Differential inclusions and robust control theory

Uncontrolled systems (x) over dot is an element of Ax, where A is a non-empty compact set of matrices, and controlled systems (x) over dot is an element of Ax + Bu are considered. Higher-order systems 0 is an element of Px - Du, where and are sets of differential polynomials, are also studied. It is shown that, under natural conditions commonly occurring in robust control theory, with some mild additional restrictions, asymptotic stability of differential inclusions is guaranteed. The main results are variants of small-gain theorems and the principal technique used is the Krasnosel'skii-Pokrovskii principle of absence of bounded solutions.

Luck and the control theory of knowledge

The dissertation accomplishes two aims: 1) to diagnose what prevents true beliefs from being knowledge; 2) to give an positive account of knowledge. Concerning the first aim, it offers an account of the notion of luck. It defends the view that luck is a form of risk and distinguishes two types of luck. Then, it applies the account to the problem of epistemic luck and distinguishes, accordingly, two types of epistemic luck. It is argued that these two types of epistemic luck explain the whole range of cases of not-known true belief. Concerning the second aim, the dissertation advances an account of knowledge in terms of the notion of cognitive control that deals with the two forms of epistemic luck distinguished.

Optimal control theory for a unitary operation under dissipative evolution

We show that optimizing a quantum gate for an open quantum system requires the time evolution of only three states irrespective of the dimension of Hilbert space. This represents a significant reduction in computational resources compared to the complete basis of Liouville space that is commonly believed necessary for this task. The reduction is based on two observations: the target is not a general dynamical map but a unitary operation; and the time evolution of two properly chosen states is sufficient to distinguish any two unitaries. We illustrate gate optimization employing a reduced set of states for a controlled phasegate with trapped atoms as qubit carriers and a iSWAP gate with superconducting qubits.

Mapping and controlling molecular processes: The application of control theory and system identification algorithms to ASOPS and other fast pulse spectroscopies

Asynchronous Optical Sampling (ASOPS) [1,2] and frequency comb spectrometry [3] based on dual Ti:saphire resonators operated in a master/slave mode have the potential to improve signal to noise ratio in THz transient and IR sperctrometry. The multimode Brownian oscillator time-domain response function described by state-space models is a mathematically robust framework that can be used to describe the dispersive phenomena governed by Lorentzian, Debye and Drude responses. In addition, the optical properties of an arbitrary medium can be expressed as a linear combination of simple multimode Brownian oscillator functions. The suitability of a range of signal processing schemes adopted from the Systems Identification and Control Theory community for further processing the recorded THz transients in the time or frequency domain will be outlined [4,5]. Since a femtosecond duration pulse is capable of persistent excitation of the medium within which it propagates, such approach is perfectly justifiable. Several de-noising routines based on system identification will be shown. Furthermore, specifically developed apodization structures will be discussed. These are necessary because due to dispersion issues, the time-domain background and sample interferograms are non-symmetrical [6-8]. These procedures can lead to a more precise estimation of the complex insertion loss function. The algorithms are applicable to femtosecond spectroscopies across the EM spectrum. Finally, a methodology for femtosecond pulse shaping using genetic algorithms aiming to map and control molecular relaxation processes will be mentioned.

The Mathematics of Control Theory

This text contains papers presented at the Institute of Mathematics and its Applications Conference on Control Theory, held at the University of Strathclyde in Glasgow. The contributions cover a wide range of topics of current interest to theoreticians and practitioners including algebraic systems theory, nonlinear control systems, adaptive control, robustness issues, infinite dimensional systems, applications studies and connections to mathematical aspects of information theory and data-fusion.

Applying robust control theory to solve problems in bio-medical sciences: study of an apoptotic model

Biological models of an apoptotic process are studied using models describing a system of differential equations derived from reaction kinetics information. The mathematical model is re-formulated in a state-space robust control theory framework where parametric and dynamic uncertainty can be modelled to account for variations naturally occurring in biological processes. We propose to handle the nonlinearities using neural networks.

On some extension of optimal control theory

Some problems of Calculus of Variations do not have solutions in the class of classic continuous and smooth arcs. This suggests the need of a relaxation or extension of the problem ensuring the existence of a solution in some enlarged class of arcs. This work aims at the development of an extension for a more general optimal control problem with nonlinear control dynamics in which the control function takes values in some closed, but not necessarily bounded, set. To achieve this goal, we exploit the approach of R.V. Gamkrelidze based on the generalized controls, but related to discontinuous arcs. This leads to the notion of generalized impulsive control. The proposed extension links various approaches on the issue of extension found in the literature.

Predicting Problematic Approach Behavior Toward Politicians: Exploring the Potential Contributions of Control Theory

The potential merits of Carver and Scheier's (1981) control theory in the prediction of targeted violence are reviewed and several novel indicators of risk that are consistent with this theory are suggested for study. It was hypothesized that: (a) similarity between inappropriate contact with politicians and extremist group literature and writings; (b) the temporal proximity to violent or otherwise criminal actions and notable anniversaries of such groups; (c) detailed specification of a plan to engage in problematic approach behavior, and; (d) self-focus, will be significant predictors of problematic approach behavior. A sample of 506 individuals who engaged in threatening or otherwise inappropriate contact toward members of the United States Congress was drawn from the case files of the United States Capitol Police. Results of the present research indicated that detailed specification of a plan to engage in problematic approach behavior was strongly predictive of actually engaging in problematic approach. Furthermore, high self-focus was significantly related to problematic approach between-persons, although within-person, higher-than-average self-focus showed no such relation. Neither temporal proximity to notable acts of extremist violence nor similarity to known extremist group writings was found to be associated with problematic approach in this sample.

Integrating attentional control theory and the strength model of self-control

In the present article, we argue that it may be fruitful to incorporate the ideas of the strength model of self-control into the core assumptions of the well-established attentional control theory (ACT). In ACT, it is assumed that anxiety automatically leads to attention disruption and increased distractibility, which may impair subsequent cognitive or perceptual-motor performance, but only if individuals do not have the ability to counteract this attention disruption. However, ACT does not clarify which process determines whether one can volitionally regulate attention despite experiencing high levels of anxiety. In terms of the strength model of self-control, attention regulation can be viewed as a self-control act depending on the momentary availability of self-control strength. We review literature that has revealed that self-control strength moderates the anxiety-performance relationship, discuss how to integrate these two theoretical models, and offer practical recommendations of how to counteract negative anxiety effects.

Choking under Pressure und Ego Depletion: Eine Erweiterung der Attentional Control Theory und mögliche Interventionsmaßnahmen

In Leistungssituationen sind Athletinnen und Athleten nicht immer dazu in der Lage, ihr Leistungsoptimum abzurufen. Auch wenn die Befundlage zum Angst-Leistungszusammenhang äußerst heterogen ist, so geht höheres Angsterleben häufig mit Leistungsbeeinträchtigungen einher. In dem vorliegenden Manuskript wird ein Überblick über verschiedene theoretische Modelle zur Erklärung des Angst-Leistungszusammenhangs gegeben. Der Fokus wird dabei auf die Attentional Control Theory gelegt, die besagt, dass unter Druck die Aufmerksamkeitsregulation weniger effizient ausfällt und folglich erhöhte Ablenkbarkeit die Leistung negativ beeinflusst. Es wird weiterhin argumentiert, dass die Selbstkontrollkraft den Angst-Leistungszusammenhang moderiert, so dass nur bei Personen mit temporär erschöpfter Selbstkontrollkraft ein negativer Angst-Leistungszusammenhang erwartet wird, wohingegen Personen mit momentan verfügbarer Selbstkontrollkraft trotz erhöhten Angsterlebens Höchstleistung erbringen können. Abschließend werden offene Fragestellungen thematisiert, alternative Erklärungsansätze vorgestellt sowie praktische Implikationen für die Sportpsychologie abgeleitet.