A víz alatti mozgás mechanikája és idegi szabályozása = Mechanics and neural control of aquatic locomotion

A kutatómunka során víz közegben történő mozgás szabályzásának mechanikai és idegtudományi kérdéseivel foglalkoztam, beleértve egyes egyedek, illetve állatcsoportok mozgásának vizsgálatát. A legprimitívebb felépítésű gerinces állatcsoport (az ingolák) vizsgálata során kimutattuk, hogy a mozgást vezérlő idegi hálózat kísérleti adatok alapján felépített modelljei hibásak, és ezért nem egyezik meg viselkedésük a valódi állatokéval. A számítógépes modellek komplexitását redukálva analitikus eszközökkel egy új, a korábbiaknál jobb viselkedést mutató mozgásvezérlő mechanizmusra tettem javaslatot. Az összehangolt csoportos mozgás kérdéskörében is a legegyszerűbb hatékony szabályozási mechanizmus azonosítására törekedtem. Kimutattam, hogy kétdimenziós térben mozgó koherens állatcsoportok viszonylag kis egyedszám esetén képesek spontán ütközések útján hatékonyan ’kommunikálni’, míg nagy egyedszám esetén a mechanikai kölcsönhatások fontosak, de önmagukban nem elég hatékonyak. | The mechanical and neural aspects of aquatic locomotion have been investigated on the level of individual agents as well as of coherent groups of individuals. We focused on central pattern generators of lampreys – a group of primitive vertebrates – and found that computational models of these networks of neurons fail to capture the behavior and the underlying mechanism of the real system. By reducing the complexity of existing models and by the use of analytic techniques a new mechanism of better performance has been proposed. Another focus of the research was the coherent motion of groups, where we again intended to identify the simplest underlying mechanism. It has been shown that relatively small groups of individuals are able to effectively communicate and come to ‘agreement’ with respect to a common direction of motion through spontaneous collisions; in bigger groups, the same mechanism is important but insufficient in itself

Intermediate Stable Phase Locked States In Oscillator Networks

The study of nonlinear oscillations is important in a variety of physical and biological contexts (especially in neuroscience). Synchronization of oscillators has been a problem of interest in recent years. In networks of nearest neighbor coupled oscillators it is possible to obtain synchrony between oscillators, but also a variety of constant phase shifts between 0 and pi. We coin these phase shifts intermediate stable phase-locked states. In neuroscience, both individual neurons and populations of neurons can behave as complex nonlinear oscillators. Intermediate stable phase-locked states are shown to be obtainable between individual oscillators and populations of identical oscillators.These intermediate stable phase-locked states may be useful in the construction of central pattern generators: autonomous neural cicuits responsible for motor behavior. In large chains and two-dimenional arrays of oscillators, intermediate stable phase-locked states provide a mechanism to produce waves and patterns that cannot be obtained in traditional network models. A particular pattern of interest is known as an anti-wave. This pattern corresponds to the collision of two waves from opposite ends of an oscillator chain. This wave may be relevant in the spinal central pattern generators of various fish. Anti-wave solutions in both conductance based neuron models and phase oscillator models are analyzed. It is shown that such solutions arise in phase oscillator models in which the nonlinearity (interaction function) contains both higher order odd and even Fourier modes. These modes are prominent in pairs of synchronous oscillators which lose stability in a supercritical pitchfork bifurcation

A Method to Accomplish the Optimal Control of Continuous Dynamical Systems with Impulse Controls via Discrete Optimal Control and Utilizing Optimal Control Theory to Explore the Emergence of Synchrony.

This research concerns the development of new optimal control methodologies and applications. In the first chapter we consider systems of ordinary differential equations subject to a restricted number of impulse controls. Examples of such systems include tumor growth, in which case the impulsive control is the administration of medication, and ecological invasion, in which case the impulse control is the release of predator species. Impulse control problems are typically solved via related partial differential equations known as quasi-variational inequalities. We show that these types of impulse control problems can be formulated as a discrete optimal control problems. Furthermore, this formulation is advantageous because it simplifies numerical calculations. In the second chapter we consider how optimal control can be used to investigate the emergence of synchrony in networks of coupled oscillators. In particular, we apply optimal control to a network of Kuramoto oscillators with time-varying coupling in order to relate network synchrony to network connectivity. To the best of our knowledge this is the first such use of optimal control theory

Mathematical frameworks for oscillatory network dynamics in neuroscience

The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear—for example, heteroclinic network attractors. In this review we present a set of mathemat- ical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical frame- work for further successful applications of mathematics to understanding network dynamics in neuroscience

Engineering limit cycle systems:adaptive frequency oscillators and applications to adaptive locomotion control of compliant robots

In this thesis, we present a dynamical systems approach to adaptive controllers for locomotion control. The approach is based on a rigorous mathematical framework using nonlinear dynamical systems and is inspired by theories of self-organization. Nonlinear dynamical systems such as coupled oscillators are an interesting approach for the on-line generation of trajectories for robots with many degrees of freedom (e.g. legged locomotion). However, designing a nonlinear dynamical system to satisfy a given specification and goal is not an easy task, and, hitherto no methodology exists to approach this problem in a unified way. Nature presents us with satisfactory solutions for the coordination of many degrees of freedom. One central feature observed in biological subjects is the ability of the neural systems to exploit natural dynamics of the body to achieve efficient locomotion. In order to be able to exploit the body properties, adaptive mechanisms must be at work. Recent work has pointed out the importance of the mechanical system for efficient locomotion. Even more interestingly, such well suited mechanical systems do not need complicated control. Yet, in robotics, in most approaches, adaptive mechanisms are either missing or they are not based on a rigorous framework, i.e. they are based on heuristics and ad-hoc approaches. Over the last three decades there has been enormous progress in describing movement coordination with the help of Synergetic approaches. This has led to the formulation of a theoretical framework: the theory of dynamic patterns. This framework is mathematically rigorous and at the same time fully operational. However, it does not provide any guidelines for synthetic approaches as needed for the engineering of robots with many degrees of freedom, nor does it directly help to explain adaptive systems. We will show how we can extend the theoretical framework to build adaptive systems. For this purpose, we propose the use of multi-scale dynamical systems. The basic idea behind multi-scale dynamical systems is that a given dynamical system gets extended by additional slow dynamics of its parameters, i.e. some of the parameters become state variables. The advantages of the framework of multi-scale dynamical systems for adaptive controllers are 1) fully dynamic description, 2) no separation of learning algorithm and learning substrate, 3) no separation of learning trials or time windows, 4) mathematically rigorous, 5) low dimensional systems. However, in order to fully exploit the framework important questions have to be solved. Most importantly, methodologies for designing the feedback loops have to be found and important theoretical questions about stability and convergence properties of the devised systems have to be answered. In order to tackle this challenge, we first introduce an engineering view on designing nonlinear dynamical systems and especially oscillators. We will highlight the important differences and freedom that this engineering view introduces as opposed to a modeling one. We then apply this approach by first proposing a very simple adaptive toy-system, consisting of a dynamical system coupled to a spring-mass system. Due to its spring-mass dynamics, this system contains clear natural dynamics in the form of resonant frequencies. We propose a prototype adaptive multi-scale system, the adaptive frequency oscillator, which is able to adapt its intrinsic frequency to the resonant frequency of the body dynamics. After a small sidetrack to show that we can use adaptive frequency oscillators also for other applications than for adaptive controllers, namely for frequency analysis, we then come back to further investigation of the adaptive controller. We apply the same controller concept to a simple spring-mass hopper system. The spring-mass system consists of a body with two legs attached by rotational joints. The legs contain spring-damper elements. Finally, we present results of the implementation of the controller on a real robot, the experimental robot PUPPY II. This robot is a under-actuated robot with spring dynamics in the knee joints. It will be shown, that due to the appropriate simplification and concentration on relevant features in the toy-system the controller concepts works without a fundamental change on all systems from the toy system up to the real robot

Novel central pattern generator elements for autonomous modular robots

Tesis doctoral inédita. Universidad Autónoma de Madrid, Escuela Politécnica Superior, junio de 201

Engineering Dynamics and Life Sciences

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

A complex systems approach to education in Switzerland

The insights gained from the study of complex systems in biological, social, and engineered systems enables us not only to observe and understand, but also to actively design systems which will be capable of successfully coping with complex and dynamically changing situations. The methods and mindset required for this approach have been applied to educational systems with their diverse levels of scale and complexity. Based on the general case made by Yaneer Bar-Yam, this paper applies the complex systems approach to the educational system in Switzerland. It confirms that the complex systems approach is valid. Indeed, many recommendations made for the general case have already been implemented in the Swiss education system. To address existing problems and difficulties, further steps are recommended. This paper contributes to the further establishment complex systems approach by shedding light on an area which concerns us all, which is a frequent topic of discussion and dispute among politicians and the public, where billions of dollars have been spent without achieving the desired results, and where it is difficult to directly derive consequences from actions taken. The analysis of the education system's different levels, their complexity and scale will clarify how such a dynamic system should be approached, and how it can be guided towards the desired performance