A Discrete-Time Traffic and Topology Adaptive Routing Algorithm for LEO Satellite Networks

“Minimizing path delay” is one of the challenges in low Earth orbit (LEO) satellite network routing algo-rithms. Many authors focus on propagation delays with the distance vector but ignore the status information and processing delays of inter-satellite links. For this purpose, a new discrete-time traffic and topology adap-tive routing (DT-TTAR) algorithm is proposed in this paper. This routing algorithm incorporates both inher-ent dynamics of network topology and variations of traffic load in inter-satellite links. The next hop decision is made by the adaptive link cost metric, depending on arrival rates, time slots and locations of source-destination pairs. Through comprehensive analysis, we derive computation formulas of the main per-formance indexes. Meanwhile, the performances are evaluated through a set of simulations, and compared with other static and adaptive routing mechanisms as a reference. The results show that the proposed DT-TTAR algorithm has better performance of end-to-end delay than other algorithms, especially in high traffic areas.

Algorithms to Compute the Largest Invariant Set Contained in an Algebraic Set for Continuous-Time and Discrete-Time Nonlinear Systems

In this paper, some computational tools are proposed to determine the largest invariant set, with respect to either a continuous-time or a discrete-time system, that is contained in an algebraic set. In particular, it is shown that if the vector field governing the dynamics of the system is polynomial and the considered analytic set is a variety, then algorithms from algebraic geometry can be used to solve the considered problem. Examples of applications of the method(spanning from the characterization of the stability to the computation of the zero dynamics) are given all throughout the paper.

Convergence Analysis of a Kind of Deterministic Discrete-Time PCA Algorithm

We proposed a generalized adaptive learning rate (GALR) PCA algorithm, which could be guaranteed that the algorithm’s convergence process would not be affected by the selection of the initial value. Using the deterministic discrete time (DDT) method, we gave the upper and lower bounds of the algorithm and proved the global convergence. Numerical experiments had also verified our theory, and the algorithm is effective for both online and offline data. We found that choosing different initial vectors will affect the convergence speed, and the initial vector could converge to the second or third eigenvectors by satisfying some exceptional conditions.

Optimal Tracking Control for a Class of Unknown Discrete-time Systems with Actuator Saturation via Data-based ADP Algorithm

为有致动器浸透和未知动力学的分离时间的系统的一个班的一个新奇最佳的追踪控制方法在这份报纸被建议。计划基于反复的适应动态编程(自动数据处理) 算法。以便实现控制计划，一个 data-based 标识符首先为未知系统动力学被构造。由介绍 M 网络，稳定的控制的明确的公式被完成。以便消除致动器浸透的效果， nonquadratic 表演功能被介绍，然后一个反复的自动数据处理算法被建立与集中分析完成最佳的追踪控制解决方案。为实现最佳的控制方法，神经网络被用来建立 data-based 标识符，计算性能索引功能，近似最佳的控制政策并且分别地解决稳定的控制。模拟例子被提供验证介绍最佳的追踪的控制计划的有效性。

Discrete-time Markov-based dynamic control approach for compressed sampling

To solve the problem that the signal sparsity level is time-varying and not known as a priori in most cases,a signal sparsity level prediction and optimal sampling rate determination scheme is proposed.The discrete-time Markov chain is used to model the signal sparsity level and analyze the transition between different states.According to the current state,the signal sparsity level state in the next sampling period and its probability are predicted.Furthermore,based on the prediction results,a dynamic control approach is proposed to find out the optimal sampling rate with the aim of maximizing the expected reward which considers both the energy consumption and the recovery accuracy.The proposed approach can balance the tradeoff between the energy consumption and the recovery accuracy.Simulation results show that the proposed dynamic control approach can significantly improve the sampling performance compared with the existing approach.

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.

A novel reaching law approach of quasi-sliding-mode control for uncertain discrete-time systems

A novel discrete-time reaching law was proposed for uncertain discrete-time system,which contained process noise and measurement noise.The proposed method reserves all the advantages of discrete-time reaching law,which not only decreases the band width of sliding mode and strengthens the system robustness,but also improves the dynamic performance and stability capability of the system.Moreover,a discrete-time sliding mode control strategy based on Kalman filter method was designed,and Kalman filter was employed to eliminate the influence of system noise.Simulation results show that there is no chattering phenomenon in the output of controller and the state variables of controlled system,and the proposed algorithm is also feasible and has strong robustness to external disturbances.

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.

Adaptive Control and Function Projective Synchronization in 2D Discrete-Time Chaotic Systems

This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discretetime chaotic systems. In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems. Numerical results demonstrate the effectiveness of the proposed control scheme.

LMI-based robust control of uncertain discrete-time piecewise affine systems

The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine （PWA） systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bounded uncertainties respectively.The basic idea of the proposed approaches is to construct piecewise-quadratic （PWQ） Lyapunov functions to guarantee the stability of the closed-loop systems.The partition information of the PWA systems is taken into account and each polytopic operating region is outer approximated by an ellipsoid,then sufficient conditions for the robust stabilization are derived and expressed as a set of linear matrix inequalities （LMIs）.Two examples are given to illustrate the proposed theoretical results.

Approximation law for discrete-time variable structure control systems

Two approximation laws of sliding mode for discrete-time variable structure control systems are proposed to overcome the limitations of the exponential approximation law and the variable rate approximation law. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems, the stability of origin can be guaranteed, and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of approximation laws, the problem that the system control input is restricted is also considered, which is very important in practical systems. Finally a simulation example shows the effectiveness of the two approximation laws proposed.

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.

Variable structure control with sliding mode prediction for discrete-time nonlinear systems

A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining feedback correction and receding horizon optimization methods which are extensively applied on predictive control strategy, a discrete-time variable structure control law is constructed. The closed-loop systems are proved to have robustness to uncertainties with unspecified boundaries. Numerical simulation and pendulum experiment results illustrate that the closed-loop systems possess desired performance, such as strong robustness, fast convergence and chattering elimination.

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.

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.

Robust stability and H-infinity control for uncertain discrete-time Markovian jump singular systems

The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent （r.s.e.） transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality （LMI） conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.

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.

Composite nonlinear feedback control for output regulation problem of linear discrete-time systems with input saturation

Transient performance for output regulation problems of linear discrete-time systems with input saturation is addressed by using the composite nonlinear feedback（CNF） control technique. The regulator is designed to be an additive combination of a linear regulator part and a nonlinear feedback part. The linear regulator part solves the regulation problem independently which produces a quick output response but large oscillations. The nonlinear feedback part with well-tuned parameters is introduced to improve the transient performance by smoothing the oscillatory convergence. It is shown that the introduction of the nonlinear feedback part does not change the solvability conditions of the linear discrete-time output regulation problem. The effectiveness of transient improvement is illustrated by a numeric example.

Stability Criterion with Less LMI Variables for Linear Discrete-time Systems with Additive Time-delays

In this correspondence paper, an equivalent stability criterion with minimal number of linear matrix inequality （LMI） variables is presented for a delay-dependent stability criterion reported recently in the International Journal of Automation and Computing for a class of linear discrete-time systems with additive time delays. The reported stability criterion for the additive timedelay systems has more number of matrix variables in the LMI and, hence, demand additional computational burden. The proposed equivalent stability criterion, unlike the reported one, does not involve free-weighing matrices and encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criterion mathematically less complex and computationally more effective.

Non-fragile guaranteed cost control of discrete-time fuzzy bilinear system

This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems（DFBS）.Based on the parallel distributed compensation（PDC） approach,the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the cost function value is no more than a certain upper bound in the presence of the additive controller gain perturbations.The non-fragile guaranteed cost controller can be obtained by solving a set of bilinear matrix inequalities（BMIs）.The Van de Vusse model is utilized to demonstrate the validity and effectiveness of the proposed approach.