Discrete time transfer matrix method for dynamics of multibody system with flexible beams moving in space

In this paper, by defining new state vectors and developing new transfer matrices of various elements mov- ing in space, the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of multibody system with flexible beams moving in space. Formulations and numerical example of a rigid- flexible-body three pendulums system moving in space are given to validate the method. Using the new method to study the dynamics of multi-rigid-flexible-body system mov- ing in space, the global dynamics equations of system are not needed, the orders of involved matrices of the system are very low and the computational speed is high, irrespec- tive of the size of the system. The new method is simple, straightforward, practical, and provides a powerful tool for multi-rigid-flexible-body system dynamics.

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.

IMPULSIVE EXPONENTIAL SYNCHRONIZATION OF FRACTIONAL-ORDER COMPLEX DYNAMICAL NETWORKS WITH DERIVATIVE COUPLINGS VIA FEEDBACK CONTROL BASED ON DISCRETE TIME STATE OBSERVATIONS

This article aims to address the global exponential synchronization problem for fractional-order complex dynamical networks(FCDNs)with derivative couplings and impulse effects via designing an appropriate feedback control based on discrete time state observations.In contrast to the existing works on integer-order derivative couplings,fractional derivative couplings are introduced into FCDNs.First,a useful lemma with respect to the relationship between the discrete time observations term and a continuous term is developed.Second,by utilizing an inequality technique and auxiliary functions,the rigorous global exponential synchronization analysis is given and synchronization criterions are achieved in terms of linear matrix inequalities(LMIs).Finally,two examples are provided to illustrate the correctness of the obtained results.

Stabilization of a class of nonlinear discrete time systems with time varying delay

The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii functional method, a sufficient delaydependent condition for asymptotic stability of nonlinear systems is offered. Then, this condition is used to design a new efficient delayed state feedback controller(DSFC) for stabilization of such systems. These conditions are in the linear matrix inequality(LMI) framework. Illustrative examples confirm the improvement of the proposed approach over the similar cases. Furthermore, the obtained stability and stabilization conditions will be extended to uncertain discrete time delayed systems(UDTDS) with polytopic parameter uncertainties and also with norm-bounded parameter uncertainties.

On discrete time hedging errors in a fractional Black-Scholes model

In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging error due to discrete-time trading when the true strategy is known for the trader, is investigated. The result provides new statistical tools to study and detect the effect of the long-memory and the Hurst parameter for the error of discrete time hedging.

More relaxed condition for dynamics of discrete time delayed Hopfield neural networks

The dynamics of discrete time delayed Hopfield neural networks is investigated. By using a difference inequality combining with the linear matrix inequality, a sufficient condition ensuring global exponential stability of the unique equilibrium point of the networks is found. The result obtained holds not only for constant delay but also for time-varying delays.

Robust sliding mode control for uncertain discrete time systems

A novel variable structure control (VSC) strategy with a dynamic disturbance compensator based on the reaching law for a class of uncertain discrete systems is presented. The robust stability to disturbance and the system dynamics in the vicinity of the switching plane are studied. A measure of the uncertain parameters and external disturbance is obtained through delaying every sampling time. Theoretical analysis and experimental simulation results demonstrate that the dynamic performance and robustness of the closed-loop system are improved effectively.

The permanence of a higher order discrete time system

The permanence of a nonlinear higher order discrete time system from macroeconomics is studied, and a sufficient condition is proposed for the permanence of the system described by 11(,...,)nnnnkxrxfxx---=+ where :kfRR, the initial values 01,,kxx-are real numbers and [0,1)r is constant after exploring the relationship between this equation and 1(,...,)nnnkxfxx--= for certain classes of function f. As an application a short proof is given to a known result in a simpler way than ever reported.

On the Distribution of Duration of First Negative Surplus for a Discrete Time Risk Model with Random Interest Rate

In this paper, we examine further annuity-due risk model presented by Cai （Probability in the Engineering and Informational Sciences, 16（2002）, 309-324）. We consider the computation for the distribution of duration of first negative surplus and the algorithm is shown for calculating probability that ruin occurs and the duration of first negative surplus takes any nonnegative integers values. Numerical illustration for the main result is given.

The MAP/PH(PH/PH)/1 Discrete-time Queuing System with Repairable Server

In this paper, we discuss a discrete time repairable queuing system with Markovian arrival process, where lifetime of server, service time and repair time of server are all discrete phase type random variables. Using the theory of matrix geometric solution, we give the steady state distribution of queue length and waiting time. In addition, the stable availability of the system is also provided.

Iterative Learning Control for Discrete-time Stochastic Systems with Quantized Information

An iterative learning control (ILC) algorithm using quantized error information is given in this paper for both linear and nonlinear discrete-time systems with stochastic noises. A logarithmic quantizer is used to guarantee an adaptive improvement in tracking performance. A decreasing learning gain is introduced into the algorithm to suppress the effects of stochastic noises and quantization errors. The input sequence is proved to converge strictly to the optimal input under the given index. Illustrative simulations are given to verify the theoretical analysis. © 2014 Chinese Association of Automation.

Discrete time multiple spacecraft formation flying attitude optimal control in presence of relative state constraints

This paper addresses the challenge of synchronized multiple spacecraft attitude reorientation in presence of pointing and boundary constraints with limited inter-spacecraft communication link.Relative attitude pointing constraint among the fleet of spacecraft has also been modeled and considered during the attitude maneuvers toward the desired states.Formation fling control structure that consists of decentralized path planners based on virtual structure approach joint with discrete time optimal local controller is designed to achieve the mission's goals.Due to digital computing of spacecraft's onboard computer,local optimal controller based on discrete time prediction and correction algorithm has been utilized.The time step of local optimal algorithm execution is designed so that the spacecraft track their desired attitudes with appropriate error bound.The convergence of the proposed architecture and stability of local controller's tracking error within appropriate upper bound are proved.Finally,a numerical simulation of a stereo imaging scenario is presented to verify the performance of the proposed architecture and the effectiveness of the algorithm.

H_∞ State Feedback Delay-dependent Control for Discrete Systems with Multi-time-delay

In this paper, H ∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a discrete system with multi-time-delay to satisfy H ∞ performance indices is induced, and then a strategy for H ∞ state feedback control with delay values for plant with multi-time-delay is obtained. By solving corresponding LMI, a delay-dependent state feedback controller satisfying H ∞ performance indices is designed. Finally, a simulation example demonstrates the validity of the proposed approach. Keywords Multi-time-delay - discrete time system - LMI - delay-dependent - H ∞ control Bai-Da Qu received B. S. degree in electrical automation from Fuxin Mining Institute, China in 1982, M. Eng. degree from Hefei University of Polytechnology in 1990, and Ph.D from Northerneastern University in 1999. He was an electro-mechanical engineer at Erdaohezi Mine, Heilongjiang, China from 1982 to 1990, a Lecturer, Senior Engineer, Associate Professor and Professor in Shenyang Institue of Technology from 1990 to 2002. He is currently a professor in Communication and Control Engineering School, Southern Yangtze University. His research interests include control theory and applications (robust control, H ∞ control, time-delay systems, complex systems), system engineering (modeling, analysis and simulation, MIS,CMIS), power-electronics and electrical driving, signal detecting and process, industrial automation.

Leslie’s prey–predator model in discrete time

We consider the Leslie’s prey–predator model with discrete time.This model is given by a nonlinear evolution operator depending on five parameters.We show that this operator has two fixed points and define type of each fixed point depending on the parameters.Finding two invariant sets of the evolution operator,we study the dynamical systems generated by the operator on each invariant set.Depending on the parameters,we classify the dynamics between a predator and a prey of the Leslie’s model.

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS TO A DISCRETE TIME NON-AUTONOMOUS COMPETING SYSTEM WITH FEEDBACK CONTROLS

In this paper,a class of discrete time non-autonomous competing system with feedback controls is considered. With the help of differential equations with piecewise constant arguments,we first propose a discrete model of a continuous non-autonomous competing system with feedback controls. Then,using the coincidence degree and the related continuation theorem as well as some priori estimations,a suficient condition for the existence of positive solutions to difference equations is obtained.

A Discrete-Time Stochastic Traffic Assignment Model

A discrete time stochastic traffic assignment model is proposed. The model provides a discrete time description of the variations of flows on a road network during a day or a peak period. The congestion effect at links and link junctions are taken into account. The first in first out principle is enforced on all links at all periods of the day. A stochastic user equilibrium assignment is achieved when the tripmaker is unable to find better travel alternatives. A computational procedure is also presented.

NECESSARY AND SUFFICIENT CONDITIONS FOR QUADRATIC STABILITY OF UNCERTAIN DISCRETE TIME SYSTEMS

The robust stability analysis of discrete time systems with fast time varying uncertainties is considered in this paper. The necessary and sufficient conditions for quadratic stability are presented. Moreover, the stability robustness index is introduced as the measurement of the stability robustness. For the systems with given uncertain parameter bounds, checking the necessary and sufficient conditions and calculating the stability robust index are converted to solving minimax problems. It is shown that the maximization can be reduced to comparisons between the functional values of the corners when the parameter region is bounded by hyperpolydredon, and any local minimum value in the minimization is exactly the global minimum.

Asymptotic controllability of a class of discrete-time systems with disturbances

This article deals with the uniformly globally asymptotic controllability of discrete nonlinear systems with disturbances.It is shown that the system is uniformly globally asymptotic controllability with respect to a closed set if and only if there exists a smooth control Lyapunov function.Further, it is obtained that the control Lyapunov function may be used to construct a feedback law to stabilize the closed-loop system.In addition, it is proved that for periodic discrete systems, the resulted control Lyapunov functions are also time periodic.

Periodic Solutions of a Discrete Time Predator-Prey System

In this paper, we discuss a discrete predator-prey system with a non-monotonic functional response, which models the dynamics of the prey and the predator having non-overlapping generations. By using the coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solutions.

Noise-Tolerant ZNN-Based Data-Driven Iterative Learning Control for Discrete Nonaffine Nonlinear MIMO Repetitive Systems

Aiming at the tracking problem of a class of discrete nonaffine nonlinear multi-input multi-output(MIMO) repetitive systems subjected to separable and nonseparable disturbances, a novel data-driven iterative learning control(ILC) scheme based on the zeroing neural networks(ZNNs) is proposed. First, the equivalent dynamic linearization data model is obtained by means of dynamic linearization technology, which exists theoretically in the iteration domain. Then, the iterative extended state observer(IESO) is developed to estimate the disturbance and the coupling between systems, and the decoupled dynamic linearization model is obtained for the purpose of controller synthesis. To solve the zero-seeking tracking problem with inherent tolerance of noise,an ILC based on noise-tolerant modified ZNN is proposed. The strict assumptions imposed on the initialization conditions of each iteration in the existing ILC methods can be absolutely removed with our method. In addition, theoretical analysis indicates that the modified ZNN can converge to the exact solution of the zero-seeking tracking problem. Finally, a generalized example and an application-oriented example are presented to verify the effectiveness and superiority of the proposed process.