Output consensus analysis and design for high-order linear swarm systems: Partial stability method

Output consensus analysis and design problems for high-order linear time-invariant swarm systems with directed interaction topologies are investigated. Firstly, as foundations of our approaches, several conclusions about partial stability are given. Then, two subspaces of the output space of swarm systems, namely an output consensus subspace and a complement output consensus subspace, are introduced. Based on output projection onto the two subspaces and partial stability, necessary and/or sufficient conditions for output consensus and limited-control-energy consensus are proposed respectively, an explicit expression of the output consensus function is presented based on the different contributions of initial states of agents and protocols, and an approach independent of the number of agents is shown to determine the gain matrices of output consensus protocols. Finally, a numerical example is given to demonstrate the theoretical results.     

Output consensus for high-order linear time-invariant swarm systems

Output consensus analysis and design problems of high-order linear time-invariant swarm systems are investigated. First, an output consensus subspace and a complement output consensus subspace are introduced. By output projection onto the two subspaces and the partial stability theory, a necessary and sufficient condition for output consensus is presented, and an explicit expression of the output consensus function, which is jointly determined by the interaction topology and initial states of all agents, is given. Especially, it is shown that the output consensus function is completely determined by initial states of all agents if the interaction topology is balanced. Then, an approach to determine gain matrices in consensus protocols of swarm systems is proposed, which has less calculation complexity. Finally, a numerical example is shown to demonstrate theoretical results.     

Distributed admissible consensus control for singular swarm systems with switching topologies

The interaction topologies of swarm systems may be time varying due to the motions of agents or the failure of communication equipment. The current paper focuses on admissible consensus analysis and design problems for singular swarm systems with switching topologies. Admissible consensus analysis problems are converted into admissible ones of a reduced‐order switching subsystem by the state projection on the consensus subspace and the complement consensus subspace. Furthermore, an approach to determine the consensus function is proposed by the first equivalent form. Moreover, by the Riccati equation, admissible consensus design criteria are presented, which can guarantee the scalability of singular swarm systems because they are independent of the number of agents. Finally, numerical examples are presented to check the correctness of theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Admissible consensus analysis for high‐order linear singular swarm systems with multiple time‐varying delays and topology variances

Admissible consensus analysis problems for high‐order linear time‐invariant singular swarm systems with multiple time delays and time‐varying interaction topologies are investigated. First, necessary and sufficient conditions for admissible consensus are presented, and admissible consensus problems are transformed into admissible problems of multiple lower dimensional singular systems. Then, on the basis of the first equivalent form, explicit expressions of consensus functions are given, where the impacts of initial states of agents and protocols, time delays and topology variances are determined, respectively. Moreover, it is shown that if interaction topologies are balanced, then swarm systems with the same initial states but different interaction topologies and different time delays have an identical consensus function. Finally, numerical simulations are given to demonstrate theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

Practical consensus for high-order linear time-invariant swarm systems with interaction uncertainties,time-varying delays and external disturbances

Practical consensus problems for general high-order linear time-invariant swarm systems with interaction uncertainties and time-varying external disturbances on directed graphs are investigated in this article. A dynamic consensus protocol with non-uniform time-varying delays is adopted to deal with the practical consensus problem. Using state space decomposition, practical consensus problems of a swarm system are converted into stability problems of a disagreement subsystem. Based on the Lyapunov–Krasovskii functional approach and the linear matrix inequality technique, sufficient conditions for swarm systems to achieve practical consensus are proposed where the time-varying external disturbance can be in L ₂ or L _∞. Numerical simulations are presented to demonstrate theoretical results.     

Guaranteed‐Cost Consensus Control For High‐Order Linear Swarm Systems

Guaranteed‐cost consensus analysis and design problems for high‐order linear time‐invariant swarm systems are dealt with in this paper. First, a guaranteed‐cost consensus control problem is introduced to obtain a trade‐off design object between consensus regulation performances and control energy consumptions. Then, sufficient conditions for guaranteed‐cost consensus and consensualization are presented respectively, an upper bound of the cost function is determined, and explicit expressions of consensus functions are given, which are independent of interaction topologies of swarm systems. Finally, a numerical example is shown to demonstrate theoretical results.     

Containment analysis and design for high‐order linear time‐invariant singular swarm systems with time delays

Containment analysis and design problems for high‐order linear time‐invariant singular swarm systems on directed graphs with time delays are investigated. To eliminate impulse terms in singular swarm systems and ensure that the singular swarm systems can achieve containment, time‐delayed protocols are presented for leaders and followers, respectively. By model transformation, containment problems of singular swarm systems are converted into stability problems of multiple low‐dimensional time‐delayed systems. In terms of linear matrix inequality, sufficient conditions are presented for time‐delayed singular swarm systems to achieve containment, which are independent of the number of agents. By using the method of changing variables, an approach is provided to determine the gain matrices in the protocols. Numerical simulations are shown to demonstrate theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Two‐stage stability control for strict‐feedback systems with input delays and input nonlinear uncertainties

In this paper, a two‐stage control procedure is proposed for stabilization of a class of strict‐feedback systems with unknown constant time delays and nonlinear uncertainties in the input. A nominal controller is first designed to compensate input time delays without considering input nonlinear uncertainties. Extended from backstepping algorithm, input delay compensation is realized by means of predicted states that are computed through integration of cascaded system dynamics, making the nominal closed‐loop system asymptotically stable. Based on the nominal controller presented for the input delay system, a multi‐timescale system is subsequently developed to estimate the unknown input nonlinearity and make the estimate approach the nominal control input as fast as possible. It is proved that the proposed control scheme can make states of the strict‐feedback systems converge to zero and all the signals of the closed‐loop systems are guaranteed to be bounded in the presence of input time delays and nonlinear uncertainties. Simulation verification is carried out to illuminate the effectiveness of the proposed control approach.     

Necessary and Sufficient Conditions for Consensus of Delayed Fractional‐order Systems

In this paper, we study the consensus problem of fractional‐order systems with input delays. Using Laplace transform method, the stability of the fractional‐order systems is first discussed in the frequency domain. Based on the generalized Nyquist stability criterion, a necessary and sufficient condition is further derived to ensure the consensus of fractional‐order systems with identical input delays over directed interaction topology. Furthermore, when the interaction topology is undirected, the consensus condition of fractional‐order systems with heterogeneous input delays is explicitly given. Finally, some illustrative examples are presented to show the effectiveness and advantages of the theoretical results.     

Adaptive Fuzzy Control for Nonlinear Time‐Delay Systems with Dynamical Uncertainties

In this paper, an adaptive fuzzy backstepping robust control approach is proposed for a class of SISO nonlinear strict‐feedback systems. The nonlinear systems addressed in this paper are assumed to possess three uncertainties: (i) the unstructured uncertainties; (ii) the time delays; and (iii) the dynamics uncertainties. In adaptive backstepping recursive design, fuzzy logic systems are used to approximate the unstructured uncertainties. A nonlinear damping technique and Lyapunov–Krasovskii functions are introduced to cancel the effects of the dynamics uncertainties and deal with the time delays, respectively. Combining the backstepping technique and a small gain approach, a stable adaptive fuzzy robust control approach is developed. It is proved that all the signals of the closed‐loop system are semi‐golablly uniformaly ultimately bounded (SUUB). The effectiveness of the proposed approach is illustrated by a simulation example.     

Heterogeneous consensus of higher‐order multi‐agent systems with mismatched uncertainties using sliding mode control

A robust consensus controller is proposed for heterogeneous higher‐order nonlinear multi‐agent systems, when the agent dynamics are involved with mismatched uncertainties. A distributed consensus protocol based on a time‐varying nonhomogeneous finite‐time disturbance observer and sliding mode control is designed to realize the network consensus of higher‐order multi‐agent systems. The time‐varying finite‐time disturbance observer overcomes the problem of peaking value near the initial time caused by the constant gain one and is designed to estimate the uncertainties and to mitigate the effect of mismatched uncertainties during the sliding mode. To eliminate the chattering phenomenon and ensure finite‐time convergence to the sliding surface, the control law is designed by using the super twisting algorithm. Finally numerical simulations are given to illustrate the validity of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Stable‐protocol output consensualization for high‐order swarm systems with switching topologies

Stable‐protocol (SP) output consensus analysis and design for high‐order linear time‐invariant swarm systems with switching topologies are dealt with. Firstly, on the basis of observability decomposition, a dynamic output feedback consensus protocol with switching topologies is given. Then, a necessary and sufficient condition for SP output consensus is shown, and an explicit expression of the output consensus function is presented, which is independent of switching topologies. Furthermore, necessary and/or sufficient conditions for SP output consensualization, which are independent of the number of agents, are shown respectively. Finally, a numerical example is shown to demonstrate theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.     

Absolute stability of Lurie networked control systems

This paper is concerned with the absolute stability problem of networked control systems (NCSs) with the controlled plant being Lurie systems (Lurie NCSs), in which the network‐induced delays are assumed to be time‐varying and bounded. First, in consideration of both the time‐varying network‐induced delays and data packet dropouts, the Lurie NCSs can be modeled as a multiple‐delays Lurie system. Then, a delay‐dependent absolute stability condition is established by using the Lyapunov–Krasovskii method. Next, two approaches to controller design are proposed in the terms of simple algebra criteria, which are easily solved via the toolbox in Matlab. Furthermore, the main results can be extended to robust absolute stability of Lurie NCSs with the structured uncertainties, where robust absolute stability conditions and approaches to robust controller design are presented. Finally, two numerical examples are worked out to illustrate the feasibility and the effectiveness of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust fault detection and isolation of time-delay systems using a geometric approach

This paper investigates the development of Fault Detection and Isolation (FDI) filters for both retarded and neutral time-delay systems with unknown time-varying delays. Using a geometric framework, the notion of a finite unobservability subspace is introduced for time-delay systems and an algorithm for its construction is presented. A bank of residual generators is then designed so that each residual is affected by one fault and is partially decoupled from the others while the H_∞ norm of the transfer function between the disturbances and the uncertainties in delays and the residuals are guaranteed to remain less than a prescribed value. Furthermore, it is shown that in the case of known delays it is possible to generate residuals that enjoy perfect decoupling properties among faults. Simulation results presented demonstrate the effectiveness of our proposed FDI algorithms.     

Robust semi‐global coordinated tracking of linear multi‐agent systems with input saturation

This paper investigates the problem of coordinated tracking of a linear multi‐agent system subject to actuator magnitude saturation and dead zone characteristic with input additive uncertainties and disturbances. Distributed consensus and swarm tracking protocols are developed from a low‐and‐high gain feedback approach. Under the assumption that each agent is asymptotically null controllable with bounded controls, it is shown that robust semi‐global consensus tracking and swarm tracking of the multi‐agent system can always be reached provided that the networks are connected. Numerical examples are provided to illustrate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

LMI APPROACH TO ROBUST FILTERING FOR DISCRETE TIME‐DELAY SYSTEMS WITH NONLINEAR DISTURBANCES

This paper investigates the problem of robust filtering for a class of uncertain nonlinear discrete‐time systems with multiple state delays. It is assumed that the parameter uncertainties appearing in all the system matrices reside in a polytope, and that the nonlinearities entering into both the state and measurement equations satisfy global Lipschitz conditions. Attention is focused on the design of robust full‐order and reduced‐order filters guaranteeing a prescribed noise attenuation level in an H∞ or l₂‐l∞ sense with respect to all energy‐bounded noise disturbances for all admissible uncertainties and time delays. Both delay‐dependent and independent approaches are developed by using linear matrix inequality (LMI) techniques, which are applicable to systems either with or without a priori information on the size of delays.     

Consensus seeking via iterative learning for multi‐agent systems with switching topologies and communication time‐delays

This paper deals with the high‐precision consensus seeking problem of multi‐agent systems when they are subject to switching topologies and varying communication time‐delays. By combining the iterative learning control (ILC) approach, a distributed consensus seeking algorithm is presented based on only the relative information between every agent and its local (or nearest) neighbors. All agents can be enabled to achieve consensus exactly on a common output trajectory over a finite time interval. Furthermore, conditions are proposed to guarantee both exponential convergence and monotonic convergence for the resulting ILC processes of multi‐agent consensus systems. In particular, the linear matrix inequality technique is employed to formulate the established convergence conditions, which can directly give formulas for the gain matrix design. An illustrative example is included to validate the effectiveness of the proposed ILC‐motivated consensus seeking algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Delay‐Dependent Robust Stability Criteria For Uncertain Neutral Systems With Mixed Time‐Varying Discrete And Neutral Delays

In this paper, a new class of augmented quasi full size Lypunov‐Krasovskii functional is introduced for the robust stability of uncertain neutral systems with mixed time‐varying discrete and neutral delays. The nonlinear parameter perturbations and norm‐bounded uncertainties are taken into consideration separately. Delay‐dependent robust stability criteria are derived in the form of linear matrix inequalities. Numerical examples are presented to illustrate the significant improvement on the conservativeness of the delay bound over some reported results in the literature.     

利用子空间划分的局部离群数据挖掘算法

目前大多数局部离群数据挖掘算法需人为事先设置参数或阈值,且难以应用到高维数据集.给出一种新的局部离群数据挖掘算法PSO-SPLOF,该算法首先将数据集划分为互不相交的子空间,利用偏斜度判断子空间划分的优劣,并采用微粒群算法搜索最优划分子空间集;其次针对每个最优划分子空间,计算其数据对象的局部离群因子SPLOF值,并用SPLOF值来度量数据对象的局部偏离程度.最后采用离散化的天体光谱数据作为数据集,实验验证了PSO-SPLOF算法具有受人为因素影响小、伸缩性强和运算效率高等优点.