A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY

Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential stabilization.In comparison with autonomous cases,non-autonomous systems are of great interest and represent an important challenge.Accordingly,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted.It should be noted,in particular,that the stabilization can be achieved not only in the routine H_∞ and exponential forms,but also the polynomial form and even a general form.

Discrete Choice Models and Artificial Intelligence Techniques for Predicting the Determinants of Transport Mode Choice--A Systematic Review

Forecasting travel demand requires a grasp of individual decision-making behavior.However,transport mode choice(TMC)is determined by personal and contextual factors that vary from person to person.Numerous characteristics have a substantial impact on travel behavior(TB),which makes it important to take into account while studying transport options.Traditional statistical techniques frequently presume linear correlations,but real-world data rarely follows these presumptions,which may make it harder to grasp the complex interactions.Thorough systematic review was conducted to examine how machine learning(ML)approaches might successfully capture nonlinear correlations that conventional methods may ignore to overcome such challenges.An in-depth analysis of discrete choice models(DCM)and several ML algorithms,datasets,model validation strategies,and tuning techniques employed in previous research is carried out in the present study.Besides,the current review also summarizes DCM and ML models to predict TMC and recognize the determinants of TB in an urban area for different transport modes.The two primary goals of our study are to establish the present conceptual frameworks for the factors influencing the TMC for daily activities and to pinpoint methodological issues and limitations in previous research.With a total of 39 studies,our findings shed important light on the significance of considering factors that influence the TMC.The adjusted kernel algorithms and hyperparameter-optimized ML algorithms outperform the typical ML algorithms.RF(random forest),SVM(support vector machine),ANN(artificial neural network),and interpretable ML algorithms are the most widely used ML algorithms for the prediction of TMC where RF achieved an R2 of 0.95 and SVM achieved an accuracy of 93.18%;however,the adjusted kernel enhanced the accuracy of SVM 99.81%which shows that the interpretable algorithms outperformed the typical algorithms.The sensitivity analysis indicates that the most significant parameters influencing TMC are the age,total trip time,and the number of drivers.

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.

Model Order Reduction Methods for Discrete Systems via Discrete Pulse Orthogonal Functions

This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear systems are expanded in the space spanned by DPOFs,and two recurrence formulas for the expansion coefficients of the system’s state variables are obtained.Then,a modified Arnoldi process is applied to both recurrence formulas to construct the orthogonal projection matrices,by which the reduced-order systems are obtained.Theoretical analysis shows that the output variables of the reducedorder systems can match a certain number of the expansion coefficients of the original system’s output variables.Finally,two numerical examples illustrate the feasibility and effectiveness of the proposed methods.

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.

Optimal Guaranteed Cost Control via Static Output Feedback for Uncertain Discrete Time Systems

Aim To study the optimal guaranteed cost control problem via static output feedback for uncertain linear discrete time systems with norm bounded parameter uncertainty in both the state and the control input matrices of the state space model. Methods\ An upper bound on a quadratic cost index was found for all admissible parameter uncertainties and minimized by using Lagrange multiplier approach. Results and Conclusion\ Sufficient conditions are given for the existence of a controller guaranteeing the closed loop system quadratic stability and providing an optimized bound. A numerical algorithm for solving the output feedback gain is also presented.

Stabilization of discrete nonholonomic chained system

Aimed at the stabilization of the nonholonomic chained system under fixed sample control, two control laws were proposed. The discrete model of the nonholonomic chained system under zero-hold was obtained through the integrate method to the continuous model. And the discrete model was transformed to the form with two linear subsystems through coordinate transformation. Two feedback control laws, time-invariant control law and time-varying control law, were proposed; and the local stabilization and global stabilization were realized respectively. The simulation results show the effectiveness of the proposed control laws. The discrete nonholonomic chained system can converge to zero from any initial state exponentially, and the convergence rate can be changed through changing the parameters of the control laws.

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.

The discrete variational principle and the first integrals of Birkhoff systems＊

This paper shows that first integrals of discrete equation of motion for Birkhoff systems can be determined explicitly by investigating the invariance properties of the discrete Pfaffian. The result obtained is a discrete analogue of theorem of Noether in the calculus of variations. An example is given to illustrate the application of the results.

Robust Stability and Stabilization of Discrete Singular Systems with Interval Time-varying Delay and Linear Fractional Uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

Geo-engineered buffer capacity of two-layered absorbing system under the impact of rock avalanches based on Discrete Element Method

Many rock avalanches were triggered by the Wenchuan earthquake on May 12, 2008 in southwest China. Protection galleries covered with a single soil layer are usually used to protect against rockfall. Since one-layer protection galleries do not have sufficient buffer capacity, a two-layered absorbing system has been designed. This study aims to find whether an expanded poly-styrol （EPS） cushion, which is used in the soil-covered protection galleries for shock absorption, could be positioned under dynamic loadings. The dynamic impacts of the two-layered absorbing system under the conditions of rock avalanches are numerically simulated through a 2D discrete dement method. By selecting reasonable parameters, a series of numerical experiments were conducted to find the best combination for the two- layered absorbing system. The values of the EPS layer area as a percentage of the total area were set as 0% （Sl）, 22~ （S2）, and 70% （$3）. 22~ of the area of the EPS layer was found to be a reasonable value, and experiments were conducted to find the best position of the EPS layer in the two-layered absorbing system. The numerical results yield useful conclusions regarding the interaction between the impacting avalanches and the two-layered absorbing system. The soil layer can absorb the shock energy effectively and S2 （0.4-m thick EPS cushion covered with soil layer） is the most efficient combination, which can reduce the impact force, compared with the other combinations.

Discrete variational principle and first integrals for Lagrange-Maxwell mechanico-electrical systems

This paper presents a discrete vaxiational principle and a method to build first-integrals for finite dimensional Lagrange-Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function. The discrete variational principle and the corresponding Euler-Lagrange equations are derived from a discrete action associated to these systems. The first-integrals are obtained by introducing the infinitesimal transformation with respect to the generalized coordinates and electric quantities of the systems. This work also extends discrete Noether symmetries to mechanico-electrical dynamical systems. A practical example is presented to illustrate the results.

Discrete Event System Framework for Fault Diagnosis with Measurement Inconsistency:Case Study of Rogue DHCP Attack

Fault detection and diagnosis(FDD) facilitates reliable operation of systems. Various approaches have been proposed for FDD like Analytical redundancy(AR), Principal component analysis(PCA), Discrete event system(DES) model etc., in the literature. Performance of FDD schemes greatly depends on accuracy of the sensors which measure the system parameters.Due to various reasons like faults, communication errors etc.,sensors may occasionally miss or report erroneous values of some system parameters to FDD engine, resulting in measurement inconsistency of these parameters. Schemes like AR, PCA etc.,have mechanisms to handle measurement inconsistency, however,they are computationally heavy. DES based FDD techniques are widely used because of computational simplicity, but they cannot handle measurement inconsistency efficiently. Existing DES based schemes do not use Measurement inconsistent(MI)parameters for FDD. These parameters are not permanently unmeasurable or erroneous, so ignoring them may lead to weak diagnosis. To address this issue, we propose a Measurement inconsistent discrete event system(MIDES) framework, which uses MI parameters for FDD at the instances they are measured by the sensors. Otherwise, when they are unmeasurable or erroneously reported, the MIDES invokes an estimator diagnoser that predicts the state(s) the system is expected to be in, using the subsequent parameters measured by the other sensors. The efficacy of the proposed method is illustrated using a pumpvalve system. In addition, an MIDES based intrusion detection system has been developed for detection of rogue dynamic host configuration protocol(DHCP) server attack by mapping the attack to a fault in the DES framework.

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.

PARALLEL ANALYSIS OF COMBINED FINITE/DISCRETE ELEMENT SYSTEMS ON PC CLUSTER

A computational strategy is presented for the nonlinear dynamic analysis of large- scale combined finite/discrete element systems on a PC cluster.In this strategy,a dual-level domain decomposition scheme is adopted to implement the dynamic domain decomposition.The domain decomposition approach perfectly matches the requirement of reducing the memory size per processor of the calculation.To treat the contact between boundary elements in neighbouring subdomains,the elements in a subdomain are classified into internal,interfacial and external elements.In this way,all the contact detect algorithms developed for a sequential computation could be adopted directly in the parallel computation.Numerical examples show that this implementation is suitable for simulating large-scale problems.Two typical numerical examples are given to demonstrate the parallel efficiency and scalability on a PC cluster.

Dynamic Analysis of Deep-Ocean Mining Pipe System by Discrete Element Method

The dynamic analysis of a pipe system is one of the most crucial problems for the entire mining system. A discrete element method （DEM） is proposed for the analysis of a deep-ocean mining pipe system, including the lift pipe, pump, buffer and flexible hose. By the discrete element method, the pipe is divided into some rigid elements that are linked by flexible connectors. First, two examples representing static analysis and dynamic analysis respectively are given to show that the DEM model is feasible. Then the three-dimensional DEM model is used for dynamic analysis of the mining pipe system. The dynamic motions of the entire mining pipe system under different work conditions are discussed. Some suggestions are made for the actual operation of deep-ocean mining systems.

Discrete Fractional Lagrange Equations of Nonconservative Systems

In order to study discrete nonconservative system,Hamilton's principle within fractional difference operators of Riemann-Liouville type is given. Discrete Lagrange equations of the nonconservative system as well as the nonconservative system with dynamic constraint are established within fractional difference operators of Riemann-Liouville type from the view of time scales. Firstly,time scale calculus and fractional calculus are reviewed.Secondly,with the help of the properties of time scale calculus,discrete Lagrange equation of the nonconservative system within fractional difference operators of Riemann-Liouville type is presented. Thirdly,using the Lagrange multipliers,discrete Lagrange equation of the nonconservative system with dynamic constraint is also established.Then two special cases are discussed. Finally,two examples are devoted to illustrate the results.

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.

Immune algorithm for discretization of decision systems in rough set theory

Rough set theory plays an important role in knowledge discovery, but cannot deal with continuous attributes, thus discretization is a problem which we cannot neglect. And discretization of decision systems in rough set theory has some particular characteristics. Consistency must be satisfied and cuts for discretization is expected to be as small as possible. Consistent and minimal discretization problem is NP-complete. In this paper, an immune algorithm for the problem is proposed. The correctness and effectiveness were shown in experiments. The discretization method presented in this paper can also be used as a data pre- treating step for other symbolic knowledge discovery or machine learning methods other than rough set theory.

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.