A Survey of the Probability Density Function Control for Stochastic Dynamic Systems

Probability density function (PDF) control strategy investigates the controller design approaches in order to to realise a desirable distributions shape control of the random variables for the stochastic processes. Different from the existing stochastic optimisation and control methods, the most important problem of PDF control is to establish the evolution of the PDF expressions of the system variables. Once the relationship between the control input and the output PDF is formulated, the control objective can be described as obtaining the control input signals which would adjust the system output PDFs to follow the pre-specified target PDFs. This paper summarises the recent research results of the PDF control while the controller design approaches can be categorised into three groups: 1) system model-based direct evolution PDF control; 2) model-based distribution-transformation PDF control methods and 3) databased PDF control. In addition, minimum entropy control, PDF-based filter design, fault diagnosis and probabilistic decoupling design are also introduced briefly as extended applications in theory sense

Interaction of external forcing and noise in bio-inspired oscillator systems

Biologische und bioinspirierte Oszillatoren sind faszinierende Systeme, die aus technischer Sicht untersucht werden sollten. Biologische Oszillatoren sind von Natur aus verrauscht, erzeugen aber dennoch stabile Schwingungsrhythmen und passen ihre Periode an die Periode der Eingangssignale an, ein Prozess, der als Entrainment bekannt ist. Oszillatorsysteme kommen nicht nur in der Natur, sondern auch in vielen vom Menschen geschaffenen Systemen vor, zum Beispiel in Bewegungsgeneratoren für Roboter oder in elektrischen Schaltkreisen. Daher ist ein besseres Verständnis der Konstruktionsprinzipien biologischer Oszillatoren und ihrer Strategien, mit Rauschen umzugehen oder es sogar zu nutzen, um ihr Entrainment an die Eingangssignale zu unterstützen, für ein besseres Verständnis der oszillatorischen Systeme und ihrer technischen Anwendungen unerlässlich. Der Hauptbeitrag der vorliegenden Arbeit ist die numerische Untersuchung und Analyse einer Population stochastischer Oszillatoren unter wechselnden Parametern des Eingangssignals und variierender Rauschintensität. Das theoretische Kapitel der Arbeit zeigt, dass Rauschen die Empfindlichkeit gegenüber schwachen externen Signalen erhöhen kann und somit die Anpassung an einen größeren Bereich von Eingangsamplituden und -perioden im Vergleich zu einem äquivalenten deterministischen System ermöglicht. Das Rauschen erhöht auch die Phasenreaktion auf einen stufenförmigen Eingangsimpuls und beschleunigt die Erholung von einer Jet-Lag-artigen Störung. Es wird ferner gezeigt, dass diese Effekte nicht nur auf biologische Oszillatoren beschränkt sind, sondern auch für eine größere Anzahl von generischen Oszillatorsystemen mit einem Grenzzyklus zu gelten scheinen. Im letzten Teil des theoretischen Kapitels wird ein neuartiger schrittweiser Anpassungsalgorithmus vorgestellt, der eine Parameteranpassung von stochastischen Oszillatorpopulationen ermöglicht. Alle im theoretischen Kapitel entwickelten Methoden wurden als Open-Source-Softwarepaket zur Verfügung gestellt. Im letzten Teil der Arbeit wird eine praktische Anwendung für die entwickelten Methoden vorgestellt. Hier wird ein stochastisches Gleichungsmodell entwickelt, um die Tag-Nacht-Rhythmen in Zebrafisch-Zelllinien zu untersuchen. Das Modell wird anschließend verwendet, um festzustellen, wie verschiedene Medikamente die Synchronisation und Stochastizität der biologischen Uhr beeinflussen

Benelux meeting on systems and control, 23rd, March 17-19, 2004, Helvoirt, The Netherlands

Book of abstract

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...

Biomimetic Manipulator Control Design for Bimanual Tasks in the Natural Environment

As robots become more prolific in the human environment, it is important that safe operational procedures are introduced at the same time; typical robot control methods are often very stiff to maintain good positional tracking, but this makes contact (purposeful or accidental) with the robot dangerous. In addition, if robots are to work cooperatively with humans, natural interaction between agents will make tasks easier to perform with less effort and learning time. Stability of the robot is particularly important in this situation, especially as outside forces are likely to affect the manipulator when in a close working environment; for example, a user leaning on the arm, or task-related disturbance at the end-effector. Recent research has discovered the mechanisms of how humans adapt the applied force and impedance during tasks. Studies have been performed to apply this adaptation to robots, with promising results showing an improvement in tracking and effort reduction over other adaptive methods. The basic algorithm is straightforward to implement, and allows the robot to be compliant most of the time and only stiff when required by the task. This allows the robot to work in an environment close to humans, but also suggests that it could create a natural work interaction with a human. In addition, no force sensor is needed, which means the algorithm can be implemented on almost any robot. This work develops a stable control method for bimanual robot tasks, which could also be applied to robot-human interactive tasks. A dynamic model of the Baxter robot is created and verified, which is then used for controller simulations. The biomimetic control algorithm forms the basis of the controller, which is developed into a hybrid control system to improve both task-space and joint-space control when the manipulator is disturbed in the natural environment. Fuzzy systems are implemented to remove the need for repetitive and time consuming parameter tuning, and also allows the controller to actively improve performance during the task. Experimental simulations are performed, and demonstrate how the hybrid task/joint-space controller performs better than either of the component parts under the same conditions. The fuzzy tuning method is then applied to the hybrid controller, which is shown to slightly improve performance as well as automating the gain tuning process. In summary, a novel biomimetic hybrid controller is presented, with a fuzzy mechanism to avoid the gain tuning process, finalised with a demonstration of task-suitability in a bimanual-type situation.EPSR

A Meshless Modelling Framework for Simulation and Control of Nonlinear Synthetic Biological Systems

Synthetic biology is a relatively new discipline that incorporates biology and engineering principles. It builds upon the advances in molecular, cell and systems biology and aims to transform these principles to the same effect that synthesis transformed chemistry. What distinguishes synthetic biology from traditional molecular or cellular biology is the focus on design and construction of components (e.g. parts of a cell) that can be modelled, characterised and altered to meet specific performance criteria. Integration of these parts into larger systems is a core principle of synthetic biology. However, unlike some areas of engineering, biology is highly non-linear and less predictable. In this thesis the work that has been conducted to combat some of the complexities associated with dynamic modelling and control of biological systems will be presented. Whilst traditional techniques, such as Orthogonal Collocation on Finite Elements (OCFE) are common place for dynamic modelling they have significant complexity when sampling points are increased and offer discrete solutions or solutions with limited differentiability. To circumvent these issues a meshless modelling framework that incorporates an Artificial Neural Network (ANN) to solve Ordinary Differential Equations (ODEs) and model dynamic processes is utilised. Neural networks can be considered as mesh-free numerical methods as they are likened to approximation schemes where the input data for a design of a network consists of a set of unstructured discrete data points. The use of the ANN provides a solution that is differentiable and is of a closed analytic form, which can be further utilised in subsequent calculations. Whilst there have been advances in modelling biological systems, there has been limited work in controlling their outputs. The benefits of control allow the biological system to alter its state and either upscale production of its primary output, or alter its behaviour within an integrated system. In this thesis a novel meshless Nonlinear Model Predictive Control (NLMPC) framework is presented to address issues related to nonlinearities and complexity. The presented framework is tested on a number of case studies. A significant case study within this work concerns simulation and control of a gene metabolator. The metabolator is a synthetic gene circuit that consists of two metabolite pools which oscillate under the influence of glycolytic flux (a combination of sugars, fatty acids and glycerol). In this work it is demonstrated how glycolytic flux can be used as a control variable for the metabolator. The meshless NLMPC framework allows for both Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) control. The dynamic behaviour of the metabolator allows for both top-down control (using glycolytic flux) and bottom-up control (using acetate). The benefit of using MIMO (by using glycolytic flux and acetate as the control variables) for the metabolator is that it allows the system to reach steady state due to the interactions between the two metabolite pools. Biological systems can also encounter various uncertainties, especially when performing experimental validation. These can have profound effect on the system and can alter the dynamics or overall behaviour. In this work the meshless NLMPC framework addresses uncertainty through the use of Zone Model Predictive Control (Zone MPC), where the control profile is set as a range, rather than a fixed set point. The performance of Zone MPC under the presence of various magnitudes of random disturbances is analysed. The framework is also applied to biological systems architecture, for instance the development of biological circuits from well-characterised and known parts. The framework has shown promise in determining feasible circuits and can be extended in future to incorporate a full list of biological parts. This can give rise to new circuits that could potentially be used in various applications. The meshless NLMPC framework proposed in this work can be extended and applied to other biological systems and heralds a novel method for simulation and control