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Control Seminars and Reading Group | |
The group runs a reading group. Unless otherwise stated we meet in the seminar room (2025) of Building 1.External speakers in systems and control also speak in the ISIS seminar series.We belong to the Bath-Exeter-London-Southampton seminar series: a series of mini-workshops on control theory, run at the participating institutions.
Control Seminar Series ~ 2010/11The next Control Seminar will be:
Future talks are scheduled for:
There are no future talks scheduled for this term. If you wish to give a seminar then please contact alg@ecs.soton.ac.uk
20112010/11 ~ Talks presented todate:
Abstract: The talk will describe the development of a multivariable input, multivariable output (MIMO) experimental test facility, which will be used to evaluate, benchmark and compare advanced control strategies. The MIMO system incorporates two differential gears connected back-to-back, together with a number of spring-mass-damper modules. The system can be driven by two AC induction motors with inverter drives, and also a DC brushed motor and a four-quadrant drive. It incorporates two encoders, and a torque tube mounted on the central shaft. In the standard configuration, the system has two inputs, two outputs, and an additional disturbance injection input. However, the platform has also been designed to be multi-configurable, allowing the number of inputs and outputs to be varied in order to expand the scope of the system. The test facility will be used to evaluate a significant number of Iterative Learning Control (ILC) schemes performing reference tracking tasks, and results will be compared with other control methods such as adaptive control, repetitive control and classical ILC methods.
Abstract: Loss of motor functions due to stroke has left many patients reliant on others for daily activities. Stroke rehabilitation aims to help the patients to regain their motor skills. Our system combines two types of rehabilitation techniques – functional electrical stimulation (FES) and a passive therapeutic robot, to create an suitable and interactive environment for upper limb stroke rehabilitation. The robot will provide support and measurements whilst FES is used to assist in precise movements of the upper arm. Electrical stimulation is applied to two muscles in the arm; electrical stimulation level is precisely controlled by ILC and feedback controller. An overview of the system and results from recent clinical trial will be looked at.
ABSTRACT: Controlling a bicycle poses a challenging problem as a non-linear and under actuated system with nonholonomic contact constraint [1]. Designing controller for such a system requires rigorous mathematical manipulation. Often linear approximations are used for deriving the best controllers. In this process important nonlinear constraints might be left out and the system might end up behaving unpredictably in real world. Reinforcement Learning is a machine learning algorithm that closely mimics human cognition with a trial and error basis. It is a combination of supervised and unsupervised learning which promises to provide viable controllers that could control nonlinear systems efficiently once the task has been learnt. This also provides high adaptability even to physical changes i.e.; deformity over time in the system itself. As a summer project we critically analysed controlling a bicycle using Reinforcement Learning [2], where main intent was to observe the effectiveness of the algorithm (SARSA - λ) and devise possible improvements. Other objectives of the project incorporated providing visual presentation (3D online animation) of the system as the agent learns to ride and also make it available online.
References: 1. Getz, N. H. and Marsden J. E., 1995. Control for an Autonomous Bicycle. In: IEEE (Institute of Electrical and Electronic Engineers), International Conference on Robotics and Automation. Nagoya, Japan, 21-27 May 1995. 2. Randløv, J., Alstrøm, P. (1998) Learning to ride a bicycle using reinforcement learning and shaping, Proceedings of the Fifteenth International Conference on Machine Learning, ISBN: 1-55860-556-8, 1998, pp. 463-471.
Abstract: In this talk, identification of electrically stimulated muscle, especially the impaired arm after stroke is discussed. Hammerstein structure is chosen to model the nonlinear dynamics of the electrically stimulated muscle under isometric conditions. Batch identification algorithms, a two-stage algorithm and the later two iterative algorithms, will be discussed firstly. Considering the slowly time- varying properties of the muscle system, a novel recursive identification algorithm is developed and compared with the leading technique. Finally, the identified muscle models have been used in FES control schemes for electrically stimulated muscle under isometric conditions. Besides the two nonlinear ILC approaches, several trial-dependent and adaptive control schemes has been designed and implemented.
Abstract: In this talk we present a new sufficient condition for the stability of switched positive linear systems. This condition is general in two senses. First of all, because it applies to switching systems of order n composed of k subsystems, for any n and k. Secondly, because it applies to both discrete- and continuous-time systems. Furthermore, it is easy to verify, as it amounts to check for the stability of a certain matrix. The new condition is derived from a multidimensional system analysis, where the relation between the stability of multidimensional and switched systems is investigated. A comparison with other existing tests is also presented, showing that the one proposed here allows to infer about the stability of a system in cases where other tests fail or do not apply at all. ABSTRACT: I will present work in progress (stalled since 2007) on using signal processing and system identification for speeding up slow measurement devices. The motivation comes from the following problem (page 53, Luenberger 1979): A thermometer reading 21C, which has been inside a house for a long time, is taken outside. After one minute the thermometer reads 15C; after two minutes it reads 11C. What is the outside temperature? (According to Newton's law of cooling, an object of higher temperature than its environment cools at a rate that is proportional to the difference in temperature.) Please spend at least 15 minutes trying to solve the problem. In the talk, I will discuss the following extension: Given output observations {y(1), …, y(T)} of an LTI system with unit DC-gain, generated by a step input (but not necessarily zero initial conditions), find the input step value.
Thursday 20 January, 16:00: Fitting algebraic curves to data. Dr Ivan Markovsky. (ISIS) ABSTRACT: An algebraic curve is a solution set of a system of polynomial equations with dimension one. Conic sections, for example, are algebraic curves in a two dimensional space, obtained as a solution set of a second order polynomial equation. Fitting of conic section and more specifically ellipses to data has long history. The methods can be classified as geometric and algebraic, depending on the fitting criterion. In this talk, we show that geometric fitting of conic sections is equivalent to a second order nonlinearly structured low-rank approximation and algebraic fitting can be viewed as a relaxation of the nonlinarly structured problem to a linear one. More generally, algebraic curve fitting to data is a polynomially structured low-rank approximation.
ABSTRACT: Iterative learning control is concerned with tracking a reference trajectory defined over a finite time duration, and is applied to systems which perform this action repeatedly. This technique has proved successful in our rehabilitation work, but extra flexibility is needed to control functional tasks which are clinically relevant. In this talk iterative learning schemes are developed to address the case in which the output is not critical at every time instant. It is shown that removing the necessity to track all points increases the set of feasible inputs. This freedom makes it possible to incorporate both hard and soft constraints into the control scheme. Experimental results using a robotic arm confirm practically and performance. ABSTRACT: Given a 'sufficiently informative' trajectory of an LTI system dissipative with respect to a given supply rate, the problem I aim at solving is to identify how the system exchanges energy with the external world; i.e. I am at identifying a dissipation function (and consequently a storage function) for the system. This problem is a generalization of a typical one in mechanical engineering, that of 'identification of damping coefficients'. ABSTRACT: In this talk I will give an overview of recent research which utilizes modern tools from nonlinear robust stability to approach the longstanding problem of robustness in adaptive control theory. The talk will be illustrated with examples of both classical `smooth' adaptive controllers and those from the multiple model approach. January 23: Bath-Exeter-London-Southampton seminar Building 1, room 2025. 11:30 Mark Opmeer (Bath) "Control of beams" 13:30 -- 14:30 Richard Vinter (Imperial College) "Regularity of Minimizers in Dynamic Optimization" Abstract: For a number of reasons it is useful to obtain information about the regularity of minimizers (Lipschitz continuity, differentiability etc.), before optimality conditions are derived or numerical solution of the dynamic optimization problem concerned is attempted. Certain optimality conditions which we might want to use are valid only under regularity hypotheses on the minimizers, and these must be confirmed a priori. Also, regularity of solutions might influence whether a given numerical scheme will give convergence to a minimizer with respect to the relevant domain, and effect the rate of convergence. In addition, minimizer regularity is an important property in its own right, in continuum mechanics based on variational ormulations, where, say, the occurrence of unbounded derivatives is interpreted as material failure. Some important regularity theorems, relating to problems in the calculus of variations in one independent variable and to optimal control problems (collectively referred to as 'dynamic optimization' problems), will be reviewed. These will centre on the property of Tonelli regularity, namely the situation in which minimizers are highly regular on an open subset of full measure, and on how investigating Tonelli regularity can lead to additional, stronger, regularity properties of greater practical interest. 14:30 -- 15:30 Dominic Buchstaller (Southampton) "Adaptive Control by switching strategies: robustness and performance" January 15, 15.30: Unfalsified control of linear time-invariant systems, Ivan Markovsky (ISIS) Abstract: Observers play a seminal role in the development of system theory. An observer is an algorithm that estimates an unobserved output of a dynamical system on the basis of an observed output. Classically, this problem has been formulated in the setting of stochastic processes, by assuming that there is a known statistical dependence between the observed and to-be-estimated variables. The Wiener filter and the Kalman filter are importantalgorithms that function in this stochastic setting. Later, deterministic observerswere studied based on state space models. In this talk, we first sketch the historical developments of filter and observer theory. Subsequently, we formulate the observer question in the context of dynamical systems with behavior represented in terms of high- order differential or difference equations. The use of this system representation leads to novel algorithms in which the observer parameters are deduced from equations in terms of the polynomial matrices that enter the system representation. Abstract: SotonAUV is a multidisciplinary project spanning multiple research themes including machine learning, control, signal and image processing, circuit design as well as underwater hydrodynamics, mechanical design and propulsion. The aim of the project is to design and build an Autonomous Underwater Vehicle (AUV), as part of the University of Southampton's entry into the Student Autonomous Underwater Challenge. Specifically, for the 2007 competition the autonomy and control of the vehicle was identified as a key area for development. Our control module is formed by an ensemble of software agents (SAs), each of which is responsible for a different aspect of the AUV's autonomous behaviour. The set of sensors employed by the control module consists of a pressure sensor, a 3-axis magnetometer,an inertial measurement unit and 3 cameras. The navigation capability of SotonAUV relies largely on the Simultaneous Localisation and Mapping (SLAM) accomplished through the real-time processing of the visual imaging of the tank/sea floor. Building on the success in the SAUC-E 2007 competition, in 2008 we are planning to further extend and improve the autonomy of our vehicle by implementing, for instance, Bayesian inference-based sensor fusion, as well as Occupancy Grid 3-D SLAM based on imagery from multiple fish-eye-lens-equipped cameras. Abstract: STP is an old problem in the literature. R.E. Kalman proposed the solution for the same by proposing the structure of the control as function of state Transition matrix and the control weightage matrix B. We propose a solution without requiring to compute the STM.It has been treated as a simple interpolation problem. Abstract: A major collaborativeresearch programme between the Schools of Health Professions and Rehabilitation Sciences and Electronics and Computer Science (ISIS group) is investigating the use of iterative learning control in the rehabilitation of stroke victims who have a marked impairment in the function of onearm. Progress to-date has resulted in an experimental facility which is currently undergoing tests with volunteers (recruited, in the main, after a short feature article on BBC South Today). This seminar will focus on how to model the response of the upper limb and then proceed to explain how iterative learning control laws can be designed. Finally, planned future work will be briefly discussed. Abstract: This research addresses the problem of computing optimal structured treatment interruption strategies (STI) for HIV infected patients. STI represent a class of treatments in which patients are cycled on and off drug therapy at specific time instants. The problem that we consider consists in designing efficient drug-scheduling strategies, i.e. strategies which bring the immune system into a state that allows it to independently (without help from any drug) maintain immune control over the virus. Also, this transfer to a drug-independent viral control situation should be done with as low as possible drug-related systemic effects for the patients. In this presentation, we show that reinforcement learning maybe useful toextract (close-to) optimal STI strategies directly from clinical data, without the need of identifying a mathematical model of HIV infection dynamics. To support our claims, we report simulation results obtained by running a recently proposed batch-mode reinforcement learning algorithm, known as fitted Q iteration, on numerically generated data. The corresponding paper can be found here. Abstract: This seminar will examine the notion of long term robust stability and performance of iterative learning control systems in terms of the standard H2 gap metric. The subject of ILC will be briefly reviewed and some of the problems associated with ILC controllers described; in particular the issue of long-term stability. The gap metric will be explained and then applied to an ILC system to prove the existence of a non-zero stability margin. This will then be further developed to provide some measure of performance. The possibilitiesfor further work in this area will also be outlined. Abstract: In this talk I will give an introductory overview over sparse signal models, discuss some of their theoretic properties, introduce some algorithmic strategy to solve the sparse signal approximation problem and demonstrate the applicability of sparse signal modelling to a range of problems in signal processing. The talk will focus in particular on the emerging technique of compressed sensing. Compressed sensing is a signal acquisition technique that allows signals to be sampled well below the Nyquist rate, provided that the signal admits a sparse representation. Abstract: As active control technologies reach their performance limits in large scale systems, many investigators have looked toward decentralized control as a means of expanding the application horizons. Decentralized control is defined here as numerous independent controllers operating on a single system. These decentralized approaches have been shown to be effective, but not as effective as traditional centralized control. In an effort to achievecontrol performance approaching centralized control while maintaining the scalability benefits of decentralized control, the use of distributed control is considered. Distributed control consists of numerous independent control processors that are capable of communicating, and therefore cooperating, with each other. This talk will cover the basics of decentralized and distributed control, recent results in their application, and a comparison of their performance. Time permitting, recent advances in Fault Tolerant Control applied to vibro-acoustic systems will also be summarized. These systems are capable of detecting system failures and reconfiguring in order to maintain performance and stability. Abstract: Palindromic polynomials have symmetric coefficients with respect to the middle coefficient. The roots of the palindromic polynomials obeyaspecial pattern: they appear in pairs (r,1/r). Not all polynomials with such a root pattern, however, are palindromic. Polynomials whose root can be grouped into pairs (r,1/r) and have a root at +1 of an odd multiplicity are antipalindromic, i.e., their first coefficient is equal to the negative of the last one etc. In the first part of the talk, we state three corollaries of our main result about the root location of (anti)palindromic polynomials. The second part of the talk is devoted to the class of discrete-time, time-reversible systems, i.e., systems which trajectories are accompanied by their time-reversed trajectories. It turns out that any kernel representation of a scalar autonomous systems is either palindromic or antipalindromic. Similar result holds for single-input, single-output systems. In the multivariable case the statement should be relaxed to "there exists a palindromic or antipalindromic kernel representation". Abstract: This talk is concerned with the application of quadratic differential forms (QDF's) to robust stability analysis of a linear system with parametric uncertainty. The QDF plays an important role in the Lyapunov stability theory in the behavioral framework. By using QDF's, wederive an LMI condition for robust stability of a linear uncertain system described by a high-order differential-algebraic equation. This condition guarantees the existence of a parameter-dependent Lyapunov function whichallows less conservative analysis. We also show that, when applied to a state-space model, the present condition recovers some existing robust stability conditions. Abstract: Simulated annealing is a popular method for approachingthe solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. In this talk I will introduce new results which allow one to guarantee finite-time performance of simulated annealing in the optimization of functions of continuousvariables. I will first recall a result of Vidyasagar which introduced rigorous finite-time guarantees for the optimization of expected-value criteria based on independent sampling of the optimization domain. Then, I will show that a similar typeof finite-time guarantees can be achieved by the more general family of simulated annealing algorithms. The results hold universally for any optimization problem on a bounded domain and establish a connection between simulated annealing and up-to-datetheory of convergence of Markov chain Monte Carlo methods on continuous domains. Abstract: In IEEE TAC 1995 40(3) pp516--518 it has been shown that there are difficulties with certain simple input-output systems when the time axis is the whole real line. Noting that behaviouraltheory is typically considered over such a time axis, were-consider these issues in detail. Abstract: Adaptive control theory has the potential to be an elegant solution to control problems where classical control theory is unable to deliver reasonable performance guarantees or even fails to deliver them at all, i.e. simultaneous stabilization and large parameter uncertainty. In this talk we restrict our view to multiple model switched adaptive control (MMSAC) algorithms where the switching decision is based on disturbance estimates corresponding to a finite plant model set. Although being still in it's infancy, the study of this class of adaptive algorithm has shown potential to solve the simultaneous stabilization problem. However it will be shown that a wide class of MMSAC algorithms, although having a finite $l_p,\ 1\le p\le \infty$ closed loop gain, have the property that the gain is unboundedly increasing for a simple set of plants under increasing parametric uncertainty. To tackle this problem a new closed loop bound is established for time varying plant model sets and a modification to the standard MMSAC algorithm is proposed which achieves a quadratic closed loop gain function which is independent of the uncertainty set thus being invariant to parameter uncertainty. Abstract: Inthis seminar, first a class of systems known as oscillatory systems will be defined as linear differential systems that are periodic. This will be followed by a discussion of the structure and properties of QDFs associated with oscillatory systems. Specifically, the structure of conserved and zero-mean QDFs associated with such systems will be discussed. The notion of generalized Lagrangians will be defined for such systems and their properties will be shown. Next, the notion of a conservative autonomoussystem will be defined as a linear autonomous system for which there exists a conservative QDF that is positive over the behavior. It will be shown that such a system is equivalent to an oscillatory system. This notion will be extended for the case of open systems, i.e the question of what it means for an open system to be conservative will be explored. In addition, an algorithm to arrive at a total energy function of a conservative system and its split into kinetic and potential energy components will be discussed. Abstract: In this talk we consider the problem of approximating a given dissipative system by a dissipative system with lower MacMillan degree. One way to approach this problem is by constructing for the given system a state representation for which the available storage and the required supply are in some sense compatible in size. Reduction thentakes place by neglecting part of the state representation that carries external trajectories along which the difference between required supply and available storageis relatively big,i.e. along which there is a relatively big dissipation of supply. In this presentation we will discuss this approximation method, and present anumber of new error bounds. Abstract: This seminar will give an update on the EPSRC funded programme with The School of Health Professions and rehabilitation Sciences. The emphasis will be on the development of models for the `plant' and, in particular, the human arm, the design of control laws and finally give some results (graphical and video) from experiments. Ravi Vaidyanathan (School of Health Professionals and Rehabilitation Sciences and Institute of Sound and Vibration Research University of Southampton) Abstract: Significant benefits in robotic performance may be achieved through a systematic approach integrating control architectures and mechanical design. Biology can provide a wealth of inspiration for robotic systems specifically in this arena. In animals, for example, intrinsic properties of the musculoskeletal system often augment neural stabilization of the organism for an array of critical of functions. Nature can thus provide a basis for robotic capabilities including: sensor integration, context dependent behavior, multi constraint incorporation, instantaneous tracking reactions, and motion control. Invertebrates, in particular, have been able to exploit a wide range of behavioral niches, because they utilize a body plan that can be readily modified to create specialized versions of individuals optimized for a particular role important for a particular niche. The talk will review basic methodologies for the enhancement of engineering design based upon biological studies of invertebrate behavior. Approaches for biological inspiration will be summarized with specific examples from contemporary research and the speaker's past work. Applications will be highlighted specifically in medical and mobile robotic systems. Abstract: In the classical approach to control, a mathematical model of the plant (in state-space, transfer function, etc. form) and a performance criterion are used in order to come up with a mathematical description of a controller to be used in achieving the control objectives. In the data-driven approach, instead, one trajectory of the plant variables is given, together with the performance criterion; the objective is to compute from this data a suitable control input signal. In this talk we concentrate on the discrete-time finite-horizon quadratic control problem with prescribed "initial conditions", given in the form of a prefix of a trajectory which needs to be extended over the whole time-interval so as to minimize the cost. We give a solution of this problem, and we illustrate some results of our data-driven investigation. Among these is an intrinsic justification of the optimality of the state-feedback control input law which is prominent in the state-space approach; we show that this fact can be established from first principles, and is not only a more-or-less direct consequence of the use of state-space representations in the classical framework to control. Wojciech Paszke (University of Zielona Gora, Institute of Control and Computation Engineering) Undergraduates Daisy Tong, Thabiso Maupong and Tebogo Mogaleemang will be giving three short talkson their current and future project work ondata-based control. 12:00 Ivan Markovsky (KU Leuven), "Data-driven simulation and control", 14:00 Malcolm Smith (Cambridge), "A behavioural approach to play in mechanical networks", 15:00 Zhenqing Ke (Bath) "Low-gain sampled-data control for a class of stable infinite-dimensionalsystems". Control Seminar Series ~ 2009/10 ABSTRACT: In the presentation we consider the problem of finding the norm bounded uncertainty of minimal volume enclosing the given set of matrices, usually very large. We focus especially on the time aspect allowing some volume redundancy. We propose the heuristic method that is based on the computation of Minimum Volume Enclosing Ellipsoid. In the method we treat norm bounded uncertainty as an ellipsoid in a vector space. In comparison to the existing method the polynomial time complexity is reduced by one degree. ABSTRACT: In this talk, the recursive identification of Hammerstein structures will be addressed. Firstly, the well-developed Recursive Least Squares (RLS) algorithm is applied to the reformulated Hammerstein structure and then Singular Value Decomposition (SVD) is employed to recover the linear and nonlinear parameters. Then a novel recursive identification algorithm is proposed, in which the linear and nonlinear parameters are recursively identified in an alternate manner. This method is termed the Alternately Recursive Least Squares (ARLS) algorithm. A numerical example is used to compare these two recursive algorithms in terms of best fit rate and error norm. Real experimental data from human muscles are also used to illustrate the superiority of ARLS over RLS. ABSTRACT: A duality theory has been shown to exist between iterative learning and repetitive control, in which both paradigms differ only in the location of an internal model of the disturbance, and controller design equates to a regularisation problem. This talk demonstrates how this theory can be applied in order to derive new controllers, and enlarges the framework to encompass a quarterion consisting of iterative learning and repetitive control designs each using both state and output feedback to solve the tracking problem. Linear quadratic solutions are formulated for all four cases, and are applied experimentally to an industrial gantry robot system. ABSTRACT: This seminar will begin by introducing the gap metric, including a brief history and motivation. Following this, a biased gap metric will be used to develop a tool for examining the robust stability of a plant-controller pair engaged in trajectory tracking. This method is applicable to a very general set of systems and is applied in a 2D setting to examine the robust stability of an iterative learning control algorithm. ABSTRACT: The National Oceanography Centre, Southampton has a long history of developing Autonomous Underwater vehicles for Marine Science. The Autosub, Autosub2, Autosub3 and Autosub6000 Autonomous Underwater Vehicle (AUV) have performed hundreds of oceanographic surveys that would be impractical or impossible using ship based instrumentation. They have had many successes and several failures, most notable the loss of Autosub2 beneath Antarctica s Fimbul Ice Shelf in February 2005.
ABSTRACT: The "Adjoint" and "Phaselead" ILC algorithms have been remarkably successful in the last few years due to their simplicity and comparative ease of analysis. Appearing in a large number of papers, they also proved extremely effective when applied in the stroke rehabilitation field, after a suitable linearizing controller was applied to make the underlying system approximately SISO. Indeed, these where algorithms used clinically with patients, and showed that our approach was working. With recent work within ISIS/EPE focussing on extending stroke rehabilitation to the case where full 3D arm movements are considered, the possibility of still being able to use simple ILC algorithms on the resulting non-linear MIMO system is extremely appealing. This presentation provides initial results that show that direct extension is possible, and high performance is possible using simple algorithms.
ABSTRACT: A framework is developed which enables a general class of linear Iterative Learning Control (ILC) algorithms to be applied to tracking tasks which require the plant output to reach given points at predetermined time instants, without the need for intervening reference points to be stipulated. It is shown that superior convergence and robustness properties are obtained compared with those associated with using the original class of ILC algorithm to track a prescribed arbitrary reference trajectory satisfying the point-to-point position constraints. Experimental results using a non-minimum phase test facility are presented to confirm the theoretical findings. Stabilization of well-posed linear systems by dynamicsampled-data feedback. Prof. Harmut Logemann (Bath) ABSTRACT: In the talk, we will present necessary and sufficient conditions for the existence of stabilizing dynamic sampled-data controllers for well-posed infinite-dimensional linear systems. The underlying stability concept for the sampled-data feedback system is inspired by the notion of input-to-state stability from nonlinear control theory. In particular, we will show that the existence of stabilizing sampled-data controllers implies the existence of finite-dimensional stabilizing sampled-data controllers. Exact identification of lossless- and dissipative systems, with applications to model reduction from data. Paolo Rapisarda (Southampton) ABSTRACT: I will illustrate an algorithm, based on ideas from dissipativity theory, to exactly identify a state-space model of a lossless/dissipative system from a given (input, output) trajectory. Performing a rank-revealing factorization of a Gramian-like matrix constructed from the data, a state sequence corresponding to the given data can be computed. The computation of the system state-space equations is then performed solving a system of linear equations. Population Modelling of Montastraea annularis. Heather Burgess (Exeter) ABSTRACT: We are studying the reef-building coral Montastraea annularis. Previously we have modelled a population of coral patches using Population Projection Matrices. This involves the discretization of size. This discretization is restrictive because there is not enough data to accurately assign transition rates between some of these discretized size classes. Therefore we are now aiming to build an Integral Projection Model for this population which assumes continuous size classes. Some initial results are presented together with a comparison to our PPM approach. ABSTRACT: In this talk I will first introduce the main issues regarding the definition of autonomy for higher-dimensional systems. I will then examine the definition of asymptotic stability of a 2-D system described by a system of higher-order linear partial difference equations given by M.E. Valcher (IEEE-CAS 2000), comparing it with some others. Then I will give a necessary and sufficient condition for asymptotic stability, namely the existence of a vector "Lyapunov functional" satisfying certain positivity conditions together with its divergence along special system trajectories. In the talk I will make strenuous use of the behavioral framework for n-D systems and of the calculus of quadratic difference forms based on four-variable polynomial algebra. I will *not* mention names of long-dead pure mathematicians *nor* use polysyllabic algebraic terms, and I will *not* trace a single commutative diagram.
The procedure has direct application to data-driven model reduction. If the rank-revealing factorization of the Gramian is performed suitably (e.g. using an SVD), then the resulting state-space equations are Riccati-balanced, and can be truncated in order to obtain a reduced-order model. A biased approach to nonlinear robust stability with applications in adaptive control. Mark French and Wenming Bian (ISIS) Pre CDC'09 presentation. |
