Search results for "Variant"

On the existence of invariant curves of twist mappings of an annulus

1983

Stick-slip and convergence of feedback-controlled systems with Coulomb friction

2020

An analysis of stick-slip behavior and convergence of trajectories in the feedback-controlled motion systems with discontinuous Coulomb friction is provided. A closed-form parameter-dependent stiction region, around an invariant equilibrium set, is proved to be always reachable and globally attractive. It is shown that only asymptotic convergence can be achieved, with at least one but mostly an infinite number of consecutive stick-slip cycles, independent of the initial conditions. Theoretical developments are supported by a number of numerical results with dedicated convergence examples.

A simplified predictive control of constrained Markov jump system with mixed uncertainties

2014

Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/475808 Open Access A simplified model predictive control algorithm is designed for discrete-time Markov jump systems with mixed uncertainties. The mixed uncertainties include model polytope uncertainty and partly unknown transition probability. The simplified algorithm involves finite steps. Firstly, in the previous steps, a simplified mode-dependent predictive controller is presented to drive the state to the neighbor area around the origin. Then the trajectory of states is driven as expected to the origin by the final-step mode-independent pre…

A New Technique of Invariant Statistical Embedding and Averaging in Terms of Pivots for Improvement of Statistical Decisions Under Parametric Uncerta…

2021

In this chapter, a new technique of invariant embedding of sample statistics in a decision criterion (performance index) and averaging this criterion via pivotal quantities (pivots) is proposed for intelligent constructing efficient (optimal, uniformly non-dominated, unbiased, improved) statistical decisions under parametric uncertainty. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, the technique of invariant statistical embedding and averaging in terms of pivotal quantities (ISE&APQ) is independent of the choice of priors and represents …

Statistical validation of rival models for observable stochastic process and its identification

2011

In this paper, for statistical validation of rival (analytical or simulation) models collected for modeling observable process in stochastic system (say, transportation or service system), a uniformly most powerful invariant (UMPI) test is developed from the generalized maximum likelihood ratio (GMLR). This test can be considered as a result of a new approach to solving the Behrens-Fisher problem when covariance matrices of multivariate normal populations (compared with respect to their means) are different and unknown. The test makes use of an invariant statistic whose distribution, under the null hypothesis, does not depend on the unknown (nuisance) parameters. The sample size and thresho…

A novel Stochastic Discretized Weak Estimator operating in non-stationary environments

2012

The task of designing estimators that are able to track time-varying distributions has found promising applications in many real-life problems. A particularly interesting family of distributions are the binomial/multiomial distributions. Existing approaches resort to sliding windows that track changes by discarding old observations. In this paper, we report a novel estimator referred to as the Stochastic Discretized Weak Estimator (SDWE), that is based on the principles of Learning Automata (LA). In brief, the estimator is able to estimate the parameters of a time varying binomial distribution using finite memory. The estimator tracks changes in the distribution by operating on a controlled…

Self-stabilizing Balls & Bins in Batches

2016

A fundamental problem in distributed computing is the distribution of requests to a set of uniform servers without a centralized controller. Classically, such problems are modelled as static balls into bins processes, where m balls (tasks) are to be distributed to n bins (servers). In a seminal work, [Azar et al.; JoC'99] proposed the sequential strategy Greedy[d] for n = m. When thrown, a ball queries the load of d random bins and is allocated to a least loaded of these. [Azar et al.; JoC'99] showed that d=2 yields an exponential improvement compared to d=1. [Berenbrink et al.; JoC'06] extended this to m ⇒ n, showing that the maximal load difference is independent of m for d=2 (in contrast…

Effective state estimation of stochastic systems

2003

In the present paper, for constructing the minimum risk estimators of state of stochastic systems, a new technique of invariant embedding of sample statistics in a loss function is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant estimator, which has smaller risk than any of the well‐known estimators. There exists a class of control systems where observations are not …

Detecting Inclusions in Electrical Impedance Tomography Without Reference Measurements

2009

We develop a new variant of the factorization method that can be used to detect inclusions in electrical impedance tomography from either absolute current-to-voltage measurements at a single, nonzero frequency or from frequency-difference measurements. This eliminates the need for numerically simulated reference measurements at an inclusion-free body and thus greatly improves the method's robustness against forward modeling errors, e.g., in the assumed body's shape.

Invariant Embedding Technique and Its Applications for Improvement or Optimization of Statistical Decisions

2010

In the present paper, for improvement or optimization of statistical decisions under parametric uncertainty, a new technique of invariant embedding of sample statistics in a performance index is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant decision rule, which has smaller risk than any of the well-known decision rules. To illustrate the proposed technique, applica…