Linear Control Theory with an ℋ∞ Optimality Criterion

This expository paper sets out the principal results in ℋ∞ control theory in the context of continuous-time linear systems. The focus is on the mathematical theory rather than computational methods

System-theoretic trends in econometrics

Economics;Estimation;econometrics

Parametric decoupling control strategy for a class of nonlinear uncertain systems via observer-based output feedback

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI linkIn this paper, the system decoupling problem has been investigated and a novel decoupling control strategy is presented for Lipschitz nonlinear uncertain multivariable systems. This control strategy consists of an explicit parametric state feedback controller and a linear state observer, where the free parameters of the controller can be adjusted to attenuate the coupling effects. In addition, the optimal parameters can be obtained using H infinity norm based performance criterion. The convergence of the observer, the robust stabilization of the controller and closed-loop system are analysed while the sufficient conditions are determined. Following the design procedure of the presented control strategy, an illustrative numerical example is given to demonstrate the effectiveness and correctness of the presented control strategy

The Magnus expansion and some of its applications

Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to built up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of preserving at any order certain symmetries of the exact solution. The goal of this review is threefold. First, to collect a number of developments scattered through half a century of scientific literature on Magnus expansion. They concern the methods for the generation of terms in the expansion, estimates of the radius of convergence of the series, generalizations and related non-perturbative expansions. Second, to provide a bridge with its implementation as generator of especial purpose numerical integration methods, a field of intense activity during the last decade. Third, to illustrate with examples the kind of results one can expect from Magnus expansion in comparison with those from both perturbative schemes and standard numerical integrators. We buttress this issue with a revision of the wide range of physical applications found by Magnus expansion in the literature.Comment: Report on the Magnus expansion for differential equations and its applications to several physical problem

Dirty RF Signal Processing for Mitigation of Receiver Front-end Non-linearity

Moderne drahtlose Kommunikationssysteme stellen hohe und teilweise gegensätzliche Anforderungen an die Hardware der Funkmodule, wie z.B. niedriger Energieverbrauch, große Bandbreite und hohe Linearität. Die Gewährleistung einer ausreichenden Linearität ist, neben anderen analogen Parametern, eine Herausforderung im praktischen Design der Funkmodule. Der Fokus der Dissertation liegt auf breitbandigen HF-Frontends für Software-konfigurierbare Funkmodule, die seit einigen Jahren kommerziell verfügbar sind. Die praktischen Herausforderungen und Grenzen solcher flexiblen Funkmodule offenbaren sich vor allem im realen Experiment. Eines der Hauptprobleme ist die Sicherstellung einer ausreichenden analogen Performanz über einen weiten Frequenzbereich. Aus einer Vielzahl an analogen Störeffekten behandelt die Arbeit die Analyse und Minderung von Nichtlinearitäten in Empfängern mit direkt-umsetzender Architektur. Im Vordergrund stehen dabei Signalverarbeitungsstrategien zur Minderung nichtlinear verursachter Interferenz - ein Algorithmus, der besser unter "Dirty RF"-Techniken bekannt ist. Ein digitales Verfahren nach der Vorwärtskopplung wird durch intensive Simulationen, Messungen und Implementierung in realer Hardware verifiziert. Um die Lücken zwischen Theorie und praktischer Anwendbarkeit zu schließen und das Verfahren in reale Funkmodule zu integrieren, werden verschiedene Untersuchungen durchgeführt. Hierzu wird ein erweitertes Verhaltensmodell entwickelt, das die Struktur direkt-umsetzender Empfänger am besten nachbildet und damit alle Verzerrungen im HF- und Basisband erfasst. Darüber hinaus wird die Leistungsfähigkeit des Algorithmus unter realen Funkkanal-Bedingungen untersucht. Zusätzlich folgt die Vorstellung einer ressourceneffizienten Echtzeit-Implementierung des Verfahrens auf einem FPGA. Abschließend diskutiert die Arbeit verschiedene Anwendungsfelder, darunter spektrales Sensing, robuster GSM-Empfang und GSM-basiertes Passivradar. Es wird gezeigt, dass nichtlineare Verzerrungen erfolgreich in der digitalen Domäne gemindert werden können, wodurch die Bitfehlerrate gestörter modulierter Signale sinkt und der Anteil nichtlinear verursachter Interferenz minimiert wird. Schließlich kann durch das Verfahren die effektive Linearität des HF-Frontends stark erhöht werden. Damit wird der zuverlässige Betrieb eines einfachen Funkmoduls unter dem Einfluss der Empfängernichtlinearität möglich. Aufgrund des flexiblen Designs ist der Algorithmus für breitbandige Empfänger universal einsetzbar und ist nicht auf Software-konfigurierbare Funkmodule beschränkt.Today's wireless communication systems place high requirements on the radio's hardware that are largely mutually exclusive, such as low power consumption, wide bandwidth, and high linearity. Achieving a sufficient linearity, among other analogue characteristics, is a challenging issue in practical transceiver design. The focus of this thesis is on wideband receiver RF front-ends for software defined radio technology, which became commercially available in the recent years. Practical challenges and limitations are being revealed in real-world experiments with these radios. One of the main problems is to ensure a sufficient RF performance of the front-end over a wide bandwidth. The thesis covers the analysis and mitigation of receiver non-linearity of typical direct-conversion receiver architectures, among other RF impairments. The main focus is on DSP-based algorithms for mitigating non-linearly induced interference, an approach also known as "Dirty RF" signal processing techniques. The conceived digital feedforward mitigation algorithm is verified through extensive simulations, RF measurements, and implementation in real hardware. Various studies are carried out that bridge the gap between theory and practical applicability of this approach, especially with the aim of integrating that technique into real devices. To this end, an advanced baseband behavioural model is developed that matches to direct-conversion receiver architectures as close as possible, and thus considers all generated distortions at RF and baseband. In addition, the algorithm's performance is verified under challenging fading conditions. Moreover, the thesis presents a resource-efficient real-time implementation of the proposed solution on an FPGA. Finally, different use cases are covered in the thesis that includes spectrum monitoring or sensing, GSM downlink reception, and GSM-based passive radar. It is shown that non-linear distortions can be successfully mitigated at system level in the digital domain, thereby decreasing the bit error rate of distorted modulated signals and reducing the amount of non-linearly induced interference. Finally, the effective linearity of the front-end is increased substantially. Thus, the proper operation of a low-cost radio under presence of receiver non-linearity is possible. Due to the flexible design, the algorithm is generally applicable for wideband receivers and is not restricted to software defined radios