Asymptotic Rejection Research Articles

On strongly dependent zero-inflated INAR(1) processes

We consider INAR(1) processes modulated by an unobserved strongly dependent 0-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0-1$$\\end{document} process. The observed process exhibits zero inflation and long memory. A simple method is proposed for estimating the INAR-parameters without modelling the unobserved modulating process. Asymptotic results for the estimators are derived, and a zero-inflation test is introduced. Asymptotic rejection regions and asymptotic power under long-memory alternatives are derived. A small simulation study illustrates the asymptotic results.

Triggered Repetitive Control: Application to Mechanically Ventilated Patients

Asymptotic rejection of a periodic disturbance can be achieved using repetitive control (RC). The aim of this article is to develop a triggered RC (TRC) framework that can handle repeating tasks that are initiated by an external disturbance induced trigger on varying intervals, which clearly violates the periodicity assumption in RC. A design method for this TRC framework is presented with a stability guarantee. Finally, through an experimental use-case, it is shown that pressure tracking performance for mechanically ventilated patients is improved significantly.

Gaussian process repetitive control: Beyond periodic internal models through kernels

Repetitive control enables the exact compensation of periodic disturbances if the internal model is appropriately selected. The aim of this paper is to develop a novel synthesis technique for repetitive control (RC) based on a new more general internal model. By employing a Gaussian process internal model, asymptotic rejection is obtained for a wide range of disturbances through an appropriate selection of a kernel. The implementation is a simple linear time-invariant (LTI) filter that is automatically synthesized through this kernel. The result is a user-friendly design approach based on a limited number of intuitive design variables, such as smoothness and periodicity. The approach naturally extends to reject multi-period and non-periodic disturbances, exiting approaches are recovered as special cases, and a case study shows that it outperforms traditional RC in both convergence speed and steady-state error.

Permutation test for heterogeneous treatment effects with a nuisance parameter

This paper proposes an asymptotically valid permutation test for heterogeneous treatment effects in the presence of an estimated nuisance parameter. Not accounting for the estimation error of the nuisance parameter results in statistics that depend on the particulars of the data generating process, and the resulting permutation test fails to control the Type 1 error, even asymptotically.In this paper we consider a permutation test based on a martingale transformation of the empirical process to render an asymptotically pivotal statistic, effectively nullifying the effect associated with the estimation error on the limiting distribution of the statistic. Under weak conditions, we show that the permutation test based on the martingale-transformed statistic results in the asymptotic rejection probability of α in general while retaining the exact control of the test level when testing for the more restrictive sharp null. We also show how our martingale-based permutation test extends to testing whether there exists treatment effect heterogeneity within subgroups defined by observable covariates. Our approach comprises testing the joint null hypothesis that treatment effects are constant within mutually exclusive subgroups while allowing the treatment effects to vary across subgroups.Monte Carlo simulations show that the permutation test presented here performs well in finite samples, and is comparable to those existing in the literature. To gain further understanding of the test to practical problems, we investigate the gift exchange hypothesis in the context of two field experiments from Gneezy and List (2006). Lastly, we provide the companion RATestR package to facilitate and encourage the application of our test in empirical research.

Stability analysis of single area power system considering parameter uncertainties

ABSTRACT In this work, the stability of a single area power system AVR loop is analysed in terms of specified gain and phase margin standpoint, by utilising an extended reduced-order observer (EROO). The design approach utilises a full-state feedback as well as an estimated signal for external disturbance (parametric uncertainties and disturbances due to change in load demands) to form the control law. Symmetric root locus (SRL) technique is used to assign the closed-loop poles (CLPs) of the system at desired locations by considering the stability margins. Parametric model uncertainty has been considered to demonstrate the robustness of control achieved by assigning a bound on the deviations in plant parameters. The proposed observer provides the estimates of unavailable states and state of the disturbance model in order to compensate system in the presence of external disturbances. The control scheme achieves performances satisfying the specified stability margins with asymptotic tracking and disturbance rejection property. The methodology provides control over peak values of the terminal voltage (with guaranteed zero steady-state errors) and control signal deviations which may be utilised to meet hardware constraints. Step by step design procedures with illustrative examples have been provided using MATLAB commands.

Moderate deviations and nonparametric inference for monotone functions

This paper considers self-normalized limits and moderate deviations of nonparametric maximum likelihood estimators for monotone functions. We obtain their self-normalized Cramer-type moderate deviations and limit distribution theorems for the nonparametric maximum likelihood estimator in the current status model and the Grenander-type estimator. As applications of the results, we present a new procedure to construct asymptotical confidence intervals and asymptotical rejection regions of hypothesis testing for monotone functions. The theoretical results can guarantee that the new test has the probability of type II error tending to 0 exponentially. Simulation studies also show that the new nonparametric test works well for the most commonly used parametric survival functions such as exponential and Weibull survival distributions.

Attitude manoeuvre control and asymptotic disturbance rejection of flexible spacecraft

This paper presents a novel approach to tackle the issues of attitude manoeuvre control and asymptotic disturbance rejection for a flexible spacecraft. The resulting attitude controller employs an internal model-based compensator to reject a class of persistent disturbances and a modal estimator for dynamic compensation of the rigid-flex coupling effect. The convergence of the modal variables can be guaranteed without the measures of them. The stability of the system is proved via the Lyapunov technique rigorously. Numerical results illustrate that improved attitude control performance and asymptotic disturbance rejection can both be achieved.

Asymptotic attenuation and rejection for a class of cascade systems with general periodic disturbances

In this article, the problem of asymptotic attenuation and rejection is investigated for a class of cascade systems with general periodic disturbances via a non-linear disturbance observer and [Formula: see text] control. First, a novel disturbance observer is developed to estimate general periodic disturbances, where the disturbances are described as a linear uncertain system with a non-linear output function. Then, a composite controller is constructed by combining the disturbance estimation with the partial state feedback control law, such that, the closed-loop system is asymptotically stable and meets [Formula: see text] performance. With the help of the Lyapunov function theory and the linear matrix inequality method, some sufficient conditions for the desired controller and observer gains are established. Finally, numerical and application examples are presented to demonstrate the effectiveness of the proposed scheme.

The leader-following rendezvous with connectivity preservation via a self-tuning adaptive distributed observer

ABSTRACTThis paper studies the leader-following rendezvous with connectivity preservation problem for multiple double-integrator systems subject to external disturbances via a self-tuning adaptive distributed observer approach. This approach offers two advantages over the existing approach. First, it removes the existing assumption that all the followers know the system matrix of the leader system. Second, the difficult task of calculating the observer gain is avoided by the employment of the dynamic observer gain. A rigorous analysis shows that our control law is capable of maintaining the connectivity of any initial connected communication network, and achieving the asymptotic tracking and disturbance rejection for a class of leader's signals and external disturbances, which can be the algebraic sum or multiplication of any polynomial functions with any unknown coefficients and sinusoidal functions with arbitrary unknown amplitudes, initial phases, and any frequencies.

Adaptive output regulation for offshore managed pressure drilling

SummaryThis paper deals with output regulation problem for an offshore managed pressure drilling system subject to sinusoidal disturbances. The disturbance is caused by the heave motion of the floating drilling rig during pipe connections, and the objective is to maintain a constant pressure at the bottom of the well. The controller for the heave disturbance attenuation consists of three cascaded parts. First, a nonlinear inversion element is applied to invert nonlinearity of choke. Second, an adaptive compensator is designed based on internal model, and certainty equivalence principles for asymptotic rejection of time‐varying heave disturbance. Third, an output feedback controller is synthesized for providing stability and improving transient performance of closed‐loop system. Robust stability of closed‐loop system is analyzed using edge theorem. Simulation results of the combined adaptive output regulator are presented, which show satisfactory set‐point tracking and attenuation of the heave disturbance. Copyright © 2016 John Wiley & Sons, Ltd.

Position Regulation of an EGR Valve Using Reset Control With Adaptive Feedforward

We propose a hybrid control system performing set-point regulation of an exhaust gas recirculation valve of a Diesel engine. The control technique is based on a first-order reset element (FORE) embedded with an adaptive feedforward action whose aim is to provide asymptotic rejection of disturbances acting at the plant input. The feedforward action is adapted by suitable resetting laws occurring whenever the FORE is reset to zero. We first provide a formal analysis of the effectiveness of the adaptive reset system to guarantee asymptotic set-point regulation, and then, we illustrate how the adaptive feedforward can be parameterized for improved transient performance. We experimentally illustrate the proposed solution on a Diesel engine testbench, which reveals substantial position accuracy improvement during a standard driving cycle, as compared with the production standard solution.

Periodic disturbance rejection with unknown frequency and unknown plant structure

This paper deals with asymptotic rejection of a multi-sinusoidal signal for linear single-input single-output stable systems with unknown structure. An adaptive orthogonal signals generator is used to both reconstruct the disturbance and cancel its effect on the system output. An interesting feature is that the disturbance is removed by the generated internal signals with no additional dynamics in the cancellation algorithm. A fractional-order controller is designed which guarantees the closed-loop stability of the system if the location of the plant frequency response at the estimated frequencies lies in a half-plane passing through the origin of the complex plane, i.e. no information about the order of the system to be controlled, the relative degree, the nature of its poles and zeros, is required. The case of multi-sinusoidal disturbance is also analyzed. Simulations and comparisons with existing approaches are presented that highlight the performances of the proposed method.

Asymptotic rejection of sinusoidal disturbances based voltage balance control in back-to-back power converters

SUMMARY This paper addresses the imbalance problem of the dc-link capacitor voltages in the three-level diode-clamped back-to-back power converter. In order to cope with it, a mathematical analysis of the capacitor voltage difference dynamics, based on a continuous model of the converter, is first carried out. It leads to an approximated model that contains explicitly several sinusoidal functions of time. In view of this result, the voltage imbalance phenomenon can be addressed as an output regulation problem, considering the sinusoidal functions of time as exogenous disturbances. Thus, a novel approach to deal with the mentioned problem in the back-to-back converter is presented. Then, the particular features of the disturbances are used to design several controllers. They all follow an asymptotic disturbance rejection approach. In this way, the estimates of the disturbances are used to apply a control law that cancels them while regulating the capacitor voltage balance as well. Finally, the performance of the proposed control laws is evaluated, presenting the simulation results obtained when the different controllers are implemented. Copyright © 2013 John Wiley & Sons, Ltd.

Exact and asymptotically robust permutation tests

Given independent samples from P and Q, two-sample permutation tests allow one to construct exact level tests when the null hypothesis is P=Q. On the other hand, when comparing or testing particular parameters $\theta$ of P and Q, such as their means or medians, permutation tests need not be level $\alpha$, or even approximately level $\alpha$ in large samples. Under very weak assumptions for comparing estimators, we provide a general test procedure whereby the asymptotic validity of the permutation test holds while retaining the exact rejection probability $\alpha$ in finite samples when the underlying distributions are identical. The ideas are broadly applicable and special attention is given to the k-sample problem of comparing general parameters, whereby a permutation test is constructed which is exact level $\alpha$ under the hypothesis of identical distributions, but has asymptotic rejection probability $\alpha$ under the more general null hypothesis of equality of parameters. A Monte Carlo simulation study is performed as well. A quite general theory is possible based on a coupling construction, as well as a key contiguity argument for the multinomial and multivariate hypergeometric distributions.

Attitude tracking of rigid spacecraft subject to disturbances of unknown frequencies

SUMMARY The asymptotic rejection of spacecraft systems under multi-tone sinusoidal disturbances has been studied recently for the case where the frequencies of the disturbance are known. In this paper, we further consider the case where the frequencies of the disturbance are unknown. We show that this case can be solved by an adaptive regulation technique. We also present some analysis on the convergence issue of the estimated frequencies to unknown frequencies. Copyright © 2013 John Wiley & Sons, Ltd.

Asymptotic rejection of unmatched general periodic disturbances with nonlinear Lipschitz internal models

This article deals with asymptotic rejection of general periodic disturbances in a class of nonlinear systems by exploiting observer design with Lipschitz output nonlinearities for the internal model design. It is shown that a class of general periodic distances can be modelled as outputs of linear systems with nonlinear output functions. Based on this observation, a nonlinear observer design with output Lipschitz nonlinearities is investigated and integrated for the internal model design to estimate the phase and amplitude of the desired feedforward input for asymptotic disturbance rejection in a class of nonlinear systems with input-to-state stable zero dynamics. A number of problems on disturbance rejection can be formulated in the disturbance rejection form shown in this article to which the proposed nonlinear Lipschitz internal model can be applied. Two examples are included to demonstrate the proposed design strategies.

Subsampling tests of parameter hypotheses and overidentifying restrictions with possible failure of identification

We introduce a general testing procedure in models with possible identification failure that has exact asymptotic rejection probability under the null hypothesis. The procedure is widely applicable and in this paper we apply it to tests of arbitrary linear parameter hypotheses as well as to tests of overidentification in time series models given by unconditional moment conditions. The main idea is to subsample classical tests, like for example the Wald or the J test. More precisely, instead of using critical values based on asymptotic theory, we compute data-dependent critical values based on the subsampling technique.We show that under full identification the resulting tests are consistent against fixed alternatives and that they have exact asymptotic rejection probabilities under the null hypothesis independent of identification failure. Furthermore, the subsampling tests of parameter hypotheses are shown to have the same local power as the original tests under full identification.An algorithm is provided that automates the block size choice needed to implement the subsampling testing procedure. A Monte Carlo study shows that the tests have reasonable size properties and often outperform other robust tests in terms of power.

Adaptive regulation for linear systems with multiple zeros at the origin

SUMMARYWe consider the problem of asymptotic rejection of exogenous harmonic inputs having unknown amplitudes, phases, and frequencies on the output for a class of uncertain and nonminimum‐phase linear systems. Special emphasis is given to the case in which the controlled system has multiple zeros at the origin. It is shown how the method recently proposed to design internal models by means of regression arguments, combined with control strategies based on the redesign of the zero dynamics of the system through redefinition of the output, can be successfully used to solve the problem in presence of plant parameter uncertainties.Copyright © 2012 John Wiley & Sons, Ltd.

Bayesian heavy-tailed models and conflict resolution: A review

We review a substantial literature, spanning 50 years, concerning the resolution of conflicts using Bayesian heavy-tailed models. Conflicts arise when different sources of information about the model parameters (e.g., prior information, or the information in individual observations) suggest quite different plausible regions for those parameters. Traditional Bayesian models based on normal distributions or other conjugate structures typically resolve conflicts by centring the posterior at some compromise position, but this is not a realistic resolution when it means that the posterior is then in conflict with the different information sources. Bayesian modelling with heavy-tailed distributions has been shown to produce more reasonable conflict resolution, typically by favouring one source of information over the other. The less favoured source is ultimately wholly or partially rejected as the conflict becomes increasingly extreme. The literature reviewed here provides formal proofs of conflict resolution by asymptotic rejection of some information sources. Results are given for a variety of models, from the simplest case of a single observation relating to a single location parameter up to models with many location parameters, location and scale parameters, or other kinds of parameters. However, these results do not begin to address models of the kind of complexity that are routinely used in practical Bayesian modelling. In addition to reviewing the available theory, we also identify clearly the gaps in the literature that need to be filled in order for modellers to be able to develop applications with appropriate “built-in robustness.”

Adaptive Asymptotic Rejection of Unmatched General Periodic Disturbances in Output-Feedback Nonlinear Systems

This note deals with asymptotic rejection of periodic disturbances in a class of nonlinear systems via output feedback. The disturbance undertaken is unmatched but the period of the disturbance is known. A novel method for estimating periodic disturbances is proposed, which ensures convergence of the estimation error to zero. By applying such estimation, a controller is constructed such that all the signals in the closed loop are bounded and the output converges to zero. A numerical example is presented to show the utility of the results presented in the note.