A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Holonomic quantum computing in symmetry-protected ground states of spin chains

While solid-state devices offer naturally reliable hardware for modern classical computers, thus far quantum information processors resemble vacuum tube computers in being neither reliable nor scalable. Strongly correlated many body states stabilized in topologically ordered matter offer the possibility of naturally fault tolerant computing, but are both challenging to engineer and coherently control and cannot be easily adapted to different physical platforms. We propose an architecture which achieves some of the robustness properties of topological models but with a drastically simpler construction. Quantum information is stored in the symmetry-protected degenerate ground states of spin-1 chains, while quantum gates are performed by adiabatic non-Abelian holonomies using only single-site fields and nearest-neighbor couplings. Gate operations respect the symmetry, and so inherit some protection from noise and disorder from the symmetry-protected ground states.Comment: 19 pages, 4 figures. v2: published versio

Robustness Analysis and Reliable Flight Regime Estimation of an Integrated Resilent Control System for a Transport Aircraft

Formal robustness analysis of aircraft control upset prevention and recovery systems could play an important role in their validation and ultimate certification. As a part of the validation process, this paper describes an analysis method for determining a reliable flight regime in the flight envelope within which an integrated resilent control system can achieve the desired performance of tracking command signals and detecting additive faults in the presence of parameter uncertainty and unmodeled dynamics. To calculate a reliable flight regime, a structured singular value analysis method is applied to analyze the closed-loop system over the entire flight envelope. To use the structured singular value analysis method, a linear fractional transform (LFT) model of a transport aircraft longitudinal dynamics is developed over the flight envelope by using a preliminary LFT modeling software tool developed at the NASA Langley Research Center, which utilizes a matrix-based computational approach. The developed LFT model can capture original nonlinear dynamics over the flight envelope with the ! block which contains key varying parameters: angle of attack and velocity, and real parameter uncertainty: aerodynamic coefficient uncertainty and moment of inertia uncertainty. Using the developed LFT model and a formal robustness analysis method, a reliable flight regime is calculated for a transport aircraft closed-loop system

LPV methods for fault-tolerant vehicle dynamic control

International audienceThis paper aims at presenting the interest of the Linear Parameter Varying methods for vehicle dynamics control, in particular when some actuators may be in failure. The cases of the semi-active suspension control problem and the yaw control using braking, steering and suspension actuators will be presented. In the first part, we will consider the semi-active suspension control problem, where some sensors or actuator (damper leakage) faults are considered. From a quarter-car vehicle model including a non linear semi-active damper model, an LPV model will be described, accounting for some actuator fault represented as some varying parameters. A single LPV fault-tolerant control approach is then developed to manage the system performances and constraints. In the second part the synthesis of a robust gain-scheduled H1 MIMO vehicle dynamic stability controller (VDSC), involving front steering, rear braking, and four active suspension actuators, is proposed to improve the yaw stability and lateral performances. An original LPV method for actuator coordination is proposed, when the actuator limitations and eventually failures, are taken into account. Some simulations on a complex full vehicle model (which has been validated on a real car), subject to critical driving situations (in particular a loss of some actuator), show the efficiency and robustness of the proposed solution

Fault-tolerant wide-area control of power systems

In this thesis, the stability and performance of closed-loop systems following the loss of sensors or feedback signals (sensor faults) are studied. The objective is to guarantee stability in the face of sensor faults while optimising performance under nominal (no sensor fault) condition. One of the main contributions of this work is to deal effectively with the combinatorial binary nature of the problem when the number of sensors is large. Several fault-tolerant controller and observer architectures that are suitable for different applications are proposed and their effectiveness demonstrated. The problems are formulated in terms of the existence of feasible solutions to linear matrix inequalities. The formulations presented in this work are described in a general form and can be applied to a large class of systems. In particular, the use of fault-tolerant architectures for damping inter-area oscillations in power systems using wide-area signals has been demonstrated. As an extension of the proposed formulations, regional pole placement to enhance the damping of inter-area modes has been incorporated. The objective is to achieve specified damping ratios for the inter-area modes and maximise the closed-loop performance under nominal condition while guaranteeing stability for all possible combinations of sensors faults. The performances of the proposed fault-tolerant architectures are validated through extensive nonlinear simulations using a simplified equivalent model of the Nordic power system.Open Acces

Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit

We critically examine the internal consistency of a set of minimal assumptions entering the theory of fault-tolerant quantum error correction for Markovian noise. These assumptions are: fast gates, a constant supply of fresh and cold ancillas, and a Markovian bath. We point out that these assumptions may not be mutually consistent in light of rigorous formulations of the Markovian approximation. Namely, Markovian dynamics requires either the singular coupling limit (high temperature), or the weak coupling limit (weak system-bath interaction). The former is incompatible with the assumption of a constant and fresh supply of cold ancillas, while the latter is inconsistent with fast gates. We discuss ways to resolve these inconsistencies. As part of our discussion we derive, in the weak coupling limit, a new master equation for a system subject to periodic driving.Comment: 19 pages. v2: Significantly expanded version. New title. Includes a debate section in response to comments on the previous version, many of which appeared here http://dabacon.org/pontiff/?p=959 and here http://dabacon.org/pontiff/?p=1028. Contains a new derivation of the Markovian master equation with periodic drivin

Fault-tolerant quantum computation

The discovery of quantum error correction has greatly improved the long-term prospects for quantum computing technology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment, or due to imperfect implementations of quantum logical operations. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. In principle, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per gate is less than a certain critical value, the accuracy threshold. It may be possible to incorporate intrinsic fault tolerance into the design of quantum computing hardware, perhaps by invoking topological Aharonov-Bohm interactions to process quantum information.Comment: 58 pages with 7 PostScript figures, LaTeX, uses sprocl.sty and psfig, to appear in "Introduction to Quantum Computation," edited by H.-K. Lo, S. Popescu, and T. P. Spille

Engineering exotic phases for topologically-protected quantum computation by emulating quantum dimer models

We use a nonperturbative extended contractor renormalization (ENCORE) method for engineering quantum devices for the implementation of topologically protected quantum bits described by an effective quantum dimer model on the triangular lattice. By tuning the couplings of the device, topological protection might be achieved if the ratio between effective two-dimer interactions and flip amplitudes lies in the liquid phase of the phase diagram of the quantum dimer model. For a proposal based on a quantum Josephson junction array [L. B. Ioffe {\it et al.}, Nature (London) {\bf 415}, 503 (2002)] our results show that optimal operational temperatures below 1 mK can only be obtained if extra interactions and dimer flips, which are not present in the standard quantum dimer model and involve three or four dimers, are included. It is unclear if these extra terms in the quantum dimer Hamiltonian destroy the liquid phase needed for quantum computation. Minimizing the effects of multi-dimer terms would require energy scales in the nano-Kelvin regime. An alternative implementation based on cold atomic or molecular gases loaded into optical lattices is also discussed, and it is shown that the small energy scales involved--implying long operational times--make such a device impractical. Given the many orders of magnitude between bare couplings in devices, and the topological gap, the realization of topological phases in quantum devices requires careful engineering and large bare interaction scales.Comment: 12 pages, 10 figure