Discrete-time Context Research Articles

Asynchronously switched control of switched linear systems with average dwell time

This paper concerns the asynchronously switched control problem for a class of switched linear systems with average dwell time (ADT) in both continuous-time and discrete-time contexts. The so-called asynchronous switching means that the switchings between the candidate controllers and system modes are asynchronous. By further allowing the Lyapunov-like function to increase during the running time of active subsystems, the extended stability results for switched systems with ADT in nonlinear setting are first derived. Then, the asynchronously switched stabilizing control problem for linear cases is solved. Given the increase scale and the decrease scale of the Lyapunov-like function and the maximal delay of asynchronous switching, the minimal ADT for admissible switching signals and the corresponding controller gains are obtained. A numerical example is given to show the validity and potential of the developed results.

An algebraic method for eye blink artifacts detection in single channel EEG recordings

Event Abstract Back to Event An algebraic method for eye blink artifacts detection in single channel EEG recordings Zoran Tiganj1*, Mamadou Mboup2, Christophe Pouzat3 and Lotfi Belkoura4 1 Nord Europe, Projcet ALIEN, INRIA Lille , France 2 Université Paris Descartes, UFR Math-Info, France 3 Université Paris Descartes, Laboratoire de Physiologie Cérébral (CNRS UMR 8118), , France 4 Université des Sciences et Technologies de Lille, LAGIS (CNRS, UMR 8146) and Project Alien, INRIA Lille - Nord Europe, France Single-channel EEG systems are very useful in EEG based applications where real time processing, low computational complexity and low cumbersomeness are critical constrains. These include brain-computer-interface and biofeedback devices and also some clinical applications such as EEG recording on babies or Alzheimer's disease recognition. In this paper we address the problem of eye blink artifacts detection in such systems. We study an algebraic approach based on numerical differentiation, which is recently introduced from operational calculus. The occurrence of an artifact is modeled as an irregularity which appears explicitly in the time (generalized) derivative of the EEG signal as a delay. Manipulating such delay is easy with the operational calculus and it leads to a simple joint detection and localization algorithm. While the algorithm is devised based on continuous-time arguments, the final implementation step is fully realized in a discrete-time context, using very classical discrete-time FIR filters. The proposed approach is compared with three other approaches: (1) the very basic threshold approach, (2) the approach that combines the use of median filter, matched filter and nonlinear energy operator (NEO) and (3) the wavelet based approach. Comparison is done on: (a) the artificially created signal where the eye activity is synthesized from real EEG recordings and (b) the real single-channel EEG recordings from 32 different brain locations. Results are presented with Receiver Operating Characteristics curves. The results show that the proposed approach compares to the other approaches better or as good as, while having lower computational complexity with simple real time implementation. Comparison of the results on artificially created and real signal leads to conclusions that with detection techniques based on derivative estimation we are able to detect not only eye blink artifacts, but also any spike shaped artifact, even if it is very low in amplitude. Conference: Biomag 2010 - 17th International Conference on Biomagnetism , Dubrovnik, Croatia, 28 Mar - 1 Apr, 2010. Presentation Type: Poster Presentation Topic: MEG Modeling Citation: Tiganj Z, Mboup M, Pouzat C and Belkoura L (2010). An algebraic method for eye blink artifacts detection in single channel EEG recordings. Front. Neurosci. Conference Abstract: Biomag 2010 - 17th International Conference on Biomagnetism . doi: 10.3389/conf.fnins.2010.06.00064 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 22 Mar 2010; Published Online: 22 Mar 2010. * Correspondence: Zoran Tiganj, Nord Europe, Projcet ALIEN, INRIA Lille, Villeneuve d'Ascq, France, zoran.tiganj@gmail.com Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Zoran Tiganj Mamadou Mboup Christophe Pouzat Lotfi Belkoura Google Zoran Tiganj Mamadou Mboup Christophe Pouzat Lotfi Belkoura Google Scholar Zoran Tiganj Mamadou Mboup Christophe Pouzat Lotfi Belkoura PubMed Zoran Tiganj Mamadou Mboup Christophe Pouzat Lotfi Belkoura Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Linearization by Output Injection under Approximate Sampling

Linearization by output injection has been studied in both continuous time and discrete-time contexts. In this paper we discuss the possible preservation of such a property under sampling. It is shown that it can be maintained under approximate sampling up to the order of the system itself.

Reduced-order controller design for the general H ∞ control problem

This paper considers reduced-order controller design for the general H ∞ control problem. Based on linear matrix inequality (LMI), two new upper bounds of order reduction are proposed in continuous- and discrete-time contexts respectively. The bounds have a clear geometric interpretation and are only determined by the generalized plant parameter matrices. Moreover, the existence conditions of the reduced-order controller have the same forms as the well-known three LMIs, but with fewer dimension matrix variables. In comparison with the previous results, one of the main advantages is that our approach is applicable to general H ∞ control. Furthermore, the existing results do not imply our results for singular H ∞ control. An illustrative example is given to show the efficiency of our approach.

Martingale Approach to Stochastic Control with Discretionary Stopping

We develop a martingale approach for continuous-time stochastic control with discretionary stopping. The relevant Dynamic Programming Equation and Maximum Principle are presented. Necessary and sufficient conditions are provided for the optimality of a control strategy; these are analogues of the "equalization" and "thriftiness" conditions introduced by Dubins and Savage (1976) in a related, discrete-time context. The existence of a thrifty control strategy is established.

Applying constrained nonlinear generalized PI strategy to PDF tracking control through square root B-spline models

For stochastic systems with non-Gaussian variables, the classical control approaches where only expectation and variance are concerned cannot cover the control requirement of the closed loop in some practical processes. In this paper, the tracking control problem for output probability density functions (PDFs) is studied using square root B-spline expansions and non-linear weight dynamical models. After the measurable output PDFs are approximated by the B-spline expansions, a non-linear dynamical model can be established between the control input and the weights related to the PDFs. The tracking control problem for the output PDFs can be reduced to a constrained tracking problem for the non-linear weight dynamics. For this non-linear weight model, a generalized proportional-integral (PI) control strategy is proposed in discrete time context. The objective of the control is to make sure that the output PDFs of the system can follow a given target function, and the closed-loop system is exponentially stable and satisfies the constraint imposed on the state vector. The LMI-based convex optimization approach is adopted to design the parameters of the proposed PI controllers. This result also generalizes some previous works for classical constrained PI tracking control of non-linear discrete-time systems. Simulations are given to demonstrate the efficiency of the proposed approach.

Quasipolynomial generalization of Lotka$ndash$Volterra mappings

In the last years it has been shown that Lotka-Volterra mappings constitute a valuable tool from both the theoretical and the applied points of view, with developments in very diverse fields such as Physics, Population Dynamics, Chemistry and Economy. The purpose of this work is to demonstrate that many of the most important ideas and algebraic methods that constitute the basis of the quasipolynomial formalism (originally conceived for the analysis of ordinary differential equations) can be extended into the mapping domain. The extension of the formalism into the discrete-time context is remarkable as far as the quasipolynomial methodology had never been shown to be applicable beyond the differential case. It will be demonstrated that Lotka-Volterra mappings play a central role in the quasipolynomial formalism for the discrete-time case. Moreover, the extension of the formalism into the discrete-time domain allows a significant generalization of Lotka-Volterra mappings as well as a whole transfer of algebraic methods into the discrete-time context. The result is a novel and more general conceptual framework for the understanding of Lotka-Volterra mappings, as well as a new range of possibilities that becomes open not only for the theoretical analysis of Lotka-Volterra mappings and their generalizations, but also for the development of new applications.

Complex dynamics of the real exchange rate in an open macroeconomic model

This paper investigates the behavior of the real exchange rate in the context of a nonlinear discrete-time dynamic system within an open-economy macroeconomic framework. Postulating that domestic prices are freely flexible, it is shown that the real exchange rate can exhibit complex dynamic behavior when the Marshall-Lerner condition is not fulfilled and that the complexity of the dynamics is due to the low degree of capital mobility. Advances in the area of nonlinear dynamics give us a chance to take a new look at the Sohmen case for flexible exchange rates from another point of view.

Optimum nonlinear filtering

This paper is composed of two parts. The first part surveys the literature regarding optimum nonlinear filtering from the (continuous-time) stochastic analysis point of view, and the other part explores the impact of recent applications of neural networks (in a discrete-time context) to nonlinear filtering. In particular, the results obtained by using a regularized form of radial basis function (RBF) networks are presented in fair detail.

Essential Orders and Nonlinear Discrete-Time Decoupling

The concept of essential orders, recently introduced in continuous-time, is here extended to the nonlinear discrete-time context. On this basis it is shown how to compute a minimum order compensator for solving the restricted noninteracting control problem for right-invertible submersive systems.

NONLINEAR DISCRETE-TIME RISK-SENSITIVE OPTIMAL CONTROL

SUMMARY This paper is devoted to the study of the connections among risk-sensitive stochastic optimal control, dynamic game optimal control, risk-neutral stochastic optimal control and deterministic optimal control in a nonlinear, discrete-time context with complete state information. The analysis worked out sheds light on the profound links among these control strategies, which remain hidden in the linear context. In particular, it is shown that, under suitable parameterizations, risk-sensitive control can be regarded as a control methodology which combines features of both stochastic risk-neutral control and deterministic dynamic game control.

Asymptotics of the run lengths of two control charts

The CUSUM control chart proposed by Page is a widely used in monitoring the quality of manufacturing processes. The Shiryayev-Roberts (S-R) control chart due to Shiryayev (1963) and Roberts (1988) is one of its competitors, This paper is concerned with the distribution properties of the run lengths of these two control charts. In context of continuous time, we first give the expansions of the higher moments of these run lengths. Then, we show that the asymptotic distributions of these run lengths are either some exponential distributions, or the distribution of the suprema of a standard Brownian motion, or some normal distributions, according to whether the μ δ/2. Here δ is the reference value of the above charts. Some similar results are also obtained in the context of discrete time.

Some results on the bomber problem

The problem of optimally allocating partially effective, defensive weapons against randomly arriving enemy aircraft so that a bomber maximizes its probability of reaching its designated target is considered in the usual continuous-time context, and in a discrete-time context. The problem becomes that of determining the optimal number of missiles K(n, t) to use against an enemy aircraft encountered at time (distance) t away from the target when n is the number of remaining weapons (missiles) in the bomber's arsenal. Various questions associated with the properties of the function K are explored including the long-standing, unproven conjecture that it is a non-decreasing function of its first variable.

Some results on the bomber problem

The problem of optimally allocating partially effective, defensive weapons against randomly arriving enemy aircraft so that a bomber maximizes its probability of reaching its designated target is considered in the usual continuous-time context, and in a discrete-time context. The problem becomes that of determining the optimal number of missiles K(n, t) to use against an enemy aircraft encountered at time (distance) t away from the target when n is the number of remaining weapons (missiles) in the bomber's arsenal. Various questions associated with the properties of the function K are explored including the long-standing, unproven conjecture that it is a non-decreasing function of its first variable.