Swarm stability for high-order linear time-invariant singular multi-agent systems

Swarm-stability and swarm-stabilisation problems for high-order linear time-invariant singular multi-agent systems with directed networks are investigated. First, necessary and sufficient conditions for swarm stability and asymptotic swarm stability are proposed, which are independent of the dimensions of Jordan blocks of the Laplacian matrix of the interaction topology. Then, an approach is given to determine the absolute motion as a whole, and it is shown that the absolute motion is completely determined by initial states if the interaction topology is balanced. Furthermore, an approach is presented to determine gain matrices for asymptotic swarm stabilisation. Moreover, leader-following swarm-stability and swarm-stabilisation problems are investigated. Finally, numerical examples are given to demonstrate theoretical results.     

Stabilization of Non‐Linear Fractional‐Order Uncertain Systems

In this paper, we present a stabilization method on the non‐linear fractional‐order uncertain systems. Firstly, a sufficient condition for the robust asymptotic stabilization of the non‐linear fractional‐order uncertain system is presented based on direct Lyapunov approach. Secondly, utilising the matrix's singular value decomposition (SVD) method, the systematic robust stabilization design algorithm is then proposed. Finally, two numerical examples are provided to illustrate the efficiency and advantage of the proposed algorithm.     

迭代粒子群算法及其在间歇过程鲁棒优化中的应用

针对无状态独立约束和终端约束的间歇过程鲁棒优化问题，将迭代方法与粒子群优化算法相结合，提出了迭代粒子群算法．对于该算法，首先将控制变量离散化，用标准粒子群优化算法搜索离散控制变量的最优解．然后在随后的迭代过程中将基准移到刚解得的最优值处，同时收缩控制变量的搜索域，使优化性能指标和控制轨线在迭代过程中不断趋于最优解．算法简洁、可行、高效，避免了求解大规模微分方程组的问题．对一个间歇过程的仿真结果证明了迭代粒子群算法可以有效地解决无状态独立约束和终端约束的间歇过程鲁棒优化问题．     

Adaptive Mittag‐Leffler Stabilization of a Class of Fractional Order Uncertain Nonlinear Systems

This paper deals with the stabilization of a class of commensurate fractional order uncertain nonlinear systems. The fractional order system concerned is of the strict‐feedback form with uncertain nonlinearity. An adaptive control scheme combined with fractional order update laws is proposed by extending classical backstepping control to fractional order backstepping scheme. The asymptotic stability of the closed‐loop system is guaranteed under the construction of fractional Lyapunov functions in the sense of generalized Mittag‐Leffler stability. The fractional order nonlinear system investigated can be stabilized asymptotically globally in presence of arbitrary uncertainty. Finally illustrative examples and numerical simulations are performed to verify the effectiveness of the proposed control scheme.     

分数阶混沌系统的延迟同步

基于分数阶线性系统的稳定性理论，结合反馈控制和主动控制方法，提出了实现分数阶混沌系统的延迟同步的一种新方法．该方案通过设计合适的控制器将分数阶混沌系统的延迟同步问题转化为分数阶线性误差系统在原点的渐近稳定性问题．分数阶Chen系统的数值模拟结果验证了该方案的有效性．     

粒子群优化算法在神经网络控制中的应用

考虑粒子群优化算法在不确定系统的自适应控制中的应用。神经网络在不确定系统的自适应控制中起着重要作用。但传统的梯度下降法训练神经网络时收敛速度慢,容易陷入局部极小,且对网络的初始权值等参数极为敏感。为了克服这些缺点,提出了一种基于粒子群算法优化的RBF神经网络整定PID的控制策略。首先,根据粒子群算法的基本原理提出了优化得到RBF神经网络输出权、节点中心和节点基宽参数的初值的算法。其次,再利用梯度下降法对控制器参数进一步调节。将传统的神经网络控制与基于粒子群优化的神经网络控制进行了对比,结果表明,后者有更好逼近精度。以PID控制器参数整定为例,对一类非线性控制系统进行了仿真。仿真结果表明基于粒子群优化的神经网络控制具有较强的鲁棒性和自适应能力。     

基于内分泌思想的改进粒子群算法

借鉴神经系统和内分泌系统对行为的高级调节作用,结合传统粒子群算法的原理,设计一种新的改进粒子群算法,充分考虑粒子周围的环境,引入内分泌调节项,对粒子的飞翔方程进行修改,达到改善粒子群算法的性能。为验证算法的有效性,将其与Dijkstra算法结合,实现机器人全局路径规划。结果表明,此方法比传统粒子群算法有较好的性能。     

Design and Implementation of Digital Fractional Order PID Controller Using Optimal Pole-Zero Approximation Method for Magnetic Levitation System

The aim of this paper is to employ fractional order proportional integral derivative (FO-PID) controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system (MLS), which is inherently nonlinear and unstable system. The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller. An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored. The controller parameters are tuned using dynamic particle swarm optimization (dPSO) technique. Effectiveness of the proposed control scheme is verified by simulation and experimental results. The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers. It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.      

基于群体多样性反馈控制的自组织微粒群算法

微粒群算法是一种新型的群智能算法,已被广泛用于各种复杂优化问题的求解,但算法依然面临着过早收敛问题.为克服算法的早熟问题,提出了自组织微粒群算法.将微粒群体视为自组织系统,引入负反馈机制.群体多样性是影响微粒群算法全局优化性能的关键因素,把群体多样性作为个体微粒可感知的群体动态信息,用于动态调整惯性权重或加速度系数,通过不同的特性参数实现微粒的集聚或分散,使群体维持适当的多样性水平以利于全局搜索.用于复杂函数优化问题的求解,并与其他典型改进算法进行了性能比较.仿真结果表明,基于多样性控制的自组织微粒群算法可以有效避免早熟问题,提高微粒群算法求解复杂函数的全局优化性能.     

基于BF-PSO的船舶电站柴油机分数阶控制器

针对船舶电力系统的频率稳定性问题,对船舶电站柴油机调速系统设计了分数阶PIλDμ控制器。采用细菌觅食-粒子群混合优化(BF-PSO)算法对分数阶PIλDμ控制器参数进行优化整定,解决了分数阶PIλDμ控制器整定参数多、设计复杂的问题。对分别采用分数阶PIλDμ控制器和传统整数阶PID控制器的柴油机调速系统进行了仿真和对比。结果表明,在同等条件下优化得到的分数阶PIλDμ控制器能够有效抑制模型参数摄动,鲁棒性更强,具有更好的控制效果。     

Self-organization of Decentralized Swarm Agents Based on Modified Particle Swarm Algorithm

In this paper, an attempt has been made by incorporating some special features in the conventional particle swarm optimization (PSO) technique for decentralized swarm agents. The modified particle swarm algorithm (MPSA) for the self-organization of decentralized swarm agents is proposed and studied. In the MPSA, the update rule of the best agent in swarm is based on a proportional control concept and the objective value of each agent is evaluated on-line. In this scheme, each agent self-organizes to flock to the best agent in swarm and migrate to a moving target while avoiding collision between the agent and the nearest obstacle/agent. To analyze the dynamics of the MPSA, stability analysis is carried out on the basis of the eigenvalue analysis for the time-varying discrete system. Moreover, a guideline about how to tune the MPSA's parameters is proposed. The simulation results have shown that the proposed scheme effectively constructs a self-organized swarm system in the capability of flocking and migration.Category (5) – Intelligent Systems / Intelligent Control / Fuzzy Control / Prosthetics / Robot Motion Planning     

Formation‐containment analysis and design for high‐order linear time‐invariant swarm systems

Formation‐containment analysis and design problems for high‐order linear time‐invariant swarm systems with directed interaction topologies are dealt with respectively. Firstly, protocols are presented for leaders and followers respectively to drive the states of leaders to realize the predefined time‐varying formation and propel the states of followers to converge to the convex hull formed by the states of leaders. Secondly, formation‐containment problems of swarm systems are transformed into asymptotic stability problems, and an explicit expression of the formation reference function is derived. Sufficient conditions for swarm systems to achieve formation containment are proposed. Furthermore, necessary and sufficient conditions for swarm systems to achieve containment and time‐varying formation are presented respectively as special cases. An approach to determine the gain matrices in the protocols is given. It is shown that containment problems, formation control problems, consensus problems and consensus tracking problems can all be treated as special cases of formation‐containment problems. Finally, numerical simulations are provided to demonstrate theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Task Scheduling in Distributed Systems Using Heap Intelligent Discrete Particle Swarm Optimization

The optimal mapping of tasks to the processors is one of the challenging issues in heterogeneous computing systems. This article presents a task scheduling problem in distributed systems using discrete particle swarm optimization (DPSO) algorithm with various neighborhood topologies. The DPSO is a recent metaheuristic population‐based algorithm. In DPSO, the set of particles in a swarm flies through the N‐dimensional search space by learning from both the personal best position and a neighborhood best position. Each particle inside the swarm belongs to a specific topology for communicating with neighboring particles in the swarm. The neighborhood topology affects the performance of DPSO significantly, because it determines the rate at which information transmits through the swarm. The proposed DPSO algorithm works on dynamic topology that is binary heap tree for communication between the particles in the swarm. The performance of the proposed topology is compared with other topologies such as star, ring, fully connected, binary tree, and Von Neumann. The three well‐known performance measures such as Makespan, mean flow time, and reliability cost are used for the comparison of the proposed topology with other neighborhood topologies. Computational simulation results indicate that the performance of DPSO algorithm has shown significant improvement with binary heap tree topology used for communication among the particles in the swarm.     

Logistic型混合自适应分数阶达尔文粒子群优化算法

针对传统的粒子群优化算法中存在的问题及分数阶达尔文微粒群优化(FDPSO)算法收敛速度慢,收敛精度不高的问题,改进其算法中分数阶速度更新策略,同时引入Logistic型混合分数阶自适应动态调整策略,得到一种改进的自适应分数阶达尔文粒子群优化(LFDPSO)算法,并通过相应理论分析,证明了该算法在给定条件下的收敛性,并由6个经典函数的数值测验表明,Logistic型混合自适应分数阶达尔文粒子群(LFDPSO)算法在收敛精度和收敛速度上得到了有效改善与提高,粒子在局部最优时的逃逸能力、全局寻优及智能搜索能力显著增强。     

基于粒子群优化的分数阶PID滑模控制参数整定

为了提高系统的控制性能,解决单一控制方法不足,将分数阶PID算法与滑模变结构算法相结合,同时为了规避分数阶PID的滑模变结构算法手动调节参数的复杂性以及不确定性,采用粒子群算法对其参数进行优化,完善分数阶PID的滑模变结构控制器,提高其控制精度.并将新型算法应用于单相全桥逆变器,通过Matlab仿真并与分数阶PID滑模变结构控制函数(PID-SMC)及滑模变结构控制(SMC)方法相比较,研究结果表明,粒子群算法整定参数收敛速度快,较短时间内可以找出最优解,整定后的算法静态误差小,上升速度快,抑制系统抖振能力强,具有较强的鲁棒性.     

基于粒子群和辅助变量法的分数阶系统辨识

针对噪声环境下分数阶系统的频域辨识问题,提出了一种结合粒子群优化算法和递推辅助变量法的辨识方法．首先将递推辅助变量法扩展到分数阶系统的频域辨识中,再将辅助变量法的抗噪声特性和粒子群算法的全局寻优能力相结合,采用粒子群算法辨识系统的阶次参数,并利用辅助变量法估计系统的分子分母多项式系数,完成了噪声环境下分数阶系统的阶次和分子分母多项式系数的整体辨识．仿真实验和对电网络阻抗的辨识实例表明了本文提出的辨识方法不仅适用于同元次分数阶系统,也适用于一般形式的分数阶系统．     

Fractional‐order–dependent global stability analysis and observer‐based synthesis for a class of nonlinear fractional‐order systems

This paper focuses on proposing novel conditions for stability analysis and stabilization of the class of nonlinear fractional‐order systems. First, by considering the class of nonlinear fractional‐order systems as a feedback interconnection system and applying small‐gain theorem, a condition is proposed for L₂‐norm boundedness of the solutions of these systems. Then, by using the Mittag‐Leffler function properties, we show that satisfaction of the proposed condition proves the global asymptotic stability of the class of nonlinear fractional‐order systems with fractional order lying in (0.5, 1) or (1.5, 2). Unlike the Lyapunov‐based methods for stability analysis of fractional‐order systems, the new condition depends on the fractional order of the system. Moreover, it is related to the H_∞‐norm of the linear part of the system and it can be transformed to linear matrix inequalities (LMIs) using fractional‐order bounded‐real lemma. Furthermore, the proposed stability analysis method is extended to the state‐feedback and observer‐based controller design for the class of nonlinear fractional‐order systems based on solving some LMIs. In the observer‐based stabilization problem, we prove that the separation principle holds using our method and one can find the observer gain and pseudostate‐feedback gain in two separate steps. Finally, three numerical examples are provided to demonstrate the advantage of the novel proposed conditions with the previous results.     

具有混合群智能行为的萤火虫群优化算法研究

萤火虫群优化算法是一种新型的群智能优化算法,基本的萤火虫群优化算法存在收敛精度低等问题。为了提高算法的性能,借鉴蜂群和鸟群的群体智能行为,改进萤火虫群优化算法的移动策略。运用均匀设计调整改进算法的参数取值。若干经典测试问题的实验仿真结果表明,引入混合智能行为大幅提升了算法的优化性能。     

一种随机粒子群算法及应用

为提高粒子群算法的优化效率,在分析量子粒子群优化算法的基础上,提出了一种随机粒子群优化算法。该算法只有一个控制参数,搜索步长由一个随机变量的取值动态决定,通过合理设计控制参数的取值,实现对目标位置的跟踪。标准测试函数极值优化和聚类优化的实验结果表明,与量子粒子群和普通粒子群算法相比,该算法在优化能力和优化效率两方面都有改进。     

Dynamic Output Feedback Consensualization of Uncertain Swarm Systems with Time Delays

Consensus analysis and design problems of high‐dimensional discrete‐time swarm systems in directed networks with time delays and uncertainties are dealt with by using output information. Two subspaces are introduced, namely a consensus subspace and a complement consensus subspace. By projecting the state of a swarm system onto the two subspaces, a necessary and sufficient condition for consensus is presented, and based on different influences of time delays and uncertainties, an explicit expression of the consensus function is given which is very important in applications of swarm systems. A method to determine gain matrices of consensus protocols is proposed. Numerical simulations are presented to demonstrate theoretical results.