Information Filtering and Array Algorithms for Discrete-Time Markovian Jump Linear Systems

This technical note develops information filter and array algorithms for a linear minimum mean square error estimator of discrete-time Markovian jump linear systems. A numerical example for a two-mode Markovian jump linear system, to show the advantage of using array algorithms to filter this class of systems, is provided.

Chaotic Synchronization in Discrete-Time Systems Connected by Bandlimited Channels

Due to the broadband characteristic of chaotic signals, many of the methods that have been proposed for synchronizing chaotic systems do not usually present a satisfactory performance when applied to bandlimited communication channels. Here, the effects of bandwidth limitations imposed by the channel on the synchronous solution of a discrete-time chaotic master-slave network are investigated. The discrete-time system considered in this study is the Henon map. It is analytically shown that synchronism can be achieved in such a network by introducing a digital filter in the feedback loop responsible for generating the chaotic signal that will be sent to the slave node. Numerical simulations relating the filter parameters, such as its order and cut-off frequency, to the maximum Lyapunov exponent of the master node, which determines if the transmitted signal is chaotic or not, are also presented. These results can be useful for practical communication schemes based on chaos.

Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a sufficient condition, based only on some positive semi-definite and kernel restrictions on some matrices, under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution fir the GCARE. We also present a solution for the discounted and long run average cost problems when the performance criterion is assumed be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables. The paper is concluded with a numerical example for pension fund with regime switching.

Anisotropy-based performance analysis of linear discrete time invariant control systems

The anisotropic norm of a linear discrete-time-invariant system measures system output sensitivity to stationary Gaussian input disturbances of bounded mean anisotropy. Mean anisotropy characterizes the degree of predictability (or colouredness) and spatial non-roundness of the noise. The anisotropic norm falls between the H-2 and H-infinity norms and accommodates their loss of performance when the probability structure of input disturbances is not exactly known. This paper develops a method for numerical computation of the anisotropic norm which involves linked Riccati and Lyapunov equations and an associated special type equation.

Introduction to fractional linear systems. Part 2: discrete-time case

IEE Proceedings - Vision, Image, and Signal Processing, Vol. 147, nº 1

Verification of system properties of polynomial systems using discrete-time approximations and set-based analysis

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2015

Computationally reliable approaches of contractive MPC for discrete-time systems

La tesis pretende explorar acercamientos computacionalmente confiables y eficientes de contractivo MPC para sistemas de tiempo discreto. Dos tipos de contractivo MPC han sido estudiados: MPC con coacción contractiva obligatoria y MPC con una secuencia contractiva de conjuntos controlables. Las técnicas basadas en optimización convexa y análisis de intervalos son aplicadas para tratar MPC contractivo lineal y no lineal, respectivamente. El análisis de intervalos clásicos es ampliado a zonotopes en la geometría para diseñar un conjunto invariante de control terminal para el modo dual de MPC. También es ampliado a intervalos modales para tener en cuenta la modalidad al calcula de conjuntos controlables robustos con una interpretación semántica clara. Los instrumentos de optimización convexa y análisis de intervalos han sido combinados para mejorar la eficacia de contractive MPC para varias clases de sistemas de tiempo discreto inciertos no lineales limitados. Finalmente, los dos tipos dirigidos de contractivo MPC han sido aplicados para controlar un Torneo de Fútbol de Copa Mundial de Micro Robot (MiroSot) y un Tanque-Reactor de Mezcla Continua (CSTR), respectivamente.

Neural network enhanced generalised minimum variance self-tuning controller for nonlinear discrete-time systems

A neural network enhanced self-tuning controller is presented, which combines the attributes of neural network mapping with a generalised minimum variance self-tuning control (STC) strategy. In this way the controller can deal with nonlinear plants, which exhibit features such as uncertainties, nonminimum phase behaviour, coupling effects and may have unmodelled dynamics, and whose nonlinearities are assumed to be globally bounded. The unknown nonlinear plants to be controlled are approximated by an equivalent model composed of a simple linear submodel plus a nonlinear submodel. A generalised recursive least squares algorithm is used to identify the linear submodel and a layered neural network is used to detect the unknown nonlinear submodel in which the weights are updated based on the error between the plant output and the output from the linear submodel. The procedure for controller design is based on the equivalent model therefore the nonlinear submodel is naturally accommodated within the control law. Two simulation studies are provided to demonstrate the effectiveness of the control algorithm.

Dynamic integrated system optimization and parameter estimation for discrete time optimal control of nonlinear systems

An algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses Dynamic Integrated System Optimization and Parameter Estimation (DISOPE), which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimization procedure. A version of the algorithm with a linear-quadratic model-based problem, implemented in the C+ + programming language, is developed and applied to illustrative simulation examples. An analysis of the optimality and convergence properties of the algorithm is also presented.

Stable reduced-order models for discrete-time systems

The Routh-stability method is employed to reduce the order of discrete-time system transfer functions. It is shown that the Routh approximant is well suited to reduce both the denominator and the numerator polynomials, although alternative methods, such as PadÃ�Â(c)-Markov approximation, are also used to fit the model numerator coefficients.

Dynamic Tracking with Zero Variation and Disturbance Rejection Applied to Discrete-Time Systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Singular perturbation problems for time-reversible systems

In this paper singularly perturbed reversible vector fields defined in R-n without normal hyperbolicity conditions are discussed. The main results give conditions for the existence of infinitely many periodic orbits and heteroclinic cycles converging to singular orbits with respect to the Hausdorff distance.

Filtering for discrete-time Markov jump systems with network transmitted mode

This paper is concerned with ℋ 2 and ℋ ∞ filter design for discrete-time Markov jump systems. The usual assumption of mode-dependent design, where the current Markov mode is available to the filter at every instant of time is substituted by the case where that availability is subject to another Markov chain. In other words, the mode is transmitted to the filter through a network with given transmission failure probabilities. The problem is solved by modeling a system with N modes as another with 2N modes and cluster availability. We also treat the case where the transition probabilities are not exactly known and demonstrate our conditions for calculating an ℋ ∞ norm bound are less conservative than the available results in the current literature. Numerical examples show the applicability of the proposed results. ©2010 IEEE.

Performance Evaluation of Material Flow Systems in Discrete Time

Im folgenden Beitrag werden zeitdiskrete analytische Methoden vorgestellt, mit Hilfe derer Informations- und Materialflüsse in logistischen Systemen analysiert und bewertet werden können. Bestehende zeitdiskrete Verfahren sind jedoch auf die Bearbeitung und Weitergabe in immer gleichen Mengen („One Piece Flow“) beschränkt. Vor allem in Materialflusssystemen kommt es, bedingt durch die Zusammenfassung von Aufträgen, durch Transporte und durch Sortiervorgänge, zur Bildung von Batches. Daher wurden analytische Methoden entwickelt, die es ermöglichen, verschiedene Sammelprozesse, Batchankünfte an Ressourcen, Batchbearbeitung und Sortieren von Batches analytisch abzubilden und Leistungskenngrößen zu deren Bewertung zu bestimmen. Die im Rahmen der Entwicklungsarbeiten entstandene Software-Lösung „Logistic Analyzer“ ermöglicht eine einfache Modellierung und Analyse von praktischen Problemen. Der Beitrag schließt mit einem numerischen Beispiel.

Transition from time-continuous systems to discrete mappings

Detailed transport studies in plasmas require the solution of the time evolution of many different initial positions of test particles in the phase space of the systems to be investigated. To reduce this amount of numerical work, one would like to replace the integration of the time-continues system with a mapping.