Asymptotic Observer Research Articles

Deflection angle of light for an observer and source at finite distance from a rotating wormhole

By using a method improved with a generalized optical metric, the deflection of light for an observer and source at finite distance from a lens object in a stationary, axisymmetric and asymptotically flat spacetime has been recently discussed [Ono, Ishihara, Asada, Phys. Rev. D 96, 104037 (2017)]. By using this method, in the weak field approximation, we study the deflection angle of light for an observer and source at finite distance from a rotating Teo wormhole, especially by taking account of the contribution from the geodesic curvature of the light ray in a space associated with the generalized optical metric. Our result of the deflection angle of light is compared with a recent work on the same wormhole but limited within the asymptotic source and observer [Jusufi, Ovgun, Phys. Rev. D 97, 024042, (2018)], in which they employ another approach proposed by Werner with using the Nazim's osculating Riemannian construction method via the Randers-Finsler metric. We show that the two different methods give the same result in the asymptotic limit. We obtain also the corrections to the deflection angle due to the finite distance from the rotating wormhole.

Performance Assessment of Discrete-Time Extended State Observers: Theoretical and Experimental Results

This paper evaluates the performance of the discrete-time linear extended state observer (ESO) for a disturbed nonlinear discrete-time system with uncertainties. Since the performance of the ESO is dominated by the choice of the gain parameter, the goal of this paper is to analyze the behavior of the observation error when the gain parameter varies from zero to infinity. We show that for the ESO considered, there exists a certain threshold such that if the gain parameter is smaller than this threshold, the observation error at steady state will become unbounded. An upper bound on the asymptotic observation error is also proposed, which is proved to be bounded and convergent utilizing set-theoretic techniques. For the case where the closed-loop matrix of the ESO is nonnegative, a tighter upper bound on the asymptotic observation error is also proposed. The proposed theoretic results are illustrated by the simulation results and the experimental verifications on a direct current motor loading platform.

Compact four–dimensional euclidean space embedded in the universe

A compact four-dimensional manifold whose metric tensor has a positive determinant (named the "Euclid ball") is considered. The Euclid ball can be immersed in the Minkovskian space (which has the negative determinant) and can exist stably through the history of the universe. Since the Euclid ball has the same solution as the Schwarzschild black hole on its three-dimensional surface, an asymptotic observer can not distinguish them. If large fraction of whole energy of the pre-universe was encapsulated in Euclid balls, they behave as the dark matter in the current universe. Euclid balls already existed at the end of the cosmological inflation, and can have a heavy mass in this model, they can be a seed of supper-massive black-holes, which are necessary to initiate a forming of galaxies in the early universe. The $\gamma$-ray burst at early universe is also a possible signal of the Euclidean ball.

Unruh effect for inertial observers through vacuum correlations

We study a dynamic version of the Unruh effect in a two dimensional collapse model forming a black hole. In this two-dimensional collapse model a scalar field coupled to the dilaton gravity, moving leftwards, collapses to form a black hole. There are two sets of asymptotic (trightarrow infty ) observers, around xrightarrow infty and xrightarrow -infty . The observers at the right null infinity witness a thermal flux of radiation associated with time dependent geometry leading to a black hole formation and its subsequent Hawking evaporation, in an expected manner. We show that even the observers at left null infinity find themselves in thermal ambiance, without experiencing any change of spacetime geometry all along their trajectories. They remain as inertial observers in a flat region of spacetime where curvature tensor identically vanishes in a portion of full spacetime. These observers find the state of the quantum field in a late time thermal configuration, with exactly the same temperature as measured by the observers at right null infinity, despite being inertial in flat spacetime region throughout their history. This is very closely related to the standard Unruh effect in the flat spacetime, except for a key difference – since they are inertial throughout and have no causally connected source in the past light cone to account for what they see. The result arises from quantum correlations which extend outside the past light cone and is conceptually similar to the EPR correlations.

Static Orbits in Rotating Spacetimes.

We show that under certain conditions an axisymmetric rotating spacetime contains a ring of points in the equatorial plane, where a particle at rest with respect to an asymptotic static observer remains at rest in a static orbit. We illustrate the emergence of such orbits for boson stars. Further examples are wormholes, hairy black holes, and Kerr-Newman solutions.

On a linear input–output approach for the control of nonlinear flat systems

ABSTRACTThe need for observers, or other means of state- or phase variables-on-line computations, is revisited from the perspective of structural integral reconstructors. The problem addressed is the regulation, via simplified pure integration dynamics, of the large class of static, or dynamic, feedback linearisable systems (i.e. differentially flat systems), subject to additive exogenous disturbances and where nonlinearities are purposefully neglected. Integral reconstructors of the simplified input-to-flat output dynamics, directly lead to generalised proportional integral controllers, which are also shown to be equivalent to classical compensation networks. Their robust version, addressed here as flat filters, are found to be quite useful in the approximate (i.e. practical) control of perturbed differentially flat systems. The controller design is based on their simplified, perturbed, and pure integration dynamics. Flat filters evade for the need of nonlinear asymptotic observers and other, on-line, explicit output time derivatives computations. Simulation and challenging experimental examples are provided to validate this linear approach to the control of nonlinear flat systems.

Hawking modes and the optimal disperser: holographic lessons from the observer's causal-patch unitarity

Based on an observer-centric methodology, we pinpoint the basic origin of the spectral Planckianity of the asymptotic Hawking modes in the conventional treatments of the evaporating horizons. By considering an observer who analyzes a causal horizon in a generic spacetime, we first clarify how the asymptotic Planckian spectrum is imposed on the exponentially redshifted Hawking modes through a geometric dispersion mechanism developed by a semiclassical environment which is composed by all the modes that build up the curvature of the causal patch of the asymptotic observer. We also discuss the actual microscopic phenomenon of the Hawking evaporation of generic causal horizons. Our quantum description is based on a novel holographic scheme of gravitational open quantum systems in which the degrees of freedom that build up the curvature of the observer’s causal patch interact with the radiated Hawking modes, initially as environmental quanta, and after a crossover time, as quantum defects. Planckian dispersion of the modes would only be developed in the strict thermodynamic limit of this quantum environment, called optimal disperser, which is nevertheless avoided holographically. Finally, we outline and characterize how our microscopic formulation of the observer-centric holography, beyond the AdS/CFT examples and for generic causal patches, does realize the information-theoretic processing of unitarity.

The Squirrel-Cage Induction Motor Model and Its Parameter Identification Via Steady and Dynamic Tests

One of the most important bases for designing robust closed-loop controllers applied to induction motor with high performance is establishing its mathematical model and state observers, as well as the parameter identification with high accuracy. In this paper, a step-by-step mathematical model of the squirrel-cage induction motor is described at αβ coordinate frame where the parameters are defined in detailed form; the rotor flux linkages and load torque are estimated via an asymptotic observer; the induction motor parameter identification is performed via a data acquisition board, applying dynamic and steady-state tests. Inductances of the induction motor model are calculated using the proposed relationships between the magnetically coupled circuit and equivalent circuit model. The mathematical model, state observers, and parameter identification procedure of squirrel-cage induction motor are validated via comparison of simulation signals with their corresponding real-time signals. This validation is made experimentally by a steady-state test, where load conditions are changed via a dynamometer which is belt coupled with the squirrel-cage induction motor.

An asymptotic observer for batch processes with single biogas measurement

In this paper we propose an observer for an example of systems for which the boundary of its domain is unobservable, and all trajectories converge to this boundary. The proposed case study, a bioreactor in batch operating conditions with one simple microbial growth reaction and gas production is standard and largely encountered in practical situations. Comparison of the proposed observer with a classical Luenberger observer has been performed: it shows that this later does not guarantee a convergence with no estimation error.

Real-Time SOSM Super-Twisting Combined With Block Control for Regulating Induction Motor Velocity

On this paper, a robust velocity controller applied to a three-phase squirrel-cage induction motor under variable load conditions is designed. The induction motor drives an induction generator representing the load which freely delivers the generated power to the utility grid. The closed-loop scheme is designed at $\alpha \beta $ coordinate frame and is based on the linearization block control technique in combination with the super-twisting algorithm. The controlled output variables are the angular mechanical velocity and the square modulus of rotor flux linkages. The motor reference velocity is set up by a pulse train above the synchronous velocity and, consequently, the impelled induction machine operates in generator mode; meanwhile, the reference of rotor flux square modulus varies according to load condition of the induction motor. In order to estimate the non-measurable variables, both a rotor flux linkages observer and a load torque observer are designed. For the first one, a non-linear state observer using first order sliding modes is applied at $\alpha \beta $ coordinate frame and, for the second one, a Luenberger reduced asymptotic observer is used. The validation of the robustness for the proposed velocity controller is performed in a real-time experiment using a work-bench.

СИНТЕЗ АСИМПТОТИЧЕСКОГО НАБЛЮДАТЕЛЯ ДЛЯ СИСТЕМЫ УПРАВЛЕНИЯ МАГНИТНЫМ СЕПАРАТОРОМ ПРИ ОБОГАЩЕНИИ ЖЕЛЕЗНОЙ РУДЫ

СИНТЕЗ АСИМПТОТИЧЕСКОГО НАБЛЮДАТЕЛЯ ДЛЯ СИСТЕМЫ УПРАВЛЕНИЯ МАГНИТНЫМ СЕПАРАТОРОМ ПРИ ОБОГАЩЕНИИ ЖЕЛЕЗНОЙ РУДЫ

Cascade observer design for a class of uncertain nonlinear systems with delayed outputs

This paper proposes a state observer with a cascade structure for a class of nonlinear systems in the presence of uncertainties in the state equations and an arbitrarily long delay in the outputs. The design of the observer is achieved under an appropriate set of assumptions allowing to establish the ultimate boundedness of the observation error. Indeed, a suitable expression of the asymptotic observation error, involving the delay, the bound of the uncertainties and the Lipschitz constant of the system nonlinearities, is derived. Besides, it is shown that this ultimate bound is a decreasing function of the cascade length and is equal to zero in the uncertainty-free case. The observer design is first carried out in the case where the output measurements are continuously available and subsequently extended to the case where the outputs are available only at (non equally spaced) sampling instants. The performance of the proposed observer and its main properties are highlighted through illustrative simulation results involving an academic example.

A Nonlinear Sampled-Data Observer of Vehicle Lateral Velocity

Modeling and control of ground vehicles have become a major research field in the last few years, due to the increasing diffusion of driver assistance technologies and the persistent need for guaranteeing safety and comfort of driver and passengers. Although vehicle control systems require a large set of measurements to perform accurate computations, due to the possible unavailability and the non-negligible cost of sensors, it is not always possible to assume the direct knowledge of some important dynamic quantities involved, among which a major role is taken by its lateral velocity. In this letter, we address the design and implementation of an asymptotic sampled-data state observer for the vehicle single-track model. The observer only exploits the knowledge of sparse yaw-rate samples, which are obtained by relatively cheap digital gyroscopic devices, to reconstruct the continuous behavior of lateral velocity and yaw rate. However, due to the inherent properties of the vehicle single-track model, the observer is theoretically guaranteed to work only in the presence of sufficiently bounded driver maneuvers. Consequently and in view of a practical exploitation in a realistic setting, we preliminarily validate the approach by means of simulations of the observer applied to a more general vehicle model, including parameter variations, unmodeled dynamics, and quantization. The results seem to confirm the potential of the approach.

An adaptive sliding mode controller based on global asymptotic convergent observer for attitude tracking of quadrotor unmanned aerial vehicles

An adaptive sliding mode controller based on global asymptotic convergent observer for attitude tracking of quadrotor unmanned aerial vehicles

Asymptotic Observables in Gapped Quantum Spin Systems

This paper gives a construction of certain asymptotic observables (Araki-Haag detectors) in ground state representations of gapped quantum spin systems. The construction is based on general assumptions which are satisfied e.g. in the Ising model in strong transverse magnetic fields. We do not use the method of propagation estimates, but exploit instead compactness of the relevant propagation observables at any fixed time. Implications for the problem of asymptotic completeness are briefly discussed.

Sliding mode tracking controller for a non-linear single link-DC motor system: An input output approach

This article presents an input-output approach to sliding mode control (SMC) using integral reconstructors for the sliding surface specification in trajectory tracking tasks associated with a full non-linear link-DC motor system. These integral reconstructors are based on input errors, output tracking errors, and linear combinations of iterated integrals of input and output errors. The approach circumvents the traditional need for state measurements, or state estimations via asymptotic observers, in the sliding surface synthesis. The main assumption is that the available output signal coincides with the systems flat output. An experimental platform was developed to assess the performance of the proposed controller in a rest-to-rest trajectory tracking problem.

A Discrete-Time State Observer Approach to Discovering Portfolio Holdings

This paper is devoted to the derivation of a new approach for discovering mutual fund holdings from returns only. The approach is based on the use of a discrete-time asymptotic observer with forgetting factor which allows to estimate on-line both the holdings and the holding changes in portfolios. A realistic example is also provided, which demonstrates the effectiveness of the proposed approach. To the best of our knowledge, such an approach has never been proposed before.

Observer design for a class of uncertain systems with delayed outputs

In this paper, a state observer is proposed for a class of nonlinear systems in the presence of uncertainties in the state equations and an arbitrarily long delay in the output. The proposed predictor has a cascade structure in such a way that the first system in the cascade allows to estimate the delayed state while each of the remaining ones is an appropriate predictor. Each predictor estimates the state of the preceding one with a prediction horizon equal to a fraction of the time delay in such a way that the state of the last predictor is an estimate of the system actual state. The design of the observer is achieved by assuming a set of conditions under which the ultimate boundedness of the estimation error is established. More specifically it is shown that the asymptotic observation error remains in a ball which radius particularly depends on the magnitudes of the delay and the Lipschitz constant of the system nonlinearities. Of primary importance, it is proven that the observation error converges exponentially to zero in the absence of uncertainties. Simulations results are given in order to illustrate the performance and the main properties of the proposed observer.

Conditioned invariance and detectability subspaces in the behavioral approach

In this paper we extend the state space geometric notions of conditioned invariance and detectability subspaces to the behavioral framework. This is achieved based on the existing notions of behavioral tracking observer and of behavioral asymptotic observer introduced by Valcher, Willems, Trentelman and Trumph, combined with a notion of behavioral invariance introduced here. Moreover, we provide characterizations for the newly defined behavioral properties.

Second-order fuzzy sliding-mode control of photovoltaic power generation systems

In order to maximize the conversion efficiency of photovoltaic systems, it is usually essential to design a maximum power point tracking controller. In this paper, a new second-order fuzzy sliding-mode controller is designed for this purpose. Since the proposed scheme is based on the second-order sliding-mode control law, it can handle nonlinear dynamics of photovoltaic systems. Compared to previously introduced controllers, the proposed control law does not depend on model parameters and thus is robust to system uncertainties. The gain of the control signal is determined using a fuzzy gain tunning algorithm. Therefore, not only the robustness of the system will be improved, but also chattering amplitude will be suppressed. The proposed scheme does not require asymptotic observers, and thus its analysis and implementation are fairly simple. The performance of the proposed control system is verified through simulation and experiment. Compared to terminal sliding mode control system, the proposed system can increase the efficiency up to 1.5%.