Maynooth University Department of Mathematics and Statistics

TITLE: Two topics:  A.  The Complexity of Automotive Engine Management; B.  Control in the Face of Uncertainty in Frequency

SPEAKER:  Prof. Keith Glover (Emeritus), University of Cambridge

ABSTRACT:

We first give an overview of the complexity of automotive engine management, where the very significant improvement in system performance in recent years has resulted from novel actuators and sensors and increased controller complexity.   In this application satisfying the constraints on the inputs and states is a pricipal concern.   In other problems the system dynamics and uncertainty dominate the controller design.  Here we outline results from Vinnicombe where there is uncertainty in the system gain and frequency scale.  It will be shown that with recent advances in controller synthesis these problems can now be addressed.

TITLE:  Using mathematical modelling and dynamic analysis to understand Parkinson's disease

SPEAKER: Prof. Peter Wellstead (Emeritus), Maynooth University

Joint work with: Mathieu Cloutier and Miriam Garcia

ABSTRACT:

Medical texts describe the usual form of Parkinson's disease (PD) as a heterogeneous condition of unknown causes. In this talk we challenge this orthodoxy.  Using mathematical analysis we develop a model of how the causes and mechanisms Parkinson's disease operate, and present the first plausible theory for the pathogenesis and spread of PD.  We begin by showing how a mathematical model of brain energy metabolism provides a unifying framework for analysing all the factors that create a vulnerability to the disease. From medical researcher's perspective, the model provides controlled environment for rapidly assessing the impact and interaction of different risk factors with obvious advantages over the conventional animal experiments and human studies of PD.

Beyond this, mathematical modelling throws important new light on the pathogenesis of PD. In particular, by adding known PD mechanisms to the brain energy metabolism model, a neurochemical bifurcation process is revealed. This consists of a neurochemical bistability that emerges within a vulnerable neuron under stress from risk factors. One of the stable points lies at the healthy homeostatic state and the other at a neurochemically toxic state associated with Parkinson's disease.  

The discovery of a bistability led us to propose:
1. The theory that the pathogenic mechanism for Parkinson's disease is a neurochemical switch mechanism activated by PD risk factors.
2. That dynamics of switching of a neuronal compartment to the toxic state at one particular point in the nervous system creates a wave mechanism that allows Parkinsonian damage to propagate through the brain that is consistent with current medical understanding. We close by reviewing current work on the PD propagation mechanism, and our views on directions disease research – current and future.

TITLE: Stability and String Stability of Formation Control Architectures for Vehicle Platooning

SPEAKER: Mr. Andres Peters, Maynooth University

ABSTRACT:

In this talk we present theoretical results involving the stability and string stability of certain types of formation control architectures for platooning. In particular we consider a string of vehicles traveling in a straight line. Each vehicle is equipped with controllers and provided with measurements of possibly several other members of the string. We consider cases where the dynamical properties of the formation control architecture are affected by specific design choices. For example, the interconnection topology, the inter-vehicle spacing policy or the communication used within the vehicle string.

TITLE: Recent advances on Input-to-State Stability Theory: From global to almost global ... and back.

SPEAKER: Dr. David Angeli, Imperial College London

ABSTRACT:

Input-to-State Stability is a well-known and studied approach to formulate external and internal stability properties for nonlinear systems subject to exogenous disturbances. While its original formulation apparently allows to quantify and qualify set-stability notions, it turns out that topological obstructions to global stability basically only allow its direct application to the case of systems with a unique GAS equilibrium (or an invariant neighborhood of it).  A first attempt to remove these limitations and include oscillators, multi-stable systems and other complex phenomena within the ISS framework has been to allow for almost global stability notions.  Only sufficient characterizations of such notions however have been derived throughout the years.

We will review some of them and show how, more recently, a surprisingly different approach still insisting on global notions but relaxing the Lyapunov stability requirement has resulted in a very natural extension to ISS theory which allows for Lyapunov necessary and sufficient characterizations.

TITLE: Diffusive systems and their properties

SPEAKER: Prof. Jonathan Partington, University of Leeds

Joint work with: Aolo Bashar Abusaksaka

ABSTRACT:

Diffusive systems are linear time-invariant systems for which the impulse response can be expressed as a Laplace transform. They were much studied by Montseny, who realized them in terms of the heat equation.  We present some of their analytical properties, including results on approximation by finite-dimensional systems (model reduction).  Some generalizations of diffusive systems are also discussed.