Models and Feedback Stabilization of Open Quantum Systems

At the quantum level, feedback-loops have to take into account measurement back-action. We present here the structure of the Markovian models including such back-action and sketch two stabilization methods: measurement-based feedback where an open quantum system is stabilized by a classical controller; coherent or autonomous feedback where a quantum system is stabilized by a quantum controller with decoherence (reservoir engineering). We begin to explain these models and methods for the photon box experiments realized in the group of Serge Haroche (Nobel Prize 2012). We present then these models and methods for general open quantum systems.Comment: Extended version of the paper attached to an invited conference for the International Congress of Mathematicians in Seoul, August 13 - 21, 201

Stabilization of cascaded nonlinear systems under sampling and delays

Over the last decades, the methodologies of dynamical systems and control theory have been playing an increasingly relevant role in a lot of situations of practical interest. Though, a lot of theoretical problem still remain unsolved. Among all, the ones concerning stability and stabilization are of paramount importance. In order to stabilize a physical (or not) system, it is necessary to acquire and interpret heterogeneous information on its behavior in order to correctly intervene on it. In general, those information are not available through a continuous flow but are provided in a synchronous or asynchronous way. This issue has to be unavoidably taken into account for the design of the control action. In a very natural way, all those heterogeneities define an hybrid system characterized by both continuous and discrete dynamics. This thesis is contextualized in this framework and aimed at proposing new methodologies for the stabilization of sampled-data nonlinear systems with focus toward the stabilization of cascade dynamics. In doing so, we shall propose a small number of tools for constructing sampled-data feedback laws stabilizing the origin of sampled-data nonlinear systems admitting cascade interconnection representations. To this end, we shall investigate on the effect of sampling on the properties of the continuous-time system while enhancing design procedures requiring no extra assumptions over the sampled-data equivalent model. Finally, we shall show the way sampling positively affects nonlinear retarded dynamics affected by a fixed and known time-delay over the input signal by enforcing on the implicit cascade representation the sampling process induces onto the retarded system

A robust LMI approach on nonlinear feedback stabilization of continuous state-delay systems with Lipschitzian nonlinearities : experimental validation

This paper suggests a novel nonlinear state-fe edback stabilization control law using linear matrix inequalities for a class oftime-delayed nonlinear dynamic systems with Lipschitz nonlinearity conditions. Based on the Lyapunov–Krasovskiistability theory, the asymptotic stabilization criterion is derived in the linear matrix inequality form and the coef¿cients ofthe nonlinear state-feedback controller are determined. Meanwhile, an appropriate criterion to ¿nd the proper feedbackgain matrix F is also provided. The robustness purpose against nonlinear functions and time delays is guaranteed in thisscheme. Moreover , the problem of robust H!performance analysis for a class of nonlinear time-delayed system s withexternal disturbance is studied in this paper. Simulations are presented to demonstrate the pro¿ciency of the offeredtechnique. For this purpos e, an unstable nonlinear numerical system and a rotary inverted pendulum system have beenstudied in the simulation section. Moreover, an experimental study of the practical rotary inverted pendul um system isprovided. These results con¿rm the expected satisfactory performance of the suggested method.Peer ReviewedPostprint (author's final draft

Online identification and nonlinear control of the electrically stimulated quadriceps muscle

A new approach for estimating nonlinear models of the electrically stimulated quadriceps muscle group under nonisometric conditions is investigated. The model can be used for designing controlled neuro-prostheses. In order to identify the muscle dynamics (stimulation pulsewidth-active knee moment relation) from discrete-time angle measurements only, a hybrid model structure is postulated for the shank-quadriceps dynamics. The model consists of a relatively well known time-invariant passive component and an uncertain time-variant active component. Rigid body dynamics, described by the Equation of Motion (EoM), and passive joint properties form the time-invariant part. The actuator, i.e. the electrically stimulated muscle group, represents the uncertain time-varying section. A recursive algorithm is outlined for identifying online the stimulated quadriceps muscle group. The algorithm requires EoM and passive joint characteristics to be known a priori. The muscle dynamics represent the product of a continuous-time nonlinear activation dynamics and a nonlinear static contraction function described by a Normalised Radial Basis Function (NRBF) network which has knee-joint angle and angular velocity as input arguments. An Extended Kalman Filter (EKF) approach is chosen to estimate muscle dynamics parameters and to obtain full state estimates of the shank-quadriceps dynamics simultaneously. The latter is important for implementing state feedback controllers. A nonlinear state feedback controller using the backstepping method is explicitly designed whereas the model was identified a priori using the developed identification procedure

Vehicle dynamics virtual sensing and advanced motion control for highly skilled autonomous vehicles

This dissertation is aimed at elucidating the path towards the development of a future generation of highly-skilled autonomous vehicles (HSAV). In brief, it is envisaged that future HSAVs will be able to exhibit advanced driving skills to maintain the vehicle within stable limits in spite of the driving conditions (limits of handling) or environmental adversities (e.g. low manoeuvrability surfaces). Current research lines on intelligent systems indicate that such advanced driving behaviour may be realised by means of expert systems capable of monitoring the current vehicle states, learning the road friction conditions, and adapting their behaviour depending on the identified situation. Such adaptation skills are often exhibited by professional motorsport drivers, who fine-tune their driving behaviour depending on the road geometry or tyre-friction characteristics. On this basis, expert systems incorporating advanced driving functions inspired by the techniques seen on highly-skilled drivers (e.g. high body slip control) are proposed to extend the operating region of autonomous vehicles and achieve high-level automation (e.g. manoeuvrability enhancement on low-adherence surfaces). Specifically, two major research topics are covered in detail in this dissertation to conceive these expert systems: vehicle dynamics virtual sensing and advanced motion control. With regards to the former, a comprehensive research is undertaken to propose virtual sensors able to estimate the vehicle planar motion states and learn the road friction characteristics from readily available measurements. In what concerns motion control, systems to mimic advanced driving skills and achieve robust path-following ability are pursued. An optimal coordinated action of different chassis subsystems (e.g. steering and individual torque control) is sought by the adoption of a centralised multi-actuated system framework. The virtual sensors developed in this work are validated experimentally with the Vehicle-Based Objective Tyre Testing (VBOTT) research testbed of JAGUAR LAND ROVER and the advanced motion control functions with the Multi-Actuated Ground Vehicle “DevBot” of ARRIVAL and ROBORACE.Diese Dissertation soll den Weg zur Entwicklung einer zukünftigen Generation hochqualifizierter autonomer Fahrzeuge (HSAV) aufzeigen. Kurz gesagt, es ist beabsichtigt, dass zukünftige HSAVs fortgeschrittene Fahrfähigkeiten aufweisen können, um das Fahrzeug trotz der Fahrbedingungen (Grenzen des Fahrverhaltens) oder Umgebungsbedingungen (z. B. Oberflächen mit geringer Manövrierfähigkeit) in stabilen Grenzen zu halten. Aktuelle Forschungslinien zu intelligenten Systemen weisen darauf hin, dass ein solches fortschrittliches Fahrverhalten mit Hilfe von Expertensystemen realisiert werden kann, die in der Lage sind, die aktuellen Fahrzeugzustände zu überwachen, die Straßenreibungsbedingungen kennenzulernen und ihr Verhalten in Abhängigkeit von der ermittelten Situation anzupassen. Solche Anpassungsfähigkeiten werden häufig von professionellen Motorsportfahrern gezeigt, die ihr Fahrverhalten in Abhängigkeit von der Straßengeometrie oder den Reifenreibungsmerkmalen abstimmen. Auf dieser Grundlage werden Expertensysteme mit fortschrittlichen Fahrfunktionen vorgeschlagen, die auf den Techniken hochqualifizierter Fahrer basieren (z. B. hohe Schlupfregelung), um den Betriebsbereich autonomer Fahrzeuge zu erweitern und eine Automatisierung auf hohem Niveau zu erreichen (z. B. Verbesserung der Manövrierfähigkeit auf niedrigem Niveau) -haftende Oberflächen). Um diese Expertensysteme zu konzipieren, werden zwei große Forschungsthemen in dieser Dissertation ausführlich behandelt: Fahrdynamik-virtuelle Wahrnehmung und fortschrittliche Bewegungssteuerung. In Bezug auf erstere wird eine umfassende Forschung durchgeführt, um virtuelle Sensoren vorzuschlagen, die in der Lage sind, die Bewegungszustände der Fahrzeugebenen abzuschätzen und die Straßenreibungseigenschaften aus leicht verfügbaren Messungen kennenzulernen. In Bezug auf die Bewegungssteuerung werden Systeme zur Nachahmung fortgeschrittener Fahrfähigkeiten und zum Erzielen einer robusten Wegfolgefähigkeit angestrebt. Eine optimale koordinierte Wirkung verschiedener Fahrgestellsubsysteme (z. B. Lenkung und individuelle Drehmomentsteuerung) wird durch die Annahme eines zentralisierten, mehrfach betätigten Systemrahmens angestrebt. Die in dieser Arbeit entwickelten virtuellen Sensoren wurden experimentell mit dem Vehicle-Based Objective Tyre Testing (VBOTT) - Prüfstand von JAGUAR LAND ROVER und den fortschrittlichen Bewegungssteuerungsfunktionen mit dem mehrfach betätigten Bodenfahrzeug ”DevBot” von ARRIVAL und ROBORACE validiert

Adaptive Stabilization of Stochastic Nonlinear Systems Disturbed by Unknown Time Delay and Covariance Noise

This paper considers a more general stochastic nonlinear time-delay system driven by unknown covariance noise and investigates its adaptive state-feedback control problem. As a remarkable feature, the growth assumptions imposed on delay-dependent nonlinear terms are removed. Then, with the help of Lyapunov-Krasovskii functionals and adaptive backstepping technique, an adaptive state-feedback controller is constructed by overcoming the negative effects brought by unknown time delay and covariance noise. Based on the designed controller, the closed-loop system can be guaranteed to be globally asymptotically stable (GAS) in probability. Finally, a simulation example demonstrates the effectiveness of the proposed scheme