycle regulatory subnetwork of Saccharomyces cerevisiae from experimental microarray data References Stochastic effects in biological control systems Introduction Stochastic modelling and simulation A framework for analysing the effect of stochastic noise on stability Case Study XIII: Stochastic effects on the stability of cAMP oscillations in aggregating Dictyostelium cells Case Study XIV: Stochastic effects on the robustness of cAMP oscillations in aggregating Dictyostelium cells References Index

Design and Piloted Simulation of a Robust Integrated Flight and Propulsion Controller

A robust integrated e ight and propulsion controller is designed for an experimental short takeoff and vertical landing aircraftcone guration,using themethod of 1 loop-shaping. Theaircraftmodelused in thestudy isbased on the Harrier airframe with the Pegasus engine replaced by a thermodynamic simulation of a Rolls-Royce Spey power plant, to allow the incorporation of advanced engine control concepts. The controller follows a two-inceptor strategy to command e ight-path angle rate and velocity along the e ight path, whilesimultaneously keeping several airframeandenginevariableswithinspecie edsafetylimits.Thecentralizedintegratede ightandpropulsioncontrol system is evaluated in piloted simulation trials. Results indicate that level 1 or 2 e ying qualities are achieved over the low-speed powered lift region of the e ight envelope.

Elucidating the mechanisms of cooperative calcium-calmodulin interactions: a structural systems biology approach

BackgroundCalmodulin is an important multifunctional molecule that regulates the activities of a large number of proteins in the cell. Calcium binding induces conformational transitions in calmodulin that make it specifically active to particular target proteins. The precise mechanisms underlying calcium binding to calmodulin are still, however, quite poorly understood.ResultsIn this study, we adopt a structural systems biology approach and develop a mathematical model to investigate various types of cooperative calcium-calmodulin interactions. We compare the predictions of our analysis with physiological dose-response curves taken from the literature, in order to provide a quantitative comparison of the effects of different mechanisms of cooperativity on calcium-calmodulin interactions. The results of our analysis reduce the gap between current understanding of intracellular calmodulin function at the structural level and physiological calcium-dependent calmodulin target activation experiments.ConclusionOur model predicts that the specificity and selectivity of CaM target regulation is likely to be due to the following factors: variations in the target-specific Ca2+ dissociation and cooperatively effected dissociation constants, and variations in the number of Ca2+ ions required to bind CaM for target activation.

Stochastic Noise and Synchronisation during Dictyostelium Aggregation Make cAMP Oscillations Robust

Stable and robust oscillations in the concentration of adenosine 3′, 5′-cyclic monophosphate (cAMP) are observed during the aggregation phase of starvation-induced development in Dictyostelium discoideum. In this paper we use mathematical modelling together with ideas from robust control theory to identify two factors which appear to make crucial contributions to ensuring the robustness of these oscillations. Firstly, we show that stochastic fluctuations in the molecular interactions play an important role in preserving stable oscillations in the face of variations in the kinetics of the intracellular network. Secondly, we show that synchronisation of the aggregating cells through the diffusion of extracellular cAMP is a key factor in ensuring robustness of the oscillatory waves of cAMP observed in Dictyostelium cell cultures to cell-to-cell variations. A striking and quite general implication of the results is that the robustness analysis of models of oscillating biomolecular networks (circadian clocks, Ca2+ oscillations, etc.) can only be done reliably by using stochastic simulations, even in the case where molecular concentrations are very high.

Least-squares methods for identifying biochemical regulatory networks from noisy measurements

BackgroundWe consider the problem of identifying the dynamic interactions in biochemical networks from noisy experimental data. Typically, approaches for solving this problem make use of an estimation algorithm such as the well-known linear Least-Squares (LS) estimation technique. We demonstrate that when time-series measurements are corrupted by white noise and/or drift noise, more accurate and reliable identification of network interactions can be achieved by employing an estimation algorithm known as Constrained Total Least Squares (CTLS). The Total Least Squares (TLS) technique is a generalised least squares method to solve an overdetermined set of equations whose coefficients are noisy. The CTLS is a natural extension of TLS to the case where the noise components of the coefficients are correlated, as is usually the case with time-series measurements of concentrations and expression profiles in gene networks.ResultsThe superior performance of the CTLS method in identifying network interactions is demonstrated on three examples: a genetic network containing four genes, a network describing p53 activity and mdm2 messenger RNA interactions, and a recently proposed kinetic model for interleukin (IL)-6 and (IL)-12b messenger RNA expression as a function of ATF3 and NF-κ B promoter binding. For the first example, the CTLS significantly reduces the errors in the estimation of the Jacobian for the gene network. For the second, the CTLS reduces the errors from the measurements that are corrupted by white noise and the effect of neglected kinetics. For the third, it allows the correct identification, from noisy data, of the negative regulation of (IL)-6 and (IL)-12b by ATF3.ConclusionThe significant improvements in performance demonstrated by the CTLS method under the wide range of conditions tested here, including different levels and types of measurement noise and different numbers of data points, suggests that its application will enable more accurate and reliable identification and modelling of biochemical networks.

Nonlinear robust performance analysis using complex-step gradient approximation

In this paper, the complex-step method is applied in the setting of numerical optimisation problems involving dynamical systems modelled as nonlinear differential equations. The main advantage of the complex-step method for gradient approximation is that it entails no subtractive cancellation error, and therefore the truncation error can be made arbitrarily (to machine precision) small. The method is applied to two robust performance analysis problems. The accuracy and convergence rate of the solutions computed using the proposed approach are seen to be significantly better than those achieved using standard gradient approximation methods.

Validation and invalidation of systems biology models using robustness analysis

Robustness, the ability of a system to function correctly in the presence of both internal and external uncertainty, has emerged as a key organising principle in many biological systems. Biological robustness has thus become a major focus of research in Systems Biology, particularly on the engineering-biology interface, since the concept of robustness was first rigorously defined in the context of engineering control systems. This review focuses on one particularly important aspect of robustness in Systems Biology, that is, the use of robustness analysis methods for the validation or invalidation of models of biological systems. With the explosive growth in quantitative modelling brought about by Systems Biology, the problem of validating, invalidating and discriminating between competing models of a biological system has become an increasingly important one. In this review, the authors provide a comprehensive overview of the tools and methods that are available for this task, and illustrate the wide range of biological systems to which this approach has been successfully applied.

Anti-windup synthesis for nonlinear dynamic inversion controllers

Abstract An anti-windup compensation method is proposed for a class of constrained nonlinear systems which, in the absence of saturation, are controlled by certain types of nonlinear dynamic inversion controllers. The anti-windup compensation scheme shares a similar architecture to that proposed by the authors in prior work for linear systems subject to saturation constraints. An encouraging aspect of the proposed scheme is that for globally exponentially stable systems, a particularly simple choice of anti-windup compensator exists and, moreover, this could be regarded as a “nonlinear„ internal model control based anti-windup compensator. More generally, a framework for synthesising optimal anti-windup compensators is suggested, based on nonlinear partial differential matrix inequalities. Finally, a simple example illustrates the effectiveness of the scheme.