Novel Computing Paradigms using Oscillators

This dissertation is concerned with new ways of using oscillators to perform computational tasks. Specifically, it introduces methods for building finite state machines (for general-purpose Boolean computation) as well as Ising machines (for solving combinatorial optimization problems) using coupled oscillator networks.But firstly, why oscillators? Why use them for computation?An important reason is simply that oscillators are fascinating. Coupled oscillator systems often display intriguing synchronization phenomena where spontaneous patterns arise. From the synchronous flashing of fireflies to Huygens' clocks ticking in unison, from the molecular mechanism of circadian rhythms to the phase patterns in oscillatory neural circuits, the observation and study of synchronization in coupled oscillators has a long and rich history. Engineers across many disciplines have also taken inspiration from these phenomena, e.g., to design high-performance radio frequency communication circuits and optical lasers. To be able to contribute to the study of coupled oscillators and leverage them in novel paradigms of computing is without question an interesting andfulfilling quest in and of itself.Moreover, as Moore's Law nears its limits, new computing paradigms that are different from mere conventional complementary metal–oxide–semiconductor (CMOS) scaling have become an important area of exploration. One broad direction aims to improve CMOS performance using device technology such as fin field-effect transistors (FinFET) and gate-all-around (GAA) FETs. Other new computing schemes are based on non-CMOS material and device technology, e.g., graphene, carbon nanotubes, memristive devices, optical devices, etc.. Another growing trend in both academia and industry is to build digital application-specific integrated circuits (ASIC) suitable for speeding up certain computational tasks, often leveraging the parallel nature of unconventional non-von Neumann architectures. These schemes seek to circumvent the limitations posed at the device level through innovations at the system/architecture level.Our work on oscillator-based computation represents a direction that is different from the above and features several points of novelty and attractiveness. Firstly, it makes meaningful use of nonlinear dynamical phenomena to tackle well-defined computational tasks that span analog and digital domains. It also differs from conventional computational systems at the fundamental logic encoding level, using timing/phase of oscillation as opposed to voltage levels to represent logic values. These differences bring about several advantages. The change of logic encoding scheme has several device- and system-level benefits related to noise immunity and interference resistance. The use of nonlinear oscillator dynamics allows our systems to address problems difficult for conventional digital computation. Furthermore, our schemes are amenable to realizations using almost all types of oscillators, allowing a wide variety of devices from multiple physical domains to serve as the substrate for computing. This ability to leverage emerging multiphysics devices need not put off the realization of our ideas far into the future. Instead, implementations using well-established circuit technology are already both practical and attractive.This work also differs from all past work on oscillator-based computing, which mostly focuses on specialized image preprocessing tasks, such as edge detection, image segmentation and pattern recognition. Perhaps its most unique feature is that our systems use transitions between analog and digital modes of operation --- unlike other existing schemes that simply couple oscillators and let their phases settle to a continuum of values, we use a special type of injection locking to make each oscillator settle to one of the several well-defined multistable phase-locked states, which we use to encode logic values for computation. Our schemes of oscillator-based Boolean and Ising computation are built upon this digitization of phase; they expand the scope of oscillator-based computing significantly.Our ideas are built on years of past research in the modelling, simulation and analysis of oscillators. While there is a considerable amount of literature (arguably since Christiaan Huygens wrote about his observation of synchronized pendulum clocks in the 17th century) analyzing the synchronization phenomenon from different perspectives at different levels, we have been able to further develop the theory of injection locking, connecting the dots to find a path of analysis that starts from the low-level differential equations of individual oscillators and arrives at phase-based models and energy landscapes of coupled oscillator systems. This theoretical scaffolding is able not only to explain the operation of oscillator-based systems, but also to serve as the basis for simulation and design tools. Building on this, we explore the practical design of our proposed systems, demonstrate working prototypes, as well as develop the techniques, tools and methodologies essential for the process

Dynamic optimization with path constraints

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 1998.Includes bibliographical references (p. 381-391).by William Francis Feehery.Ph.D

Robust stability assessment for future power systems

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018.Cataloged from PDF version of thesis. "Due to the condition of the original material, there are unavoidable flaws in this reproduction. Some pages in the original document contain text that is illegible"--Disclaimer Notice page.Includes bibliographical references (pages 119-128).Loss of stability in electrical power systems may eventually lead to blackouts which, despite being rare, are extremely costly. However, ensuring system stability is a non-trivial task for several reasons. First, power grids, by nature, are complex nonlinear dynamical systems, so assessing and maintaining system stability is challenging mainly due to the co-existence of multiple equilibria and the lack of global stability. Second, the systems are subject to various sources of uncertainties. For example, the renewable energy injections may vary depending on the weather conditions. Unfortunately, existing security assessment may not be sufficient to verify system stability in the presence of such uncertainties. This thesis focuses on new scalable approaches for robust stability assessment applicable to three main types of stability, i.e., long-term voltage, transient, and small-signal stability. In the first part of this thesis, I develop a novel computationally tractable technique for constructing Optimal Power Flow (OPF) feasibility (convex) subsets. For any inner point of the subset, the power flow problem is guaranteed to have a feasible solution which satisfies all the operational constraints considered in the corresponding OPF. This inner approximation technique is developed based on Brouwer's fixed point theorem as the existence of a solution can be verified through a self-mapping condition. The self-mapping condition along with other operational constraints are incorporated in an optimization problem to find the largest feasible subsets. Such an optimization problem is nonlinear, but any feasible solution will correspond to a valid OPF feasibility estimation. Simulation results tested on several IEEE test cases up to 300 buses show that the estimation covers a substantial fraction of the true feasible set. Next, I introduce another inner approximation technique for estimating an attraction domain of a post-fault equilibrium based on contraction analysis. In particular, I construct a contraction region where the initial conditions are "forgotten", i.e., all trajectories starting from inside this region will exponentially converge to each other. An attraction basin is constructed by inscribing the largest ball in the contraction region. To verify contraction of a Differential-Algebraic Equation (DAE) system, I also show that one can rely on the analysis of extended virtual systems which are reducible to the original one. Moreover, the Jacobians of the synthetic systems can always be expressed in a linear form of state variables because any polynomial system has a quadratic representation. This makes the synthetic system analysis more appropriate for contraction region estimation in a large scale. In the final part of the thesis, I focus on small-signal stability assessment under load dynamic uncertainties. After introducing a generic impedance-based load model which can capture the uncertainty, I propose a new robust small signal (RSS) stability criterion. Semidefinite programming is used to find a structured Lyapunov matrix, and if it exists, the system is provably RSS stable. An important application of the criterion is to characterize operating regions which are safe from Hopf bifurcations. The robust stability assessment techniques developed in this thesis primarily address the needs of a system operator in electrical power systems. The results, however, can be naturally extended to other nonlinear dynamical systems that arise in different fields such as biology, biomedicine, economics, neuron networks, and optimization. As the robust assessment is based on sufficient conditions for stability, there is still room for development on reducing the inevitable conservatism. For example, for OPF feasibility region estimation, an important open question considers what tighter bounds on the nonlinear residual terms one can use instead of box type bounds. Also, for attraction basin problem, finding the optimal norms and metrics which result in the largest contraction domain is an interesting potential research question.by Hung Dinh Nguyen.Ph. D

SCEE 2008 book of abstracts : the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE 2008), September 28 – October 3, 2008, Helsinki University of Technology, Espoo, Finland

This report contains abstracts of presentations given at the SCEE 2008 conference.reviewe

Nonparametric Identification of nonlinear dynamic Systems

In der vorliegenden Arbeit wird eine nichtparametrische Identifikationsmethode für stark nichtlineare Systeme entwickelt, welche in der Lage ist, die Nichtlinearitäten basierend auf Schwingungsmessungen in Form von allgemeinen dreidimensionalen Rückstellkraft-Flächen zu rekonstruieren ohne Vorkenntnisse über deren funktionale Form. Die Vorgehensweise basiert auf nichtlinearen Kalman Filter Algorithmen, welche durch Ergänzung des Zustandsvektors in Parameterschätzer verwandelt werden können. In dieser Arbeit wird eine Methode beschrieben, die diese bekannte parametrische Lösung zu einem nichtparametrischen Verfahren weiterentwickelt. Dafür wird ein allgemeines Nichtlinearitätsmodell eingeführt, welches die Rückstellkräfte durch zeitvariable Koeffizienten der Zustandsvariablen beschreibt, die als zusätzliche Zustandsgrößen geschätzt werden. Aufgrund der probabilistischen Formulierung der Methode, können trotz signifikantem Messrauschen störfreie Rückstellkraft-Charakteristiken identifiziert werden. Durch den Kalman Filter Algorithmus ist die Beobachtbarkeit der Nichtlinearitäten bereits durch eine Messgröße pro Systemfreiheitsgrad gegeben. Außerdem ermöglicht diese Beschreibung die Durchführung einer vollständigen Identifikation, wobei die restlichen konstanten Parameter des Systems zusätzlich geschätzt werden. Die Leistungsfähigkeit des entwickelten Verfahrens wird anhand von virtuellen und realen Identifikationsbeispielen nichtlinearer mechanischen Systeme mit ein und drei Freiheitsgraden demonstriert

Real-time Optimal Energy Management System for Plug-in Hybrid Electric Vehicles

Air pollution and rising fuel costs are becoming increasingly important concerns for the transportation industry. Hybrid electric vehicles (HEVs) are seen as a solution to these problems as they off er lower emissions and better fuel economy compared to conventional internal combustion engine vehicles. A typical HEV powertrain consists of an internal combustion engine, an electric motor/generator, and a power storage device (usually a battery). Another type of HEV is the plug-in hybrid electric vehicle (PHEV), which is conceptually similar to the fully electric vehicle. The battery in a PHEV is designed to be fully charged using a conventional home electric plug or a charging station. As such, the vehicle can travel further in full-electric mode, which greatly improves the fuel economy of PHEVs compared to HEVs. In this study, an optimal energy management system (EMS) for a PHEV is designed to minimize fuel consumption by considering engine emissions reduction. This is achieved by using the model predictive control (MPC) approach. MPC is an optimal model-based approach that can accommodate the many constraints involved in the design of EMSs, and is suitable for real-time implementations. The design and real-time implementation of such a control approach involves control-oriented modeling, controller design (including high-level and low-level controllers), and control scheme performance evaluation. All of these issues will be addressed in this thesis. A control-relevant parameter estimation (CRPE) approach is used to make the control-oriented model more accurate. This improves the EMS performance, while maintaining its real-time implementation capability. To reduce the computational complexity, the standard MPC controller is replaced by its explicit form. The explicit model predictive controller (eMPC) achieves the same performance as the implicit MPC, but requires less computational effort, which leads to a fast and reliable implementation. The performance of the control scheme is evaluated through different stages of model-in-the-loop (MIL) simulations with an equation-based and validated high-fidelity simulation model of a PHEV powertrain. Finally, the CRPE-eMPC EMS is validated through a hardware-in-the-loop (HIL) test. HIL simulation shows that the proposed EMS can be implemented to a commercial control hardware in real time and results in promising fuel economy figures and emissions performance, while maintaining vehicle drivability

Numerical Solution of Optimal Control Problems with Explicit and Implicit Switches

This dissertation deals with the efficient numerical solution of switched optimal control problems whose dynamics may coincidentally be affected by both explicit and implicit switches. A framework is being developed for this purpose, in which both problem classes are uniformly converted into a mixed–integer optimal control problem with combinatorial constraints. Recent research results relate this problem class to a continuous optimal control problem with vanishing constraints, which in turn represents a considerable subclass of an optimal control problem with equilibrium constraints. In this thesis, this connection forms the foundation for a numerical treatment. We employ numerical algorithms that are based on a direct collocation approach and require, in particular, a highly accurate determination of the switching structure of the original problem. Due to the fact that the switching structure is a priori unknown in general, our approach aims to identify it successively. During this process, a sequence of nonlinear programs, which are derived by applying discretization schemes to optimal control problems, is solved approximatively. After each iteration, the discretization grid is updated according to the currently estimated switching structure. Besides a precise determination of the switching structure, it is of central importance to estimate the global error that occurs when optimal control problems are solved numerically. Again, we focus on certain direct collocation discretization schemes and analyze error contributions of individual discretization intervals. For this purpose, we exploit a relationship between discrete adjoints and the Lagrange multipliers associated with those nonlinear programs that arise from the collocation transcription process. This relationship can be derived with the help of a functional analytic framework and by interrelating collocation methods and Petrov–Galerkin finite element methods. In analogy to the dual-weighted residual methodology for Galerkin methods, which is well–known in the partial differential equation community, we then derive goal–oriented global error estimators. Based on those error estimators, we present mesh refinement strategies that allow for an equilibration and an efficient reduction of the global error. In doing so we note that the grid adaption processes with respect to both switching structure detection and global error reduction get along with each other. This allows us to distill an iterative solution framework. Usually, individual state and control components have the same polynomial degree if they originate from a collocation discretization scheme. Due to the special role which some control components have in the proposed solution framework it is desirable to allow varying polynomial degrees. This results in implementation problems, which can be solved by means of clever structure exploitation techniques and a suitable permutation of variables and equations. The resulting algorithm was developed in parallel to this work and implemented in a software package. The presented methods are implemented and evaluated on the basis of several benchmark problems. Furthermore, their applicability and efficiency is demonstrated. With regard to a future embedding of the described methods in an online optimal control context and the associated real-time requirements, an extension of the well–known multi–level iteration schemes is proposed. This approach is based on the trapezoidal rule and, compared to a full evaluation of the involved Jacobians, it significantly reduces the computational costs in case of sparse data matrices

Simulation of Transient Effects in High-Temperature Superconducting Magnets

Particle colliders for high-energy physics are important tools for investigating the fundamental structure of matter. In circular accelerators, the collision energy of particles is proportional to the bending magnetic field and the radius of the machine. As a consequence, circular accelerators such as the Large Hadron Collider at CERN have traditionally relied on high-field magnets made of low-temperature superconductors, confining the particle beams within a complex of acceptable dimensions. This class of superconductors shows a practical limit in the achievable magnetic field in the magnet aperture of about 8 T for a Nb-Ti alloy, and 16 T for a Nb3Sn compound. Overcoming these limits requires the use of high-temperature superconductors (HTS) in accelerator magnets, in particular rare-earth barium copper oxide (ReBCO) tapes. With respect to the low-temperature counterpart, accelerator magnets based on ReBCO tapes are known to behave differently in terms of magnetic field quality and protection from quench events. The tapes are equivalent to wide and anisotropic mono-filaments, resulting in screening currents detrimentally affecting the magnetic field quality, in particular at low currents. At the same time, quenches are less likely to occur due to the enhanced thermal stability of the tapes, but are more difficult to detect and mitigate. Moreover, the dynamic behavior of accelerator magnets is also affected by the surrounding circuitry which must be taken into account, leading to multiphysics, multirate and multiscale problems. Numerical methods play a crucial role for overcoming the challenges related to magnetic field quality and quench protection. In this work, the magnetothermal dynamics in high-temperature superconducting magnets is modeled by means of an eddy-current problem in the time domain. A mixed field formulation is developed to cope with the nonlinear resistivity law of superconducting materials. The formulation is complemented with distribution functions for the coupling of external voltage and/or current source quantities. Further simplifications are discussed in case of tapes with high aspect ratio, and multifilamentary conductors. Moreover, a field-circuit coupling interface is derived as an optimized Schwarz transmission condition, such that the formulation can be used in field-circuit coupled problems by means of co-simulation methods. The implementation of the formulation in the finite element method is verified against analytical and reference solutions available in literature, and validated against measurements on the HTS-based dipole magnet Feather-M2. As a case-study, the formulation is applied to proof-of-concept ReBCO screens for the passive field-error cancellation in accelerator magnets. The proposed design is called HALO (harmonics-absorbing layered object) as it is made of stacks of tapes arranged in layers which are fully scalable and expandable. The screens are positioned such that their persistent magnetization shapes the magnetic field in the magnet aperture, canceling the undesired field imperfections. Experimental measurements at 77 K in liquid nitrogen show a significant reduction of the field error, up to a factor of four. Moreover, numerical extrapolation for accelerator-like conditions shows that a careful design of the superconducting screens allows matching the typical field quality requirements for accelerator magnets

Nonparametric identification of nonlinear dynamic systems

A nonparametric identification method for highly nonlinear systems is presented that is able to reconstruct the underlying nonlinearities without a priori knowledge of the describing nonlinear functions. The approach is based on nonlinear Kalman Filter algorithms using the well-known state augmentation technique that turns the filter into a dual state and parameter estimator, of which an extension towards nonparametric identification is proposed in the present work