Second-Order Consensus of Multi-agent Systems via Periodically Intermittent Pinning Control

In this paper, we investigate the leader-following consensus of second-order multi-agent systems with nonlinear dynamics and time delay by employing periodically intermittent pinning control. All member agents and the virtual leader share the same nonlinear dynamics relating to the velocity and delayed velocity information. Based on Lyapunov stability theory, we obtain a novel criterion that is independent of the time delay and control width to guarantee the second-order consensus of multi-agent systems with time delay and periodically intermittent controllers. Numerical simulations are presented to illustrate the theoretical results.     

基于脉冲控制的时延异构多智能体编队控制

为提高编队系统鲁棒性,降低系统对通信条件的要求,针对异构多智能体系统的编队控制问题,提出一种基于脉冲控制的编队控制方法.考虑异构多智能体的切换拓扑与变时延情况,根据一致性理论,提出基于领航跟随者模型的脉冲控制协议.利用矩阵分析方法将异构多智能体编队系统的变时延问题转化为时延上界问题,通过构造Lyapunov函数并利用Lyapunov稳定理论得到系统实现编队控制一致性的充分条件.同时,为比较不同控制协议的优劣性,提出切换拓扑下多智能体编队控制的平均通信代价指标.仿真结果验证了所提脉冲控制方法的有效性和优越性.     

不同延迟下离散多智能体系统的一致性

移动多智能体系统的一致性问题是复杂动力学系统中非常有现实意义的问题。针对有向通信拓扑网络下具有不同延迟的一阶和二阶离散系统,该文提出一种一致性的协议,并进一步得到该系统离散域的传递函数。接着利用广义Nyquist判据和盖尔圆方法,对系统进行频域分析,推导出了传递函数一致性收敛的充分条件,给出了通信延迟的具体约束范围。最后给出数值算例,仿真结果验证了结论的正确性。     

Constrained Control of Positive Discrete-Time Systems With Delays

This brief addresses the control problem of linear time-invariant discrete-time systems with delays. The control is under positivity constraint, which means that the resulting closed-loop systems are not only stable, but also positive. The contribution lies in three aspects. First, a necessary and sufficient condition is established for the existence of such controllers for discrete-time delayed systems. Second, a sufficient condition is provided under the additional constraint of bounded control, which means that the control inputs and the states of the closed-loop systems are bounded. Third, sufficient conditions are proposed for discrete-time delayed systems with uncertainties, whether or not bounded control is considered. All the results are formulated as linear programming problems, hence easy to be verified. And the controllers are explicitly constructed if existent.     

Robust l2 - l∞ Control for Uncertain Discrete-Time Switched Systems with Delays

This paper is concerned with the problem of robust l₂ - l_∞ control for uncertain discrete-time switched systems with time delay in the state. The uncertainty is assumed to be of structured linear fractional form which includes the norm-bounded uncertainty as a special case. The control design approach is facilitated by introducing some additional instrumental matrix variables. The additional matrix variables decouple the Lyapunov and system matrices, which make the control design feasible. The proposed approach leads to less conservativeness of previous design methods, and the results also generalize earlier works for a more general parametric uncertainty structure. A numerical example is also given to demonstrate the effectiveness and the potential of the proposed techniques.     

Improved Delay-Dependent Stability Criteria for Discrete-Time Systems with Time-Varying Delays

This paper considers the stability problem for discrete-time systems with interval time-varying delays. By construction of a suitable Lyapunov–Krasovskii (L–K) functional and utilization of Finsler’s lemma, novel delay-dependent criteria for asymptotic stability of the systems are established in terms of linear matrix inequalities (LMIs) which can easily be solved by various effective optimization algorithms. Three numerical examples are given to illustrate the effectiveness of the proposed method.     

Networked Predictive Control Systems Based on the Hammerstein Model

In this paper, a novel predictive control-based approach is proposed for a networked control system with random delays containing an input nonlinear process based on a Hammerstein model. The method uses a time-delay two-step generalized predictive control scheme, which consists of two parts: one is to deal with the input nonlinearity of the Hammerstein model and the other is to compensate for the network-induced delay in the networked control system. A theoretical result using the Popov criterion is presented for the closed-loop stability of the system in the case of a constant delay. Simulation examples illustrating the validity of the approach are also presented.     

Stability and Constrained Control of a Class of Discrete-Time Fuzzy Positive Systems with Time-Varying Delays

This paper deals with the stability of nonlinear discrete-time positive systems with time-varying delays represented by the Takagi–Sugeno (T–S) fuzzy model. The time-varying delays in the systems can be unbounded. Sufficient conditions of stability which are not relevant to the magnitude of delays are derived by a solution trajectory. Based on the stability results, the problems of controller design via the parallel distributed compensation (PDC) scheme are solved. The control is under the positivity constraint, which means that the resulting closed-loop systems are not only stable, but also positive. Constrained control is also considered, further requiring that the state trajectory of the closed-loop system be bounded by a prescribed boundary if the initial condition is bounded by the same boundary. The stability results and control laws are formulated as linear matrix inequalities (LMIs) and linear programs (LPs). A numerical example and a real plant are studied to demonstrate the application of the proposed methods.     

First- and Second-Order Differentiators Based on Coupled-Line Directional Couplers

First- and second-order differentiators based on coupled-line directional couplers are presented. The time-derivative effect of coupled-line directional couplers is shown theoretically by applying Kirchhoff's laws to infinitesimal electromagnetically coupled transmission line sections. The time-derivation is accurate under the condition $Delta Tf_{0}gg 1/4$, where $Delta T$ is the pulse width and $f_{0}$ is the coupler center frequency; the required coupler operation frequency is thus inversely proportional to the pulse duration. The first-order differentiator, which is a simple coupled-line coupler, and the second-order differentiator, which requires in addition an interconnecting delay line, are demonstrated experimentally, and compared to ideal (mathematical) derivators.      

Robust Non-Fragile Guaranteed Cost Control for Nonlinear Time Delay Discrete-Time Systems Based on T-S Model

This paper concerns the robust non-fragile guaranteed cost control for nonlinear time delay discrete-time systems based on Takagi-Sugeno （T-S） model. The problem is to design a guaranteed cost state feedback controller which can tolerate uncertainties from both models and gain variation. Sufficient conditions for the existence of such controller are given based on the linear matrix inequality （LMI） approach combined with Lyapunov method and inequality technique. A numerical example is given to illustrate the feasibility and effectiveness of our result.     

具有领航者的时延多智能体系统的一致性

本文研究了具有不同通信时延和不同输入时延的移动多智能体算法的一致性.假设多智能体系统有n个智能体和一个Leader组成,网络连接拓扑是非对称有向加权图,智能体Leader为拓扑图的全局可达节点.应用频域控制理论和广义Nyquist判据研究了时延多智能体算法的一致性,得到保证系统一致性的收敛条件.该一致性条件是一个应用节...     

Stability Analysis of Uncertain Discrete-Time Piecewise Linear Systems with Time Delays

This paper considers the stability analysis of uncertain discrete-time piecewise linear systems with time delays based on piecewise Lyapunov-Krasovskii functionals. It is shown that the stability can be established for the control systems if there is a piecewise Lyapunov-Krasovskii functional, and moreover, the functional can be obtained by solving a set of linear matrix inequalities （LMIs） that are numerically feasible. A numerical example is given to demonstrate the efficiency and advantage of the proposed method.     

Robust Model Predictive Control for Piecewise Affine Systems

In this paper, we study a robust model predictive control (MPC) strategy for piecewise affine (PWA) systems with uncertainty that is described as a set of polytopic parameter-varying models in a polytope corresponding to each partition of the PWA systems. First, an infinite horizon MPC technique for guaranteeing robust stability is developed for uncertain PWA systems. According to the condition of the PWA system states, the sequence of piecewise linear feedback controller at each sampling time is derived on-line by solving a convex optimization problem involving linear matrix inequalities. The feasible PWA control law design can robustly stabilize the uncertain PWA systems. However, the on-line optimization problems may lead to a computational burden. Then we further propose an improved robust MPC algorithm. When the current state is outside of the region of PWA systems containing the origin, the proposed on-line robust MPC algorithm is utilized; once the current state enters the region with the origin, sequence attraction domains where the origin is included are constructed off-line one within another, and the explicit control laws corresponding to different attraction domains can drive the state to the origin. The two algorithms are illustrated with a numerical example. The simulation results show that both controller design methods can stabilize the PWA systems with polytopic uncertainty, and the improved algorithm can reduce the on-line computation cost.     

基于大通讯时滞的二阶多智能体系统的一致性分析

在有向网络拓扑下,该文研究了2阶大时滞多智能体系统的一致性,提出具有加权项的时滞状态导数反馈协议,改进了大通讯时滞导致系统震荡的问题。首先引入具有加权项的时滞状态导数反馈协议,并给出2阶多智能体系统的闭环形式;然后采用频域分析法求出2阶多智能体系统渐近实现稳态一致的充要条件,并证明与传统一致性协议相比,2阶多智能体系统...     

基于大通讯时滞的二阶多智能体系统的一致性分析

在有向网络拓扑下,该文研究了2阶大时滞多智能体系统的一致性,提出具有加权项的时滞状态导数反馈协议,改进了大通讯时滞导致系统震荡的问题。首先引入具有加权项的时滞状态导数反馈协议,并给出2阶多智能体系统的闭环形式;然后采用频域分析法求出2阶多智能体系统渐近实现稳态一致的充要条件,并证明与传统一致性协议相比,2阶多智能体系统在具有加权项的时滞状态导数反馈协议下能够容忍更大的通讯时滞;最后通过数值仿真验证了具有加权项的时滞状态导数反馈协议的优势。     

Improved Numerical Model for the Average Transfer Matrix of First- and Second-Order PMD

An improved model for the average transfer matrix of first- and second-order polarization-mode dispersion (F&SO-PMD) in optical fibers is derived from numerical simulations of the frequency dependence of the differential phase shifts and cross coupling between signal components that are transmitted in two principal states of polarization (PSPs). The mean differential phase shifts and cross-coupling phases are calculated for various given values of the differential group delay (DGD) and the second-order PMD parameter that characterizes the coupling between PSPs. It is found that the mean differential phase delays are equal to the DGDs only over a narrow optical bandwidth, beyond which they decrease with increasing frequency offset and in some cases even reverse sign. Similarly, the mean cross-coupling phases increase less rapidly with frequency than assumed in other popular models and always approach an asymptotic value, at which half of the optical power is coupled from one PSP to the other. Moreover, it is shown that these mean differential phase shifts and cross-coupling phases define a transfer matrix for F&SO-PMD that nicely predicts the average eye-opening penalties in return-to-zero-formatted digital optical signals that are transmitted in one of the two PSPs. These predictions are particularly accurate when the average polarization-dependent chromatic dispersion (PCD) is included in the PSP phases. Additional simulations of F&SO-PMD compensation reveal that the signal impairments caused by PCD, on average, are substantially smaller than those introduced by the cross coupling between PSPs     

Input-Output Finite-Time Stability of Discrete-Time Impulsive Switched Linear Systems with State Delays

This paper is concerned with the problem of input-output finite-time stability (IO-FTS) for discrete impulsive switched systems with state delays. Sufficient conditions are presented for the existence of IO-FTS for such systems under the cases of certain switching, arbitrary switching, and uncertain switching. All the obtained results are formulated in a set of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness of the proposed results.     

Interference Analysis of UWB Systems for IEEE Channel Models Using First- and Second-Order Moments

Statistical moments of the inter-path interference, the inter-chip interference and the intersymbol interference in a direct-sequence binary phase shift keying ultra-wide bandwidth (UWB) system are analyzed for the IEEE UWB channel models. Exact expressions for the first- and second-order moments are derived. The effects of the duration of the monocycle pulse, the spreading gain, and the number of interfering symbols on the average powers of the interferences are examined.