The Complexity in Complete Graphic Characterizations of Multiagent Controllability

Zero-Norm Distance to Controllability of Linear Dynamic Networks

In this article, we consider the "nearest distance" from a given uncontrollable dynamical network to the set of controllable ones. We consider networks whose behaviors are represented via linear dynamical systems. The problem of interest is then finding the smallest number of entries/parameters in the system matrices, corresponding to the smallest number of edges of the networks, that need to be perturbed to achieve controllability. Such a value is called the zero-norm distance to controllability (ZNDC). We show genericity exists in this problem, so that other matrix norms (such as the 2-norm or the Frobenius norm) adopted in this notion are nonsense. For ZNDC, we show it is NP-hard to compute, even when only the state matrices can be perturbed. We then provide some nontrivial lower and upper bounds for it. For its computation, we provide two heuristic algorithms. The first one is by transforming the ZNDC into a problem of structural controllability of linearly parameterized systems, and then greedily selecting the candidate links according to a suitable objective function. The second one is based on the weighted -norm relaxation and the convex-concave procedure, which is tailored for ZNDC when additional structural constraints are involved in the perturbed parameters. Finally, we examine the performance of our proposed algorithms on several typical uncontrollable networks arising in multiagent systems.

Controllability on impulsive systems with delays in both input and impulse and its applications to multi-agent networks

This paper investigates the controllability of impulsive systems with input delay and impulse delay and its applications in multi-agent networks. We adopt the geometric and algebraic analytical tools to establish some easily verified controllability conditions for the considered system model. First, the analytic solution of the considered system is established on every impulsive interval by using ordinary differential equation theory. Then, according to the solution derived, some sufficient complete controllability criteria are developed to reveal the role of the Gramian matrices in different subintervals. By introducing a row matrix of different kinds of Gramian matrices, a complete controllability condition that is proved to be necessary and sufficient is further obtained. By using the relevant geometric matrix theory, the derived algebraic controllability condition is then converted to a geometric one. On other hand, we introduce a multi-agent network with delayed input and impulse and investigate its controllability. By resorting to graph theory and matrix theory, several factors affecting the controllability of the considered multi-agent networks are investigated, such as the topology structure, the inner coupling matrix, and the dynamics of each agent. Finally, two numerical examples are worked out to verify the derived controllability criteria.

Fuzzy adaptive event-triggered distributed control for a class of nonlinear multi-agent systems

In this work, we examine an adaptive and event-triggered distributed controller for nonlinear multi-agent systems (MASs). Second, we present a fuzzy adaptive event-triggered distributed control approach using a Lyapunov-based filter and the backstepping recursion technique. Next, the controller and adaptive rule presented guarantee that all tracking errors between the leader and the follower converge in a limited area close to the origin. According to the Lyapunov stability theory, this demonstrates that all other signals inside the closed loop are assured to be semi-globally, uniformly and finally constrained. Finally, simulation tests are conducted to illustrate the effectiveness of the control mechanism.

Data-Driven Distributed Information-Weighted Consensus Filtering in Discrete-Time Sensor Networks With Switching Topologies

This article proposes a data-driven distributed filtering method based on the consensus protocol and information-weighted strategy for discrete-time sensor networks with switching topologies. By introducing a data-driven method, a linear-like state equation is designed by utilizing only the input and output (I/O) data without a controlled object model. In the identification step, data-driven adaptive optimization recursive identification (DD-AORI) is exploited to identify the recurrence of time-varying parameters. It is proved that for discrete-time switching networks, estimation errors of all nodes are ultimately bounded when data-driven distributed information-weighted consensus filtering (DD-DICF) is executed. The algorithm combines with the received neighbors and direct or indirect observations for the target node to produce modified gains, resulting in a novel state estimator containing an information interaction mechanism. Subsequently, convergence analysis is performed on the basis of the Lyapunov equation to guarantee the boundedness of DD-DICF estimate error. Simulations verify the performance of the DD-DICF against the theoretical results as well as in comparison with some existing filtering algorithms.

Improved multi-agent controllability processing technique based on equitable partition

In this paper, we study the controllability of multi-agent systems by equitable partition and automorphism. For the case that cells are incompletely connected outside but completely connected inside, a necessary condition for controllability is given from the perspective of the rank of connection matrix. For the case of multiple cells being completely connected outside and incompletely connected inside, in terms of the eigenvalues and eigenvectors of L and L_π, several sufficient and necessary conditions for controllability are presented. Once the quotient graph is controllable under single input or all nodes in nontrivial cells are leaders, the lower bound of controllable subspace is determined. Finally, we give the gap between the necessary condition and the sufficient condition for controllability from the aspect of equitable partition. One highlight of the results in this paper is that we show sufficient conditions to judge controllability by equitable partition and automorphism, which, for specific cases, provides one method that how to break through the defect that equitable partition can only obtain necessary conditions.

Model-Free Adaptive Iterative Learning Bipartite Containment Control for Multi-Agent Systems

This paper studies the bipartite containment tracking problem for a class of nonlinear multi-agent systems (MASs), where the interactions among agents can be both cooperative or antagonistic. Firstly, by the dynamic linearization method, we propose a novel model-free adaptive iterative learning control (MFAILC) to solve the bipartite containment problem of MASs. The designed controller only relies on the input and output data of the agent without requiring the model information of MASs. Secondly, we give the convergence condition that the containment error asymptotically converges to zero. The result shows that the output states of all followers will converge to the convex hull formed by the output states of leaders and the symmetric output states of leaders. Finally, the simulation verifies the effectiveness of the proposed method.

Completely Event-Triggered Consensus for Multiagent Systems With Directed Switching Topologies

This article studies the leader-following consensus of multiagent systems (MASs) with completely event-triggered mechanisms (CETMs) and directed switching topologies. When most event-triggered schemes in MASs only reduce each agent's data transmissions to neighbor agents, CETMs further reduce data transmissions to actuators with one triggered function in each agent. To guarantee the switching links utilized by CETMs contain a directed spanning tree at any time, triggered decisions are improved to include the instants at which each agent's output links or leader link change. Furthermore, a less conservative method based on matrix inequalities is combined to minimize the allowable average dwell time (ADT) of switching topologies under the design conditions of CETMs. Based on multiple Lyapunov functions (MLFs), the sufficient conditions for controller gains that guarantee the leader-following consensus of MASs are proposed when the ADT of switching topologies is larger than the allowable value. Finally, an example of autonomous underwater vehicles (AUVs) is given to illustrate the effectiveness of CETMs.

Bipartite synchronization of signed networks via aperiodically intermittent control based on discrete-time state observations

In this paper, bipartite synchronization of signed networks with stochastic disturbances via aperiodically intermittent control is investigated. The aperiodically intermittent control presented is based on discrete-time state observations rather than continuous-time ones. To formulate signed networks and exhibit the competitive relation, a structurally balanced signed network is built and all the units are divided into two subcommunities. By employing Lyapunov method and graph theory, some sufficient conditions on bipartite synchronization are given. Meanwhile, when aperiodically intermittent control degenerates into periodically intermittent control and feedback control respectively, two corollaries are also provided to ensure the bipartite synchronization of the signed networks. Ultimately, two applications to coupled single-link robot arms and coupled oscillators are presented and corresponding numerical examples are respectively provided to verify the feasibility and effectiveness of the theoretical results.