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.

A Consistent Time Level Implementation Preserving Second-Order Time Accuracy via a Framework of Unified Time Integrators in the Discrete Element Approach

In this work,a consistent and physically accurate implementation of the general framework of unified second-order time accurate integrators via the well-known GSSSS framework in the Discrete Element Method is presented.The improved tangential displacement evaluation in the present implementation of the discrete element method has been derived and implemented to preserve the consistency of the correct time level evaluation during the time integration process in calculating the algorithmic tangential displacement.Several numerical examples have been used to validate the proposed tangential displacement evaluation;this is in contrast to past practices which only seem to attain the first-order time accuracy due to inconsistent time level implementation with different algorithms for normal and tangential directions.The comparisons with the existing implementation and the superiority of the proposed implementation are given in terms of the convergence rate with improved numerical accuracy in time.Moreover,several schemes via the unified second-order time integrators within the framework of the GSSSS family have been carried out based on the proposed correct implementation.All the numerical results demonstrate that using the existing state-of-the-art implementation reduces the time accuracy to be first-order accurate in time,while the proposed implementation preserves the correct time accuracy to yield second-order.

Event-Triggered Finite-Time H∞ Filtering for Discrete-Time Nonlinear Stochastic Systems

This paper addresses the problem of event-triggered finite-time H∞ filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H∞ filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H∞ filter gain matrices can be expressed in an explicit form.

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.

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.

Intrusion Detection System for PS-Poll DoS Attack in 802.11 Networks Using Real Time Discrete Event System

Wi-Fi devices have limited battery life because of which conserving battery life is imperative. The 802.11 Wi-Fi standard provides power management feature that allows stations(STAs) to enter into sleep state to preserve energy without any frame losses. After the STA wakes up, it sends a null data or PS-Poll frame to retrieve frame(s) buffered by the access point(AP), if any during its sleep period. An attacker can launch a power save denial of service(PS-DoS) attack on the sleeping STA(s) by transmitting a spoofed null data or PS-Poll frame(s) to retrieve the buffered frame(s) of the sleeping STA(s) from the AP causing frame losses for the targeted STA(s). Current approaches to prevent or detect the PS-DoS attack require encryption,change in protocol or installation of proprietary hardware. These solutions suffer from expensive setup, maintenance, scalability and deployment issues. The PS-DoS attack does not differ in semantics or statistics under normal and attack circumstances.So signature and anomaly based intrusion detection system(IDS) are unfit to detect the PS-DoS attack. In this paper we propose a timed IDS based on real time discrete event system(RTDES) for detecting PS-DoS attack. The proposed DES based IDS overcomes the drawbacks of existing systems and detects the PS-DoS attack with high accuracy and detection rate. The correctness of the RTDES based IDS is proved by experimenting all possible attack scenarios.

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.

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.

The Relation between the Stabilization Problem for Discrete Event Systems Modeled with Timed Petri Nets via Lyapunov Methods and Max-Plus Algebra

A discrete event system is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Timed Petri nets are a graphical and mathematical modeling tool applicable to discrete event systems in order to represent its states evolution where the timing at which the state changes is taken into consideration. One of the most important performance issues to be considered in a discrete event system is its stability. Lyapunov theory provides the required tools needed to aboard the stability and stabilization problems for discrete event systems modeled with timed Petri nets whose mathematical model is given in terms of difference equations. By proving stability one guarantees a bound on the discrete event systems state dynamics. When the system is unstable, a sufficient condition to stabilize the system is given. It is shown that it is possible to restrict the discrete event systems state space in such a way that boundedness is achieved. However, the restriction is not numerically precisely known. This inconvenience is overcome by considering a specific recurrence equation, in the max-plus algebra, which is assigned to the timed Petri net graphical model.

Dynamical Behavior of Discrete Ratio-Dependent Predator-Prey System

In this paper, we propose a discrete ratio-dependent predator-prey system. The stability of the fixed points of this model is studied. At the same time, it is shown that the discrete model undergoes fold bifurcation and flip bifurcation by using bifurcation theory and the method of approximation by a flow. Numerical simulations are presented not only to demonstrate the consistence with our theoretical analyses, but also to exhibit the complex dynamical behaviors, such as the cascade of period-doubling bifurcation in period-2 and the chaotic sets. The Maximum Lyapunov exponents are numerically computed to confirm further the complexity of the dynamical behaviors. These results show that the direct discrete method has more rich dynamic behaviors than the discrete model obtained by Euler method.

H_∞ Filter Design for Discrete-time Systems with Missing Measurements

For packet-based transmission of data over a network, or temporary sensor failure, etc., data samples may be missing in the measured signals. This paper deals with the problem of H∞ filter design for linear discrete-time systems with missing measurements. The missing measurements will happen at any sample time, and the probability of the occurrence of missing data is assumed to be known. The main purpose is to obtain both full-and reduced-order filters such that the filter error systems are exponentially mean-square stable and guarantee a prescribed H∞ performance in terms of linear matrix inequality (LMI). A numerical example is provided to demonstrate the validity of the proposed design approach.

Stability analysis and stabilization for discrete-time singular delay systems

Stability analysis and stabilization for discrete-time singular delay systems are addressed,respectively.Firstly,a sufficient condition for regularity,causality and stability for discrete-time singular delay systems is derived.Then,by applying the skill of matrix theory,the state feedback controller is designed to guarantee the closed-loop discrete-time singular delay systems to be regular,casual and stable.Finally,numerical examples are given to demonstrate the effectiveness of the proposed method.

Attitude sensor fault diagnosis based on Kalman filter of discrete-time descriptor system

To diagnose the fault of attitude sensors in satellites, this paper proposes a novel approach based on the Kalman filter of the discrete-time descriptor system. By regarding the sensor fault term as the auxiliary state vector, the attitude measurement system subjected to the attitude sensor fault is modeled by the discrete-time descriptor system. The condition of estimability of such systems is given. And then a Kalman filter of the discrete-time descriptor system is established based on the methodology of the maximum likelihood estimation. With the descriptor Kalman filter, the state vector of the original system and sensor fault can be estimated simultaneously. The proposed method is able to esti-mate an abrupt sensor fault as well as the incipient one. Moreover, it is also effective in the multiple faults scenario. Simulations are conducted to confirm the effectiveness of the proposed method.

On Asymptotic Stabilization of Linear Discrete-time Systems with Saturated State Feedback

As saturation is involved in the stabilizing feedback control of a linear discrete-time system, the original global-asymptotic stabilization (GAS) may drop to region-asymptotic stabilization (RAS). How to test if the saturated feedback system is GAS or RAS? The paper presents a criterion to answer this question, and describes an algorithm to calculate an invariant attractive ellipsoid for the RAS case. At last, the effectiveness of the approach is shown with examples.

Discrete-time movement model of a group of trains on a rail line with stochastic disturbance

This paper presents a discrete-time model to describe the movements of a group of trains, in which some operational strategies, including traction operation, braking operation and impact of stochastic disturbance, are defined. To show the dynamic characteristics of train traffic flow with stochastic disturbance, some numerical experiments on a railway line are simulated. The computational results show that the discrete-time movement model can well describe the movements of trains on a rail line with the moving-block signalling system. Comparing with the results of no disturbance, it finds that the traffic capacity of the rail line will decrease with the influence of stochastic disturbance. Additionally, the delays incurred by stochastic disturbance can be propagated to the subsequent trains, and then prolong their traversing time on the rail line. It can provide auxiliary information for rescheduling trains When the stochastic disturbance occurs on the railway.

LMI Consensus Condition for Discrete-time Multi-agent Systems

This paper examines a consensus problem in multiagent discrete-time systems, where each agent can exchange information only from its neighbor agents. A decentralized protocol is designed for each agent to steer all agents to the same vector. The design condition is expressed in the form of a linear matrix inequality. Finally, a simulation example is presented and a comparison is made to demonstrate the effectiveness of the developed methodology.

Suboptimal Robust Stabilization of Discrete-time Mismatched Nonlinear System

This paper proposes a discrete-time robust control technique for an uncertain nonlinear system. The uncertainty mainly affects the system dynamics due to mismatched parameter variation which is bounded by a predefined known function. In order to compensate the effect of uncertainty, a robust control input is derived by formulating an equivalent optimal control problem for a virtual nominal system with a modified costfunctional. To derive the stabilizing control law for a mismatched system, this paper introduces another control input named as virtual input. This virtual input is not applied directly to stabilize the uncertain system, rather it is used to define a sufficient condition. To solve the nonlinear optimal control problem, a discretetime general Hamilton-Jacobi-Bellman(DT-GHJB) equation is considered and it is approximated numerically through a neural network(NN) implementation. The approximated solution of DTGHJB is used to compute the suboptimal control input for the virtual system. The suboptimal inputs for the virtual system ensure the asymptotic stability of the closed-loop uncertain system. A numerical example is illustrated with simulation results to prove the efficacy of the proposed control algorithm.