Characterization of Stability Region for General Autonomous Nonlinear Dynamical Systems

The existing characterization of stability regions was developed under the assumption that limit sets on the stability boundary are exclusively composed of hyperbolic equilibrium points and closed orbits. The characterizations derived in this technical note are a generalization of existing results in the theory of stability regions. A characterization of the stability boundary of general autonomous nonlinear dynamical systems is developed under the assumption that limit sets on the stability boundary are composed of a countable number of disjoint and indecomposable components, which can be equilibrium points, closed orbits, quasi-periodic solutions and even chaotic invariant sets.

Transverse pseudo-nonlinear effects measured in solid-state laser materials using a sensitive time-resolved technique

We present a detailed study of the Baryscan technique, a new efficient alternative to the widespread Z-scan technique which has been demonstrated [Opt. Lett. 36:8, 2011] to reach among the highest sensitivity levels. This method is based upon the measurement of optical nonlinearities by means of beam centroid displacements with a position sensitive detector and is able to deal with any kind of lensing effect. This technique is applied here to measure pump-induced electronic refractive index changes (population lens), which can be discriminated from parasitic thermal effects by using a time-resolved Baryscan experiment. This method is validated by evaluating the polarizability variation at the origin of the population lens observed in the reference Cr3+:GSGG laser material.

A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.

Basketball from perspective of nonlinear complex systems

Doctoral program: Motor praxiology, physical education and sport training

Motion control and real-time systems: an approach to trajectory rebuilding in non-deterministic networks

Motion control is a sub-field of automation, in which the position and/or velocity of machines are controlled using some type of device. In motion control the position, velocity, force, pressure, etc., profiles are designed in such a way that the different mechanical parts work as an harmonious whole in which a perfect synchronization must be achieved. The real-time exchange of information in the distributed system that is nowadays an industrial plant plays an important role in order to achieve always better performance, better effectiveness and better safety. The network for connecting field devices such as sensors, actuators, field controllers such as PLCs, regulators, drive controller etc., and man-machine interfaces is commonly called fieldbus. Since the motion transmission is now task of the communication system, and not more of kinematic chains as in the past, the communication protocol must assure that the desired profiles, and their properties, are correctly transmitted to the axes then reproduced or else the synchronization among the different parts is lost with all the resulting consequences. In this thesis, the problem of trajectory reconstruction in the case of an event-triggered communication system is faced. The most important feature that a real-time communication system must have is the preservation of the following temporal and spatial properties: absolute temporal consistency, relative temporal consistency, spatial consistency. Starting from the basic system composed by one master and one slave and passing through systems made up by many slaves and one master or many masters and one slave, the problems in the profile reconstruction and temporal properties preservation, and subsequently the synchronization of different profiles in network adopting an event-triggered communication system, have been shown. These networks are characterized by the fact that a common knowledge of the global time is not available. Therefore they are non-deterministic networks. Each topology is analyzed and the proposed solution based on phase-locked loops adopted for the basic master-slave case has been improved to face with the other configurations.

Nonlinear Control Strategies for Cooperative Control of Multi-Robot Systems

This thesis deals with distributed control strategies for cooperative control of multi-robot systems. Specifically, distributed coordination strategies are presented for groups of mobile robots. The formation control problem is initially solved exploiting artificial potential fields. The purpose of the presented formation control algorithm is to drive a group of mobile robots to create a completely arbitrarily shaped formation. Robots are initially controlled to create a regular polygon formation. A bijective coordinate transformation is then exploited to extend the scope of this strategy, to obtain arbitrarily shaped formations. For this purpose, artificial potential fields are specifically designed, and robots are driven to follow their negative gradient. Artificial potential fields are then subsequently exploited to solve the coordinated path tracking problem, thus making the robots autonomously spread along predefined paths, and move along them in a coordinated way. Formation control problem is then solved exploiting a consensus based approach. Specifically, weighted graphs are used both to define the desired formation, and to implement collision avoidance. As expected for consensus based algorithms, this control strategy is experimentally shown to be robust to the presence of communication delays. The global connectivity maintenance issue is then considered. Specifically, an estimation procedure is introduced to allow each agent to compute its own estimate of the algebraic connectivity of the communication graph, in a distributed manner. This estimate is then exploited to develop a gradient based control strategy that ensures that the communication graph remains connected, as the system evolves. The proposed control strategy is developed initially for single-integrator kinematic agents, and is then extended to Lagrangian dynamical systems.

Cache-aware development of high integrity real-time systems

Cost, performance and availability considerations are forcing even the most conservative high-integrity embedded real-time systems industry to migrate from simple hardware processors to ones equipped with caches and other acceleration features. This migration disrupts the practices and solutions that industry had developed and consolidated over the years to perform timing analysis. Industry that are confident with the efficiency/effectiveness of their verification and validation processes for old-generation processors, do not have sufficient insight on the effects of the migration to cache-equipped processors. Caches are perceived as an additional source of complexity, which has potential for shattering the guarantees of cost- and schedule-constrained qualification of their systems. The current industrial approach to timing analysis is ill-equipped to cope with the variability incurred by caches. Conversely, the application of advanced WCET analysis techniques on real-world industrial software, developed without analysability in mind, is hardly feasible. We propose a development approach aimed at minimising the cache jitters, as well as at enabling the application of advanced WCET analysis techniques to industrial systems. Our approach builds on:(i) identification of those software constructs that may impede or complicate timing analysis in industrial-scale systems; (ii) elaboration of practical means, under the model-driven engineering (MDE) paradigm, to enforce the automated generation of software that is analyzable by construction; (iii) implementation of a layout optimisation method to remove cache jitters stemming from the software layout in memory, with the intent of facilitating incremental software development, which is of high strategic interest to industry. The integration of those constituents in a structured approach to timing analysis achieves two interesting properties: the resulting software is analysable from the earliest releases onwards - as opposed to becoming so only when the system is final - and more easily amenable to advanced timing analysis by construction, regardless of the system scale and complexity.

Nonlinear Control of Magnetically Actuated Spacecraft

The topic of this thesis is the feedback stabilization of the attitude of magnetically actuated spacecraft. The use of magnetic coils is an attractive solution for the generation of control torques on small satellites flying inclined low Earth orbits, since magnetic control systems are characterized by reduced weight and cost, higher reliability, and require less power with respect to other kinds of actuators. At the same time, the possibility of smooth modulation of control torques reduces coupling of the attitude control system with flexible modes, thus preserving pointing precision with respect to the case when pulse-modulated thrusters are used. The principle based on the interaction between the Earth's magnetic field and the magnetic field generated by the set of coils introduces an inherent nonlinearity, because control torques can be delivered only in a plane that is orthogonal to the direction of the geomagnetic field vector. In other words, the system is underactuated, because the rotational degrees of freedom of the spacecraft, modeled as a rigid body, exceed the number of independent control actions. The solution of the control issue for underactuated spacecraft is also interesting in the case of actuator failure, e.g. after the loss of a reaction-wheel in a three-axes stabilized spacecraft with no redundancy. The application of well known control strategies is no longer possible in this case for both regulation and tracking, so that new methods have been suggested for tackling this particular problem. The main contribution of this thesis is to propose continuous time-varying controllers that globally stabilize the attitude of a spacecraft, when magneto-torquers alone are used and when a momentum-wheel supports magnetic control in order to overcome the inherent underactuation. A kinematic maneuver planning scheme, stability analyses, and detailed simulation results are also provided, with new theoretical developments and particular attention toward application considerations.

Nonlinear constrained and saturated control of power electronics and electromechanical systems

Power electronic converters are extensively adopted for the solution of timely issues, such as power quality improvement in industrial plants, energy management in hybrid electrical systems, and control of electrical generators for renewables. Beside nonlinearity, this systems are typically characterized by hard constraints on the control inputs, and sometimes the state variables. In this respect, control laws able to handle input saturation are crucial to formally characterize the systems stability and performance properties. From a practical viewpoint, a proper saturation management allows to extend the systems transient and steady-state operating ranges, improving their reliability and availability. The main topic of this thesis concern saturated control methodologies, based on modern approaches, applied to power electronics and electromechanical systems. The pursued objective is to provide formal results under any saturation scenario, overcoming the drawbacks of the classic solution commonly applied to cope with saturation of power converters, and enhancing performance. For this purpose two main approaches are exploited and extended to deal with power electronic applications: modern anti-windup strategies, providing formal results and systematic design rules for the anti-windup compensator, devoted to handle control saturation, and “one step” saturated feedback design techniques, relying on a suitable characterization of the saturation nonlinearity and less conservative extensions of standard absolute stability theory results. The first part of the thesis is devoted to present and develop a novel general anti-windup scheme, which is then specifically applied to a class of power converters adopted for power quality enhancement in industrial plants. In the second part a polytopic differential inclusion representation of saturation nonlinearity is presented and extended to deal with a class of multiple input power converters, used to manage hybrid electrical energy sources. The third part regards adaptive observers design for robust estimation of the parameters required for high performance control of power systems.

Nonlinear Observers for Sensorless Control of Permanent Magnet Synchronous Motors

In this thesis, the industrial application of control a Permanent Magnet Synchronous Motor in a sensorless configuration has been faced, and in particular the task of estimating the unknown “parameters” necessary for the application of standard motor control algorithms. In literature several techniques have been proposed to cope with this task, among them the technique based on model-based nonlinear observer has been followed. The hypothesis of neglecting the mechanical dynamics from the motor model has been applied due to practical and physical considerations, therefore only the electromagnetic dynamics has been used for the observers design. First observer proposed is based on stator currents and Stator Flux dynamics described in a generic rotating reference frame. Stator flux dynamics are known apart their initial conditions which are estimated, with speed that is also unknown, through the use of the Adaptive Theory. The second observer proposed is based on stator currents and Rotor Flux dynamics described in a self-aligning reference frame. Rotor flux dynamics are described in the stationary reference frame exploiting polar coordinates instead of classical Cartesian coordinates, by means the estimation of amplitude and speed of the rotor flux. The stability proof is derived in a Singular Perturbation Framework, which allows for the use the current estimation errors as a measure of rotor flux estimation errors. The stability properties has been derived using a specific theory for systems with time scale separation, which guarantees a semi-global practical stability. For the two observer ideal simulations and real simulations have been performed to prove the effectiveness of the observers proposed, real simulations on which the effects of the Inverter nonlinearities have been introduced, showing the already known problems of the model-based observers for low speed applications.

Hardware/Software Design of Dynamic Real-Time Schedulers for Embedded Multiprocessor Systems

The new generation of multicore processors opens new perspectives for the design of embedded systems. Multiprocessing, however, poses new challenges to the scheduling of real-time applications, in which the ever-increasing computational demands are constantly flanked by the need of meeting critical time constraints. Many research works have contributed to this field introducing new advanced scheduling algorithms. However, despite many of these works have solidly demonstrated their effectiveness, the actual support for multiprocessor real-time scheduling offered by current operating systems is still very limited. This dissertation deals with implementative aspects of real-time schedulers in modern embedded multiprocessor systems. The first contribution is represented by an open-source scheduling framework, which is capable of realizing complex multiprocessor scheduling policies, such as G-EDF, on conventional operating systems exploiting only their native scheduler from user-space. A set of experimental evaluations compare the proposed solution to other research projects that pursue the same goals by means of kernel modifications, highlighting comparable scheduling performances. The principles that underpin the operation of the framework, originally designed for symmetric multiprocessors, have been further extended first to asymmetric ones, which are subjected to major restrictions such as the lack of support for task migrations, and later to re-programmable hardware architectures (FPGAs). In the latter case, this work introduces a scheduling accelerator, which offloads most of the scheduling operations to the hardware and exhibits extremely low scheduling jitter. The realization of a portable scheduling framework presented many interesting software challenges. One of these has been represented by timekeeping. In this regard, a further contribution is represented by a novel data structure, called addressable binary heap (ABH). Such ABH, which is conceptually a pointer-based implementation of a binary heap, shows very interesting average and worst-case performances when addressing the problem of tick-less timekeeping of high-resolution timers.

Operating System Contribution to Composable Timing Behaviour in High-Integrity Real-Time Systems

The development of High-Integrity Real-Time Systems has a high footprint in terms of human, material and schedule costs. Factoring functional, reusable logic in the application favors incremental development and contains costs. Yet, achieving incrementality in the timing behavior is a much harder problem. Complex features at all levels of the execution stack, aimed to boost average-case performance, exhibit timing behavior highly dependent on execution history, which wrecks time composability and incrementaility with it. Our goal here is to restitute time composability to the execution stack, working bottom up across it. We first characterize time composability without making assumptions on the system architecture or the software deployment to it. Later, we focus on the role played by the real-time operating system in our pursuit. Initially we consider single-core processors and, becoming less permissive on the admissible hardware features, we devise solutions that restore a convincing degree of time composability. To show what can be done for real, we developed TiCOS, an ARINC-compliant kernel, and re-designed ORK+, a kernel for Ada Ravenscar runtimes. In that work, we added support for limited-preemption to ORK+, an absolute premiere in the landscape of real-word kernels. Our implementation allows resource sharing to co-exist with limited-preemptive scheduling, which extends state of the art. We then turn our attention to multicore architectures, first considering partitioned systems, for which we achieve results close to those obtained for single-core processors. Subsequently, we shy away from the over-provision of those systems and consider less restrictive uses of homogeneous multiprocessors, where the scheduling algorithm is key to high schedulable utilization. To that end we single out RUN, a promising baseline, and extend it to SPRINT, which supports sporadic task sets, hence matches real-world industrial needs better. To corroborate our results we present findings from real-world case studies from avionic industry.

Management control systems : subcomponents, optimal design and the role of time as a contingency

Management Control System (MCS) research is undergoing turbulent times. For a long time related to cybernetic instruments of management accounting only, MCS are increasingly seen as complex systems comprising not only formal accounting-driven instruments, but also informal mechanisms of control based on organizational culture. But not only have the means of MCS changed; researchers increasingly ap-ply MCS to organizational goals other than strategy implementation.rnrnTaking the question of "How do I design a well-performing MCS?" as a starting point, this dissertation aims at providing a comprehensive and integrated overview of the "current-state" of MCS research. Opting for a definition of MCS, broad in terms of means (all formal as well as informal MCS instruments), but focused in terms of objectives (behavioral control only), the dissertation contributes to MCS theory by, a) developing an integrated (contingency) model of MCS, describing its contingencies, as well as its subcomponents, b) refining the equifinality model of Gresov/Drazin (1997), c) synthesizing research findings from contingency and configuration research concerning MCS, taking into account case studies on research topics such as ambi-dexterity, equifinality and time as a contingency.