This paper is concerned with delay‐dependent stability for linear systems with time‐varying delays. By decomposing the delay interval into multiple equidistant subintervals, on which different Lyapunov functionals are chosen, and new Lyapunov‐Krasvskii functionals are then constructed. Employing these new Lyapunov‐Krasvskii functionals, some new delay‐dependent stability criteria are established. The numerical examples show that the obtained results are less conservative than some existing ones in the literature. Copyright © 2009 John Wiley & Sons, Ltd.
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This chapter addresses a fixed-time leader–follower consensus problem for high-order integrator multi-agent systems subject to matched external disturbances. A cascade control structure, based on a fixed-time distributed observer, is developed to achieve...
This article is concerned with the distributed resilient estimation of a positive system over a sensor network. First, a heterogeneous sensor interaction framework, where each sensor is capable of sharing its local information of measurement as well as state estimate with its underlying neighbors via distinct interaction topologies, is proposed to account for different sensor communication capacities. During the information exchanges among the sensors, topological attacks are suitably modeled in such a way to incorporate the random and intermittent disruption of the heterogeneous sensor interaction topologies. Second, two sets of distributed resilient estimators are delicately constructed to cope with the resulting random denial of information exchanges within the specific repaired periods and compromised periods caused by the topological attacks. Third, the resilience performance analysis with a prescribed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -gain attenuation level is carried out, and a linear programming approach is then developed to achieve the design of the desired distributed estimators. Finally, the effectiveness of the proposed design method is verified through a vehicle formation monitoring system.
Consensus problems of multi-agent systems have attracted an ever-increasing interest in the control community due to their great potential in various applications such as cooperative unmanned air vehicles, automated highway systems scheduling, air traffic control, sensor networks. This paper presents a brief overview of theoretical development of consensus in a sampled-data setting, paying special attention to those published since 2011. Recent results in this area are categorized into several directions, such as consensus based on periodic sampling, variable sampling, stochastic sampling, and event-triggered communication. In particular, for event-triggered consensus, some typical patterns of event-triggering conditions are reviewed based on different definitions of a transmission error and a threshold.
This paper considers the robust stability problem of time-delay systems with block-diagonal uncertainty. A new stability criterion is derived using the refined discretized Lyapunov functional method. The criterion is written in the form of a linear matrix inequality. Numerical examples show the new criterion significantly improve the estimate of the stability limit over some existing results in the literature.
With the rapid development and widespread utilization of advanced communication, sensing, and computation technologies, increasing attention has been paid to develop new techniques of control and filtering for distributed networked systems. Note that the utilization of communication networks can improve efficiency, flexibility, and scalability in designing networked controllers and filters. However, communication networks usually suffer from communication resource constraints with detrimental consequences, such as long latency, increased packet dropout, reduced throughput, and so on. In order to address the challenges caused by limited communication resources, an event-triggered communication paradigm is an effective and promising technique that can significantly reduce computation/communication utilization while maintaining the desired estimation and the control performance. As a result, a variety of event-triggered control and filtering techniques for distributed networked systems have been proposed.
Game theory has emerged as a fundamental framework for modeling and analyzing strategic interactions and decision-making among multiple agents, and has witnessed rapidly growing impact in cyber–physical systems over the past decade. Its integration with dynamic systems has driven major theoretical and technological advances in a wide range of applications, including smart grids, autonomous driving, robotic swarms, and networked control systems. In particular, distributed games in dynamic systems and their equilibrium learning mechanisms have attracted increasing attention due to their scalability, lightweight information exchange, and real-time implementability. This article provides a comprehensive survey of distributed games in dynamic systems, where agents interact only with local neighbors while collectively achieving global equilibrium and stability. First, the foundational theories of distributed dynamic games under three representative classes of systems: linear dynamic systems, nonlinear dynamic systems, and uncertain dynamic systems, are presented. Then, state-of-the-art distributed equilibrium learning and control methods are reviewed, including gradient-based dynamics, payoff-based learning, best-response dynamics, and learning-based approaches. To demonstrate the practical relevance and impact of distributed games in dynamic systems, representative application domains are discussed in detail. Finally, several promising future research directions are outlined, highlighting open challenges at the intersection of distributed games, learning, and dynamic systems.
This paper is concerned with the problem of observer-based fuzzy stabilization for time-delay systems. The time-delay under consideration is assumed to be a constant time-delay, but not known exactly. A new design method is proposed for an observer-based fuzzy controller with adaptation to the time-delay. The designed controller simultaneously contains both the current and past state information of the systems and can be derived by solving a set of linear matrix inequalities (LMIs). The existence of the controller is equivalent to that of a controller for time-delay systems where the constant time-delay is known exactly. A numerical example is given to illustrate the effectiveness of the design method.
This note is concerned with the stability analysis and controller design for linear systems involving a network of sensors and actuators, which are triggered in groups by random events. These events are modeled by two independent Markov chains. A novel stability criterion is obtained by considering transmission delays in the measurement and control signals. Based on the stability criterion, the controller gain is designed. A numerical example is given to show the effectiveness of the proposed method.
The robust H/sub /spl infin// filtering problem for a class of continuous-time uncertain linear descriptor systems with time-varying discrete and distributed delays is investigated. The time-delays are assumed to be constant and known. The uncertainties under consideration are norm-bounded, and possible time-varying, uncertainties. Sufficient condition for the existence of an H/sub /spl infin// filter is expressed in terms of strict linear matrix inequalities (LMIs). Instead of using decomposition technique, a unified form of LMIs is proposed to show the exponential stability of the augmented systems. The condition for assuring the stability of the "fast" subsystem is implied from the unified form of LMIs, which is shown to be less conservative than the characteristic equation based conditions or matrix norm based conditions. The suitable filter is derived through a convex optimization problem. A numerical example is given to show the effectiveness of the method.
Distributed optimization, as a key technology for collaborative intelligence in multiagent systems, has been widely applied in sensor networks, deep learning, and smart grids. Although numerous effective algorithms have been proposed, classical methods typically rely on idealized assumptions, such as accurate objective information, perfect communication channels, and trustworthy system environments. However, these assumptions are frequently violated in real-world applications. To bridge the gap between theory and practice, distributed optimization under information constraints has emerged as a research focus. This survey provides a systematic overview of recent advances in this field. We categorize information constraints based on their origin into three primary types: i) observational constraints, including stochastic objectives, online optimization, and zeroth-order methods; ii) communication constraints, such as random network topologies, delays, asynchronous updates, and communication-efficient strategies; and iii) system-level constraints, encompassing privacy preservation and Byzantine-resilient optimization. This survey reviews the research progress and challenges associated with each constraint category. Furthermore, we use two representative case studies to analyze the practical application of these algorithms and the origins of information constraints in real-world problems. Finally, we explore promising future research directions.
The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study of this equation, proving existence, regularity, and blow-up results. In particular, precise asymptotics for the blow-up behavior are given, and it is shown that blow-up solutions are not unique.
This paper deals with the problem of practical fixed-time bipartite consensus of a nonlinear incommensurate fractional-order multiagent system (MAS) in a general coopetition network with signed directed graph, where the signed directed graph is composed of both positive and negative interaction links. By introducing a sliding-mode manifold, the incommensurate fractional-order MAS is transformed into an integer-order MAS. Then, practical fixed-time bipartite consensus protocols with constant and adaptive gains are designed, respectively, for the obtained integer-order MAS. By artfully constructing a Lyapunov function, it is shown that the practical bipartite consensus can be achieved with a settling time. Moreover, the upper bound of the settling time can be estimated explicitly, which is irrelevant to any initial conditions. Finally, the effectiveness of the proposed practical fixed-time bipartite consensus schemes is illustrated by numerical simulation.
This paper studies global synchronization between a heterogeneous dynamical network and a known target trajectory via distributed impulsive control. Synchronization with an error level, called quasi-synchronization, is analyzed by utilizing the time-varying Lyapunov function. Some sufficient quasi-synchronization conditions are presented and explicit expressions of error levels are derived. Furthermore, the effects of the pinning control matrix and the coupling strength are explored. Unlike the continuous pinning feedback control, it is shown that a large coupling strength will destroy synchronization in the present of impulsive controller, which is also verified by our simulations.
This paper is concerned with network-based modelling and dynamic output feedback control for an unmanned marine vehicle in network environments. A network-based model for the unmanned marine vehicle in the network environments is established for the first time by taking sampler-to-control station packet dropouts, network-induced delays, and packet disordering into account. This model is then extended to the unmanned marine vehicle system in the network environments subject to control station-to-actuator, and both sampler-to-control station and control station-to-actuator packet dropouts, network-induced delays, and packet disordering. Based on these models, dynamic output feedback controllers are designed to attenuate the oscillation amplitudes of the yaw velocity error and the yaw angle. It is shown through a benchmark example that (i) compared with the unmanned marine vehicle without control, the designed dynamic output feedback controllers can attenuate the oscillation amplitudes of the yaw velocity error and the yaw angle; and (ii) the designed dynamic output feedback controllers can provide much smaller oscillation amplitudes of the yaw velocity error and the yaw angle than a proportional–integral controller.
