The controllability of multiagent systems governed by node and edge dynamics on signed graphs is investigated under distinct partition rules and control algorithms. Motivated by a social network case study, dynamic models for nodes and edges are established. A novel concept “edge bidirectional mapping” is introduced, along with an associated matrix that rigorously characterizes the relationship between node and edge Laplacian matrices. Necessary and sufficient conditions for controllability equivalence between node and edge dynamics are derived across three topological regimes, determined by the cardinality relationships between the number of nodesnand edgesm, namelyn > m, n = m, andnm. Furthermore, more explicit and comprehensive criteria for controllability properties of node and edge dynamics are formulated under distinct control algorithms and partition rules. Specifically, the proposed algorithms are considered in both absolute and relative forms, while the partition rules, distance partition (DP), generalized almost equitable partition (GAEP), and generalized relaxed almost equitable partition (GRAEP), are distinguished based on the number of positive, negative, and total connections between vertices (nodes or edges) within a cell and their neighboring connections to other cells. Notably, this study systematically analyzes their hierarchical inclusion relationships for the first time. Upper and lower bounds on the dimensions of the node and edge controllable subspaces are presented. The lower bound reflects DP with edge weight considerations, while the upper bound is obtained via partition algorithms that yield the best LGRAEP. Additionally, the computational complexity and convergence properties of the proposed partition rules (DP, GEP, GREP), Algorithms 1-2, and the derived bounds for the controllable subspace dimensions are analyzed. Theoretical results are comprehensively validated through multi-level simulations, including verification of theoretical bounds, analysis of clustering effects, and comparative model evaluation.

This article proposes a new adaptive event-triggered controller with prescribed tracking performance for a class of uncertain nonlinear systems. The controller is global, instead of semiglobal, by eliminating the initial-condition-dependence on the performance function. In contrast to the existing results, the controller design is tight to reduce conservatism, in which two enablers are involved. First, the controller fully leverages available information on system nonlinearities, rather than discarding the information as is done in the context of funnel control (FC). This enables the controller to more efficiently counteract the nonlinearities, potentially avoiding unnecessarily large control effort, thereby reducing conservatism. Second, dedicated dynamic compensations are introduced with the help of tuning functions to compensate for the intrinsic uncertainties appearing in the execution error, system nonlinearities, and control coefficients. In this way, estimating conservative bounds of multiple uncertain parameters is circumvented, and especially, inequality estimates, including completing squares, are largely avoided, thereby also reducing conservatism. To further improve communication efficiency, the proposed control scheme is extended to the scenario where the information transmission from sensor to controller is also event-triggered, by delicately designing a double-sided event-triggering mechanism. A classical pendulum system is utilized to verify the effectiveness and superiority of the proposed method.

This paper seeks adaptive event-triggered output-feedback control which enables exponential stabilization for nonlinear systems with unknown growth rate. Convergence rate, as an important performance specification, is usually hard to acquire in the context of adaptive control. Besides, the event-triggered architecture could undermine convergence rate, entailing a competent compensation mechanism under reduced execution. As such, we are compelled to pursue a distinctive adaptive event-triggered output-feedback scheme. Specifically, a delicate dynamic gain incorporating exponential-type time-varying information is introduced, which would not only counteract the unknown growth rate, but particularly enable desired convergence. Correspondingly, a compatible event-triggering mechanism, capable of ensuring timely execution for adaptive compensation, is designed by suitably exploiting the gain information. In this way, an adaptive event-triggered output-feedback controller is constructed, which can render exponential convergence for system states, alongside an explicit pre-estimate for inter-execution intervalsNote to Practitioners—In the networked setup, the communication resources are usually shared but limited, entailing efficient resource utilization. Notably, event-triggered control could cater for the efficiency demand, which requires information transmission and control updating only when necessary for systems, unlike sampled-data control with a conservative prescribed rate of sampling/execution. This paper is devoted to developing a distinctive adaptive output-feedback scheme of event-triggered stabilization under the architecture with controller-to-actuator communication reduced. The scheme can not only cope with system nonlinearities with unknown growth rate (resulting from e.g., slowly-but-widely varying parameters and multiplicative disturbances) but particularly enable exponential convergence rate, an objective which is impossible for the existing schemes. Besides, the scheme allows flexible parameter choice, with which the change in the number of executions is illustrated through simulation.

The paper considers the event-triggered stabilizability of multi-agent systems (MAS). To reduce the frequency of control input update and information transmission, a novel distributed event-triggered control strategy with state estimation feedback is designed to achieve stabilizability. Event-trigger rules involving dynamic threshold are constructed, which ensure the convergence of systems states in finite time. By utilizing iSCC (independent strongly connected component) partition and Lyapunov stability theory, sufficient criteria for achieving finite time stabilizability have been obtained. Moreover, formation control under event-trigger scheme is addressed based on the obtained stabilizability results. Besides, it has been proven that the event-trigger interval has a positive lower bound, which can avoid Zeno behavior. Finally, the effectiveness of the theoretical results is verified by simulation.Note to Practitioners—In the fields of control and engineering, system stability has always been a research hotspot. Traditional stability analysis often focuses on the asymptotic stability. However, many practical scenarios require the system to reach a stable state within a finite time, i.e., finite time stabilizability, such as rapid response systems, emergency braking systems, and responding to emergencies. Hence, the research on finite time stabilizability has important practical value. In order to reduce the frequency of control updates, this paper proposes the finite time stabilizability under event-trigger scheme and designs a novel feedback controller based on state estimation, which has not been discussed before. At the same time, to explore the impact of network topology on stabilizability, the sufficient conditions for achieving finite time stabilizability of the system are obtained by iSCC graph partition. Dynamic threshold in event-triggering conditions to guarantee the implementation of finite time stabilizability is constructed. Finally, the theoretical results are applied to formation control. The research is of great significance for improving system performance and meeting real-time requirements.

The paper studies the distributed adaptive formation control in the setting of limited information transmitted between agents. The limited information, due to nonzero-kernel communication weight matrices between agents, has benefits in information security and privacy preserving, although as incomplete information, it challenges the formation control. Particularly, the multi-agent systems allow heterogeneous nonlinearities and serious uncertainties, making the formation control more difficult to achieve. In the paper, a fully-distributed adaptive control scheme is presented under appropriate conditions on the communication network, by incorporating two dynamic compensators and an auxiliary dynamic variable. The two compensators are employed to separately counteract the serious uncertainties and unavailable global information of the network resulting from unmatched states and weights. The auxiliary dynamic variable is introduced in the coordinate transformation to ensure the boundedness of the control, which cannot be derived by the traditional coordinate transformation. Two numerical examples are provided to show the effectiveness of the developed approach.

For some natural networks, edge dynamics are a scientific representation, and physical quantities can be better characterized by edges than nodes, such as transportation and social networks. Topology is a paramount determinant for characterizing system performance. To bridge the gaps between the topology structure and stabilizability, we propose a technique to achieve the desired independent strongly connected component (iSCC) partition by adding edges to change the topology structure. Besides, based on iSCC partition as the central tool for grasping the stabilizability of node and edge dynamics, it has been proven that the stabilizability realization of first-order multiagent systems directly depends on the topology structure. Furthermore, the relationship between node stabilizability and edge stabilizability is explored from a graph theory perspective through the transformation mechanism from a node digraph to an edge digraph. In particular, the stabilizability results of second-order multiagent systems reveal that the stabilizability of node dynamics and edge dynamics depends not only on the topology, but also on the feedback coefficientsk1,k2. Ultimately, simulation experiments are provided to verify the correctness and effectiveness of the proposed control protocol.

For consensus, one issue is that its various variants, such as group consensus, scaled consensus, and bipartite consensus, ought to be proposed as the expansion of research and applications. Another issue is that consensus should carry certain performance specifications, to meet some crucial demands, such as rapidity and safety. In this article, we investigate an integrated consensus (i.e., scaled plus bipartite consensus) with a prescribed convergence rate, for a class of uncertain nonlinear MASs. A funnel-based adaptive scheme is proposed for the scaled bipartite consensus. Specifically, a time-varying function is preselected to characterize the prescribed convergence rate. Utilizing this time-varying function and the relative states defined in the sense of the scaled bipartite consensus, a fully distributed protocol is designed. Therein, the funnel gains are critical ingredients to ensure the prescribed performance, since they would increase the control signal to be sufficiently large once the relative states approach the performance boundary. Particularly, the selected time-varying design function is added to act as a part of the control gain in the protocol, which is critical to forcing the ultimate convergence (to zero) of relative states. The proposed protocol is verified by a simulation example.

This article addresses global stabilization via disparate event-triggered output feedback for a class of uncertain nonlinear systems. Typically, the systems allow unknown control directions and unmeasurable-state dependent growth simultaneously. Actually, in the context of the latter ingredient, there has been no any continuous control strategy that has allowed the former ingredient so far. Hence, one cannot solve the event-triggered control problem based on corresponding continuous feedback as done in the emulation-based method. In view of the unsolvability, we pursue a nonemulation-based strategy, directly conducting event-triggered control design. First, a parameterized output feedback controller incorporating a dynamic high gain is designed, which would globally stabilize the system once the adjustable parameter therein is suitable. Then, an event-triggering mechanism is developed to not only decide when the controller is sampled/executed but also determine which constant value the adjustable parameter takes. Just due to the instantly varying (discontinuous) adjustable parameter, the feedback ability of the controller is large enough, making it possible to solve the control design problem in the event-triggered framework. A simulation example is provided to verify the effectiveness and advantage of the proposed approach.

This article addresses event-triggered output-feedback stabilization with a prescribed convergence rate for uncertain nonlinear systems. Typically, the systems allow completely unknown nonlinearities, from which no any information is available for feedback. Nevertheless, an enhanced stabilization objective is pursued in this article to guarantee not only convergence, but particularly prescribed convergence rate. To this end, a distinct event-triggered output-feedback scheme is developed by integrating a powerful compensation technique with the event-triggering mechanism. Specifically, a set of delicate gains, motivated by the funnel control method, are introduced not only to handle the completely unknown nonlinearities and the execution error, but also to guarantee a prescribed rate. Particularly, a new event-triggering mechanism is given, where the threshold and suspension time are online adjusted with respect to the gains. As such, the threshold and suspension time could become adequately small as the gains increase, ensuring timely execution for the effectiveness of the compensation technique. It turns out that the designed event-triggered output-feedback controller guarantees the system states to globally converge to zero with the prescribed convergence rate.

This paper investigates global stabilization via adaptive event-triggered output feedback for a class of uncertain nonlinear systems. Typically, unknown polynomial-function rate is admitted in the unmeasurable-state dependent growth of the systems. This calls for an advanced compensation strategy based on dynamic high gain, which in turn requires more intelligent execution in the event-triggered control architecture. To this end, a novel event-triggering mechanism is designed with two events separately evaluating the behaviors of dynamic gain and the controller signal. Particularly, the event on controller signal is enforced to suspend for a certain time after each execution to guarantee a positive lower bound for the inter-execution intervals. More importantly, the suspension time and the threshold therein are both online adjusted according to dynamic gain (rather than pre-specified), which could become small enough as the dynamic gain increases. This ensures timely execution for the effectiveness of adaptive compensation. Then, with the dynamic gain delicately designed to counteract the influence of the execution error, an event-triggered controller via adaptive output feedback is proposed to make the original system states and observer states converge to zero. Further attempt is performed for more efficient resource saving and disturbance tolerance.

In this article, the adaptive finite-time consensus problem is discussed for uncertain nonlinear multiagent systems. In contrast with the correlative literature, the systems permit multiple uncertainties (not only in control coefficients but also in inherent nonlinearities), and typically the consensus protocol is pursued in a fully distributed fashion (independent from any global information of network topology). This essentially challenges the realization of the finite-time consensus. To overcome the challenge, a new continuous fully distributed protocol is proposed by combining adaptive techniques such that the finite-time consensus of the systems under investigation is achieved. Remarkably, a dynamic high gain, rather than multiple ones in the related literature, is adequate to resist two kinds of uncertainties and to guarantee the fully distributed fashion of the consensus protocol. Moreover, the adaptive finite-time consensus protocol is specified on the scenario of leader-following multiagent systems. Simulation results of three interaction topologies are acquired to illustrate the validity and the wider applicability of the proposed protocol.

This article is devoted to explore the periodic event-triggered stabilization for continuous-time stochastic systems, and to develop analysis tools/methods for stochastic periodic event-triggered control. Notably, without real-time monitoring of system behavior as in the scenario with continuous event evaluation, it is critical to delicately estimate and govern the execution/sampling error to achieve the desired system performance. This, under stochastic effects, would be substantially challenging, since the behavior of the stochastic system is hard to predict and is disparate between trials even with the same initial conditions. In this article, a framework of global stabilization via periodic event-triggered output-feedback is established: 1) a criterion condition based on the ISS-Lyapunov function is presented for the feasibility of the desired event-triggered stabilization; 2) both the asymptotic stabilization and exponential stabilization are achieved for the systems, with delicately specifying the periodic event-triggering mechanism; and 3) the involved analysis, without applying the well-known Lyapunov theorems, can serve as a pattern from estimating sampling and execution errors to assess the closed-loop stability for stochastic periodic event-triggered control. Moreover, based on the established framework, we contribute the stabilizing controller design via periodic event-triggered output-feedback for a class of stochastic nonlinear systems.

This article is devoted to the optimal protocol for the leader-following consensus of second-order multiagent systems. Remarkably, the global consensus cost functional and the directed topology are pregiven, and the optimal protocol to be sought is distributed. This makes the Riccati-based strategies inapplicable, by which merely centralized protocol can be derived. As the main contribution of this article, an effective strategy of seeking a distributed optimal protocol is proposed for second-order agents over the digraph of the directed tree. Detailedly, the feasibility of distributed optimal protocol is first affirmed, that is, the existence of optimal gain parameters can be guaranteed. Then, by recursively deriving the completely explicit formulas of the consensus errors of relative position and velocity, an online implementable algorithm is developed to achieve the parameterization of the cost functional, that is, to obtain the explicit formula of the cost functional with respect to gain parameters of all agents. Lastly, the desired optimal gain parameters are obtained by minimizing the explicit formula.

This paper considers the global stabilization for a class of uncertain nonlinear systems with unknown powers, unknown control directions, and unknown nonlinearities. Mainly due to the presence of the unknown powers which have not known upper bound, no existing methods are applicable to the control problem to be solved. In this paper, to compensate the serious system uncertainties and particularly to overcome the major obstruction from unknown powers, we appeal to the mechanism of switching adaptive feedback. By flexibly combining the domination and the method of adding a power integrator, we propose a new adaptive controller design, whose design parameters are tuned online based on a switching logic. The designed controller will become operative as long as finite switchings happen and will not lead to Zeno phenomenon, and can guarantee the global boundedness as well as ultimate convergence of the resulting closed-loop system. Two numerical examples are given to demonstrate the effectiveness of the developed design scheme.

This paper focuses on the almost sure consensus via time-varying feedback for a class of uncertain stochastic nonlinear multiagent systems. A remarkable feature of the systems is that the nonlinearities allow serious unknowns and time-variations. Moreover, there exists no known bound for the unknown control coefficients. To handle the unknowns and time-variations, a time-varying consensus scheme is developed. The main idea of the scheme is to incorporate a delicate function of time into consensus protocols such that the unknowns and time-variations can be compensated as time increases. Based on the proposed protocols, the almost sure leaderless consensus and almost sure leader-following consensus are achieved. Finally, two simulation examples are provided to illustrate the effectiveness of the theoretical results.

This paper addresses the linear quadratic regulator optimal leader-following consensus for multiagent systems in a single-integrator form. Substantially different from the existing related works, the cost function, a global one, and the topology structure are both pregiven, and the optimal protocol to be sought is distributed (which merely depends on relative state information). This violates the optimal protocol design based on the algebraic Riccati equation, although a centralized protocol can be derived. To solve the problem, a novel design strategy of distributed optimal protocol is proposed for the multiagent systems over the digraph of a directed tree. Specifically, the dynamics of the consensus error is explicitly obtained, by which an online-implementable algorithm is given to achieve the parameterization of the cost function. Namely, the completely explicit formula with respect to the gain parameters of all agents is derived for the cost function. Based on this, the existence of optimal gain parameters is rigorously proven, which means the existence of the desired distributed optimal protocol. Furthermore, the optimal gain parameters are derived by minimizing the explicit formula. Two simulation examples are provided to illustrate the effectiveness of the theoretical results.

This paper is devoted to the problem of global stabilization by output-feedback for a class of nonlinear systems with uncertain control coefficients, stable zero-dynamics and linearly unmeasured states dependent growth. By first introducing two kinds of appropriate state transformations, the original system is converted into the new system with deterministic virtual control coefficients and the separated zero-dynamics. Then, a suitable observer based on high-gain K-filters is constructed for the new system, and the backstepping design approach is successfully proposed to the output-feedback controller. It is shown that the global asymptotic stability of the closed-loop system can be guaranteed by the appropriate choice of the design parameters.