In light of the complex and highly uncertain nature of dynamical systems requiring controls, it is not surprising that reliable system models for many high performance engineering and life science applications are unavailable. In the face of such high levels of system uncertainty, robust controllers may unnecessarily sacrifice system performance whereas adaptive controllers are clearly appropriate since they can tolerate far greater system uncertainty levels to improve system performance. In this dissertation, we develop a Lyapunov-based direct adaptive and neural adaptive control framework that addresses parametric uncertainty, unstructured uncertainty, disturbance rejection, amplitude and rate saturation constraints, and digital implementation issues. Specifically, we consider the following research topics: direct adaptive control for nonlinear uncertain systems with exogenous disturbances; robust adaptive control for nonlinear uncertain systems; adaptive control for nonlinear uncertain systems with actuator amplitude and rate saturation constraints; adaptive reduced-order dynamic compensation for nonlinear uncertain systems; direct adaptive control for nonlinear matrix second-order dynamical systems with state-dependent uncertainty; adaptive control for nonnegative and compartmental dynamical systems with applications to general anesthesia; direct adaptive control of nonnegative and compartmental dynamical systems with time delay; adaptive control for nonlinear nonnegative and compartmental dynamical systems with applications to clinical pharmacology; neural network adaptive control for nonlinear nonnegative dynamical systems; passivity-based neural network adaptive output feedback control for nonlinear nonnegative dynamical systems; neural network adaptive dynamic output feedback control for nonlinear nonnegative systems using tapped delay memory units; Lyapunov-based adaptive control framework for discrete-time nonlinear systems with exogenous disturbances; direct discrete-time adaptive control with guaranteed parameter error convergence; and hybrid adaptive control for nonlinear uncertain impulsive dynamical systems.

A robust servo control system based on Integral Variable Structure Model Following Control (IVSMFC) is proposed. The IVSMFC approach comprises a reference model part for specifying the design requirements and an Integral Variable Structure Control (IVSC) part for minimizing the errors between the plant and the model. Sliding mode thus obtained features robustness against external disturbances and parameter variations. Design procedures in both continuous-time and discrete-time have been detailed. The IVSMFC-based servo control system has been successfully applied to a DSP-based brushless DC motor drive for globoidal cam indexing system and to power system. Simulation and experimental results demonstrate that the proposed scheme can achieve fast and robust responses.

Model Reference Adaptive Control (MRAC) is a widely studied adaptive control methodology that aims to ensure that a nonlinear plant with significant modeling uncertainty behaves like a chosen reference model. MRAC methods attempt to achieve this by representing the modeling uncertainty as a weighted combination of known nonlinear functions, and using a weight update law that ensures weights take on values such that the effect of the uncertainty is mitigated. If the adaptive weights do arrive at an ideal value that best represent the uncertainty, significant performance and robustness gains can be realized. However, most MRAC adaptive laws use only instantaneous data for adaptation and can only guarantee that the weights arrive at these ideal values if and only if the plant states are Persistently Exciting (PE). The condition on PE reference input is restrictive and often infeasible to implement or monitor online. Consequently, parameter convergence cannot be guaranteed in practice for many adaptive control applications. Hence it is often observed that traditional adaptive controllers do not exhibit long-term-learning and global uncertainty parametrization. That is, they exhibit little performance gain even when the system tracks a repeated command. This thesis presents a novel approach to adaptive control that relies on using current and recorded data concurrently for adaptation. The thesis shows that for a concurrent learning adaptive controller, a verifiable condition on the linear independence of the recorded data is sufficient to guarantee that weights arrive at their ideal values even when the system states are not PE. The thesis also shows that the same condition can guarantee exponential tracking error and weight error convergence to zero, thereby allowing the adaptive controller to recover the desired transient response and robustness properties of the chosen reference models and to exhibit long-term-learning. This condition is found to be less restrictive and easier to verify online than the condition on persistently exciting exogenous input required by traditional adaptive laws that use only instantaneous data for adaptation. The concept is explored for several adaptive control architectures, including neuro-adaptive flight control, where a neural network is used as the adaptive element. The performance gains are justified theoretically using Lyapunov based arguments, and demonstrated experimentally through flight-testing on Unmanned Aerial Systems.

Το ερευνητικό αντικείμενο της Διατριβής είναι τα θέματα σθεναρότητας του προκύπτουν στα Δικτυωμένα Συστήματα Ελέγχου (Νetworked Cοntrοlled Systems - εφεξής "ΝCS"), όπου η βασική πηγή αβεβαιότητας είναι οι καθυστερήσεις λόγω δικτύου. Στο πλαίσιο αυτό παρουσιάζονται απότελέσματα του αφορούν στην ανάλυση σθεναρής ευστάθειας και στην σύνθεση σθεναρών ελεγκτών. Να επισημανθεί ότι στην Διατριβή, ο προσδιορισμός "σθεναρός" αφορά απόκλειστικά σθεναρότητα (ευστάθειας και επιδόσεων) ως προς τις αβέβαιες, χρονικά μεταβαλλόμενες, φραγμένες καθυστερήσεις. Τα μελετώμενα ΝCS απαρτίζονται από την διασύνδεση γραμμικών χρονικά αμετάβλητων συστημάτων συνεχούς χρόνου με ελεγκτές διακριτού χρόνου. Η βασική διάρθρωση των συστημάτων αυτών απαρτίζεται από έναν "οδηγούμενο από χρόνο" (time driven) αισθητήρα / δειγματολήπτη (με σταθερή περίοδο δειγματοληψίας h) που μεταδίδει μέσω του δικτύου τα δείγματα που λαμβάνει από το σύστημα στον "οδηγούμενο από γεγονότα" (event–driven) ελεγκτή. Ακολούθως ο ελεγκτής υπολογίζει την δράση ελέγχου και την μεταδίδει μέσω του δικτύου στον "οδηγούμενο από γεγονότα" (eveτιt–driven) ενεργοποιητή. Οι διαδικασίες της μοντελοποίησης, της ανάλυσης ευστάθειας και της σύνθεσης σθεναρών ελεγκτών (στατικών αλλά και κατά τμήματα γραμμικών) στην εργασία αυτή λαμβάνουν χώρα στο πεδίο του διακριτού χρόνου μετά από διακριτοποίηση του συνολικού συστήματος. Όσον αφορά στην ανάλυση σθεναρής ευστάθειας προτείνονται δύο προσεγγίσεις: • η πρώτη, βασιζόμενη σε ανάλυση ιδιαζουσών τιμών, είναι υπολογιστικά ελκυστική αλλά συνήθως δίδει συντηρητικά αποτελέσματα, • ενώ η δεύτερη, διατυπωμένη σαν ανισότητα πινάκων (LMI), είναι απαιτητική ως προς τον χρόνο υπολογισμού αλλά δίδει αποτελέσματα με μειωμένο συντηρητισμό. Όσον αφορά στην σύνθεση σθεναρών ελεγκτών ανατροφοδότησης κατάστασης μελετώνται οι εξής προσεγγίσεις: • Σύνθεση σθεναρής ευσταθειοποιούσας ανατροφοδότησης κατάστασης • Σύνθεση σθεναρής ευσταθειοποιούσας ανατροφοδότησης κατάστασης "εγγυημένου κόστους" που απαντάει στην συνδυασμένη απαίτηση ευστάθειας και επίδοσης • Σύνθεση σθεναρής ευσταθειοποιούσας ανατροφοδότησης κατάστασης με περιορισμό (Cοnstrained Controller) για ΝCS με "μικρή καθυστέρηση". Επέκταση των αποτελεσμάτων για ΝCS με "μεγάλη καθυστέρηση". Εφαρμογή των παραπάνω αποτελεσμάτων σε προβλήματα παρακολούθησης σταθερής εντολής (set point tracking). • Σύνθεση σθεναρής ευσταθειοποιούσας ανατροφοδότησης κατάστασης με περιορισμό (Constrained Controller), για ΝCS με μικρή και διακοπτική καθυστέρηση. / This research work is concerned with robustness issues arising in Νetworked Cοntrοlled Systems - ("ΝCS"), where the main sources of uncertainty are the time-varying network-induced delays. In this framework the presented results concern robust stability analysis and synthesis of robust controllers. The NCS studied consist of a Linear Time Invariant continuous time plant and a discrete time controller. This configuration includes a time driven (periodic) sampler (taking samples from the sensors with constant sampling period h) and an event–driven controller which transmits the control command via the network to the event–driven actuator. Two modeling approaches for Networked Controlled Systems (NCS) with uncertainly varying bounded transmission delays and static discrete--time control laws are presented. Different models are offered for each case, all linked to the objective of designing robust discrete-time controllers. It is analytically shown how the careful mixing of asynchronous (event--driven) and synchronized (clocked) signals can lead to discrete time uncertain (possibly switched) systems, where results form robust control analysis and synthesis can be applied. After showing the implications of these modelling results for control synthesis purposes, sufficient conditions for the robust stability are given for each approach and a comparison of the conservatism of results is discussed The first group of robust stability results (one for each of the two discrete-time NCS models) is based on a singular value formulation, which although conservative, is extremely simple and has low computational cost The second one is derived and expressed via Linear Matrix Inequalities (LMI) and yields less conservative results at the expense of higher computational cost. Regarding the synthesis of Robust controllers, the following four methodologies were developed: 1. Synthesis of Robust Static State feedback 2. Synthesis of Robust Static State feedback via the “Guaranteed Cost Formulation” which combines stability and performance design objectives 3. Synthesis of Constrained Robust feedback controller (with a Piecewise Affine Structure) which respects the constraints on the control effort and the state (or output). 4. The previous result (Constrained Robust feedback controller) is then generalized for set-point tracking and for various types of network-induced delays (small, large and switching delays)

Dans ce travail sont presentees quelques approches pour la synthese de controleurs robustes avec information partielle sur l'etat (retour de sortie) dans le cas de systemes a temps discret. Dans le cadre de commande predictive, la synthese decoule de la minimisation a chaque instant d'echantillonnage, d'une borne superieure d'un cout quadratique evalue sur un horizon temporel infini. Le probleme d'optimisation qui inclut des contraintes sur l'etat et la commande est formule comme un probleme de programmation semi definie a base d'inegalites matricielles lineaires. Deux voies generales sont poursuivies: l'une basee sur le concept d'ellipsoide invariant et synthese de compensateur dynamique de retour de sortie, l'autre basee sur une formulation etendue permettant la resolution d'un probleme de retour d'etat equivalent a celui du retour de sortie.

With the acceptance of the new Basel II banking regulation (implemented in South Africa in January 2008) the search for improved ways of modeling the most important banking activities has become very topical. Since the notion of Levy-process was introduced, it has emerged as an important tool for modeling economic variables in a Basel II framework. In this study, we investigate the stochastic dynamics of banking items that are driven by such processes. In particular, we discuss bank provisioning for loan losses and deposit withdrawals. The first type of provisioning is related to the earnings that the bank sets aside in order to cover loan defaults. In this case, we apply principles from robustness to a situation where the decision maker is a bank owner and the decision rule determines the optimal provisioning strategy for loan losses. In this regard, we formulate a dynamic banking loan loss model involving a provisioning portfolio consisting of provisions for expected losses and loan loss reserves for unexpected losses. Here, unexpected loan losses and provisioning for expected losses are modeled via a compound Poisson process and an exponential Levy process, respectively. We use historical evidence from OECD (Organization for Economic Corporation and Development) countries to support the fact that the provisions for loan losses-to-total assets ratio is negatively correlated with aggregate asset prices and the private credit-to-GDP ratio. Secondly, we construct models for provisioning for deposit withdrawals. In particular, we build stochastic dynamic models which enable us to analyze the interplay between deposit withdrawals and the provisioning for these withdrawals via Treasuries and reserves. Further insight is gained by considering a numerical problem and a simulation of the trajectory of the stochastic dynamics of the sum of the Treasuries and reserves. Since managing the risk that depositors will exercise their withdrawal option is an important aspect of this thesis, we consider the idea of a hedging provisioning strategy for deposit withdrawals in an incomplete market setting. In this spirit, we discuss an optimal risk management problem for a commercial bank whose main activity is to obtain funds through deposits from the public and use the Treasuries and reserves to cater for the resulting withdrawals. Finally, we provide a brief analysis of some of the issues arising from the dynamic models of the banking items derived. / Thesis (Ph.D. (Computer, Statistical and Mathematical Sciences))--North-West University, Potchefstroom Campus, 2008.

With the acceptance of the new Basel II banking regulation (implemented in South Africa in January 2008) the search for improved ways of modeling the most important banking activities has become very topical. Since the notion of Levy-process was introduced, it has emerged as an important tool for modeling economic variables in a Basel II framework. In this study, we investigate the stochastic dynamics of banking items that are driven by such processes. In particular, we discuss bank provisioning for loan losses and deposit withdrawals. The first type of provisioning is related to the earnings that the bank sets aside in order to cover loan defaults. In this case, we apply principles from robustness to a situation where the decision maker is a bank owner and the decision rule determines the optimal provisioning strategy for loan losses. In this regard, we formulate a dynamic banking loan loss model involving a provisioning portfolio consisting of provisions for expected losses and loan loss reserves for unexpected losses. Here, unexpected loan losses and provisioning for expected losses are modeled via a compound Poisson process and an exponential Levy process, respectively. We use historical evidence from OECD (Organization for Economic Corporation and Development) countries to support the fact that the provisions for loan losses-to-total assets ratio is negatively correlated with aggregate asset prices and the private credit-to-GDP ratio. Secondly, we construct models for provisioning for deposit withdrawals. In particular, we build stochastic dynamic models which enable us to analyze the interplay between deposit withdrawals and the provisioning for these withdrawals via Treasuries and reserves. Further insight is gained by considering a numerical problem and a simulation of the trajectory of the stochastic dynamics of the sum of the Treasuries and reserves. Since managing the risk that depositors will exercise their withdrawal option is an important aspect of this thesis, we consider the idea of a hedging provisioning strategy for deposit withdrawals in an incomplete market setting. In this spirit, we discuss an optimal risk management problem for a commercial bank whose main activity is to obtain funds through deposits from the public and use the Treasuries and reserves to cater for the resulting withdrawals. Finally, we provide a brief analysis of some of the issues arising from the dynamic models of the banking items derived. / Thesis (Ph.D. (Computer, Statistical and Mathematical Sciences))--North-West University, Potchefstroom Campus, 2008.

Thesis (Ph. D.)--Ohio State University, 2005. / Available online via OhioLINK's ETD Center; full text release delayed at author's request until 2006 Aug 15.

Ο σκοπός αυτής της διπλωματικής είναι η ανάπτυξη ενός προσαρμοστικού ελεγκτή για έναν εύκαμπτο ρομποτικό βραχίονα. Οι μετρήσεις του συστήματος θεωρούνται πως παρεμβάλλονται από θόρυβο, του οποίου τα όρια είναι γνωστά εξ’αρχής. Ένας Set Memebership εκτιμητής υπολογίζει το δυνατό set (ορθότοπο) μέσα στο οποίο βρίσκονται οι τιμές του διανύσματος των παραμέτρων. Από τις ακμές του ορθοτόπου αυτού προκύπτουν τα όρια μέσα στα οποία βρίσκονται οι παράμετροι του συστήματος, τα οποία χρησιμοποιούνται για τον υπολογισμό της αβεβαιότητας της εκτίμησης της εξόδου του συστήματος. Ο ελεγκτής καθορίζει τα κέρδη του μέσα σε μια online βελτιστοποίηση ενός κόστους, το οποίο βάζει κάποια βάρη στην προσπάθεια του ελέγχου (control effort), στην προκλημένη αβεβαιότητα στην έξοδο του συστήματος αλλά και στο σφάλμα παρακολούθησης της εξόδου με ένα σήμα αναφοράς. Μετά την εφαρμογή του ελεγκτή, ελέγχεται η ευστάθεια των οριακών κλειστών συστημάτων που προκύπτουν από την εφαρμογή κάθε πιθανού νόμου ελέγχου. Εξετάζεται επίσης η συμπεριφορά του Set Memebership εκτιμητή σε περίπτωση σφάλματος, δηλαδή στην περίπτωση που το σύστημά μας αλλάζει καθώς δουλεύει ο έλεγχος. / The development of an adaptive controller for a flexible link manipulator is the subject of this diploma thesis. The system’s measurements are assumed to be corrupted with noise of a priori known bounds. A Set Membership Identifier computes the feasible set (orthotope) within which the parameter vector resides. The orthotope’s vertices provide the parameter-vector’s bounds, which are used to compute the predicted system-output uncertainty. The controller tunes its gains through an on-line minimization of a cost that penalizes the control effort, the induced uncertainty on the system output, and the tracking error. After the application of the controller, the stability of the ‘extreme’ closed loop systems, derived from every possible control law, is checked. The behavior of the Set Membership Identifier is checked in the case where a fault occurs, which means that there is a change in our system’s structure while the controller is functioning.

Thesis (MScEng)-- Stellenbosch University, 2013. / ENGLISH ABSTRACT: In this thesis the design, analysis, implementation, and verification of a fault-tolerant unmanned aerial vehicle (UAV) flight control system which is robust to structural damage causing the natural flight dynamics of the vehicle to become asymmetric, is presented. The main purpose of the robust control architecture is to maintain flight stability after damage has occurred. The control system must be able to handle an abrupt change from an undamaged to a damaged state, and must also not depend on explicit knowledge of the damage. A robust control approach is therefore preferred above an adaptive control approach. As a secondary objective, the system must provide robust flight performance to ensure adequate response times and acceptable transients’ behaviour, both in normal flight, and after damage has occurred. An asymmetric six degrees of freedom equations of motion model is derived. The model accounts for the changes in the aerodynamic model of the aircraft as well as changes in the centre of gravity location. Vortex lattice techniques are used to determine the aerodynamic coefficients of the aircraft for damage to the main wing resulting in 0% to 40% spanwise lifting surface loss. A sequential quadratic programming optimisation algorithm is applied to the force and moment equations to find the trim flight state and actuator deflections of the asymmetric aircraft for constant airspeed and altitude. The trim flight state can be further constrained to force zero bank angle, zero sideslip angle or a desired relative weighting of nonzero bank angle and nonzero sideslip angle. The calculated trim actuator deflections are compared to the physical deflection limits to determine the feasibility of maintaining trim flight for different percentages of wing loss. Assuming that a valid trim condition exists, the relative stability of the aircraft’s natural modes is analysed as a function of percentage wing loss by tracing the locus of the open-loop poles. An acceleration-based flight control architecture is designed and implemented, and the robustness of the flight control stability and performance is analysed as a function of percentage wing loss. The robustness and performance of the flight control system is verified with a nonlinear simulation for spanwise wing loss from 0 to 40%. Practical flight tests are performed to verify the robustness and performance of the flight control systems to in-flight damage. A detachable wing with release mechanism is designed and manufactured to simulate 20% wing loss. The flight control system is implemented on a practical UAV and a successful flight test shows that it performs fully autonomous flight control, and is able to accommodate an in-flight partial wing loss. / AFRIKAANSE OPSOMMING: In hierdie tesis word die ontwerp, analise, implementasie en verifikasie van ’n fout-verdraende onbemande vliegtuig beheerstelsel wat robuust is tot strukturele skade wat die natuurlike vlug dinamika van die voertuig asimmetries maak, voorgestel. Die hoofdoel van hierdie robuuste beheer argitektuur is om stabiliteit te verseker na die skade aangerig is. Die beheerstelsel moet die skielike verandering van normale na beskadigde vlug hanteer sonder enige eksplisiete kennis daarvan. Dus word ’n robuuste beheer aanslag verkies bo ’n aanpassende beheer struktuur. Tweedens moet die vlugbeheerstelsel robuust genoeg wees om steeds die gewenste reaksietyd en aanvaarbare oorgangsverskynsels te kan hanteer, tydens beide normale en beskadigde vlug. ’n Asimmetriese ses grade van vryheid beweginsvergelykings model word afgelei. Die model het die vermoë om veranderinge in die aerodinamiese model van die vliegtuig, sowel as massamiddelpunt verskuiwing, voor te stel. “Vortex Lattice” metodes is gebruik om die aerodinamiese koëffisiënte van die beskadigde vlerk voor te stel tussen 0% en 40% verlies. ’n Sekwensiële kwadratiese programmering optimiserings algorithme is aangewend op die krag en moment vergelykings om die ekwilibrium vlug toestand en aktueerder defleksies te vind vir ’n asimmetriese vliegtuig met konstante lugspoed en hoogte. Die ekwilibrium vlug toestand word verder beperk deur ’n nul rolhoek, ’n nul sygliphoek of ’n relatiewe weging van die twee. Die bepaalde ekwilibrium defleksies word dan vergelyk met die fisiese limiete om hulle geldigheid te bepaal vir ekwilibrium vlug. As ’n geldige ekwilibrium toestand bestaan, kan die relatiewe stabiliteit van die vliegtuig se natuurlike modusse ontleed word as ’n persentasie van vlerkverlies deur die wortellokusse van die ooplus pole na te gaan. ’n Versnellings-gebaseerde vlug beheerstelsel argitektuur is ontwerp en geïmplementeer. Daarna is die robuustheid ontleed as ’n funksie van die persentasie vlerkverlies. Die robuustheid en gedrag van hierdie vlugbeheerstelsel is geverifieer met ’n nie-linêre simulasie vir 0 tot 40% vlerkverlies. Praktiese vlugtoetse is onderneem om die robuustheid en gedrag tydens/na skade gedurende ’n vlug, te verifeer. ’n Vlerkverlies meganisme is ontwerp en vervaardig om 20% vlerkverlies te simuleer. Die vlugbeheerstelsel is geïmplementeer op ’n onbemande vliegtuig en die daaropvolgende suksesvolle vlug lewer bewys dat die vlugbeheerstelsel wel skade, in die vorm van gedeeltelike vlerkverlies, tydens vlug kan hanteer.