Thresholds of Spatially Coupled Systems via Lyapunov's Method

The threshold, or saturation phenomenon of spatially coupled systems is revisited in the light of Lyapunov's theory of dynamical systems. It is shown that an application of Lyapunov's direct method can be used to quantitatively describe the threshold phenomenon, prove convergence, and compute threshold values. This provides a general proof methodology for the various systems recently studied. Examples of spatially coupled systems are given and their thresholds are computed.Comment: 6 page

Mean field modelling of human EEG: application to epilepsy

Aggregated electrical activity from brain regions recorded via an electroencephalogram (EEG), reveal that the brain is never at rest, producing a spectrum of ongoing oscillations that change as a result of different behavioural states and neurological conditions. In particular, this thesis focusses on pathological oscillations associated with absence seizures that typically affect 2–16 year old children. Investigation of the cellular and network mechanisms for absence seizures studies have implicated an abnormality in the cortical and thalamic activity in the generation of absence seizures, which have provided much insight to the potential cause of this disease. A number of competing hypotheses have been suggested, however the precise cause has yet to be determined. This work attempts to provide an explanation of these abnormal rhythms by considering a physiologically based, macroscopic continuum mean-field model of the brain's electrical activity. The methodology taken in this thesis is to assume that many of the physiological details of the involved brain structures can be aggregated into continuum state variables and parameters. The methodology has the advantage to indirectly encapsulate into state variables and parameters, many known physiological mechanisms underlying the genesis of epilepsy, which permits a reduction of the complexity of the problem. That is, a macroscopic description of the involved brain structures involved in epilepsy is taken and then by scanning the parameters of the model, identification of state changes in the system are made possible. Thus, this work demonstrates how changes in brain state as determined in EEG can be understood via dynamical state changes in the model providing an explanation of absence seizures. Furthermore, key observations from both the model and EEG data motivates a number of model reductions. These reductions provide approximate solutions of seizure oscillations and a better understanding of periodic oscillations arising from the involved brain regions. Local analysis of oscillations are performed by employing dynamical systems theory which provide necessary and sufficient conditions for their appearance. Finally local and global stability is then proved for the reduced model, for a reduced region in the parameter space. The results obtained in this thesis can be extended and suggestions are provided for future progress in this area

Model based fault diagnosis and prognosis of class of linear and nonlinear distributed parameter systems modeled by partial differential equations

With the rapid development of modern control systems, a significant number of industrial systems may suffer from component failures. An accurate yet faster fault prognosis and resilience can improve system availability and reduce unscheduled downtime. Therefore, in this dissertation, model-based prognosis and resilience control schemes have been developed for online prediction and accommodation of faults for distributed parameter systems (DPS). First, a novel fault detection, estimation and prediction framework is introduced utilizing a novel observer for a class of linear DPS with bounded disturbance by modeling the DPS as a set of partial differential equations. To relax the state measurability in DPS, filters are introduced to redesign the detection observer. Upon detecting a fault, an adaptive term is activated to estimate the multiplicative fault and a tuning law is derived to tune the fault parameter magnitude. Then based on this estimated fault parameter together with its failure limit, time-to-failure (TTF) is derived for prognosis. A novel fault accommodation scheme is developed to handle actuator and sensor faults with boundary measurements. Next, a fault isolation scheme is presented to differentiate actuator, sensor and state faults with a limited number of measurements for a class of linear and nonlinear DPS. Subsequently, actuator and sensor fault detection and prediction for a class of nonlinear DPS are considered with bounded disturbance by using a Luenberger observer. Finally, a novel resilient control scheme is proposed for nonlinear DPS once an actuator fault is detected by using an additional boundary measurement. In all the above methods, Lyapunov analysis is utilized to show the boundedness of the closed-loop signals during fault detection, prediction and resilience under mild assumptions --Abstract, page iv

14th Conference on Dynamical Systems Theory and Applications DSTA 2017 ABSTRACTS

From Preface: This is the fourteen 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 the Ministry of Science and Higher Education. It is a great pleasure that our invitation has been accepted by so many 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 welcome nearly 250 persons from 38 countries all over the world. They decided to share the results of their research and many years experiences in the discipline of dynamical systems by submitting many very interesting papers. This booklet contains a collection of 375 abstracts, which have gained the acceptance of referees and have been qualified for publication in the conference proceedings [...]

Proceedings of the NASA Conference on Space Telerobotics, volume 1

The theme of the Conference was man-machine collaboration in space. Topics addressed include: redundant manipulators; man-machine systems; telerobot architecture; remote sensing and planning; navigation; neural networks; fundamental AI research; and reasoning under uncertainty

Нелінійна динаміка — 2013

The book of Proceedings includes extended abstracts of presentations on the Fourth International conference on nonlinear dynamics