Group controllability of heterogeneous two‐time‐scale multi‐agent systems with switching topology

SummaryIn this paper, the problem of guaranteed‐performance consensus tracking of continuous‐time singular multiagent systems with Lipschitz nonlinearities and switching topologies is investigated. Consideration is that the interaction of the concerned agent network is described by a set of directed graphs with the union graph having a directed spanning tree rooted at the leader. To establish the guaranteed‐performance criterion, a quadratic performance function is constructed by utilizing the consensus errors among all agents. Then, a consensus protocol that collects the local information from neighboring agents is proposed to achieve consensus tracking and to guarantee the consensus regulation performance of the multiagent systems. On the basis of nonsingular transformation approach, singular systems theory, and Lyapunov stability analysis, the concerned guaranteed‐performance consensus tracking problem is cast into the admissibility analysis for an equivalent kind of switched singular consensus error system. Furthermore, sufficient conditions on the guaranteed‐performance consensus tracking protocol design are formulated in terms of linear matrix inequalities. Finally, numerical examples are employed to demonstrate the effectiveness of the theoretical results.

ABSTRACTThis paper focuses on controllability and observability of multi-agent systems with heterogeneous and switching topologies, where the first- and the second-order information interaction topologies are different and switching. First, based on the controllable state set, a controllability criterion is obtained in terms of the controllability matrix corresponding to the switching sequence. Next, by virtue of the subspace sequence, two necessary and sufficient algebraic conditions are established for controllability in terms of the system matrices corresponding to all the possible topologies. Furthermore, controllability is considered from the graphic perspective. It is proved that the system is controllable if the union graph of all the possible topologies is controllable. With respect to observability, two sufficient and necessary conditions are derived by taking advantage of the system matrices and the corresponding invariant subspace, respectively. Finally, some simulation examples are worked out to illustrate the theoretical results.

The problem of event‐triggered guaranteed cost consensus of discrete‐time singular multi‐agent systems with switching topologies is investigated in this paper. To save the limited network communication bandwidth of multi‐agent systems, a novel event‐triggered networked consensus mechanism is proposed. Based on the graph theory and singular system theory, sufficient conditions of guaranteed‐cost consensus of discrete‐time singular multi‐agent systems are derived and given in the form of the linear matrix inequalities, respectively. A co‐design approach of the multi‐agent consensus gain matrix and the event‐triggered parameters is presented. Furthermore, based on the approach of second class equivalent transformation for singular systems, the cost function is determined, and an explicit expression of consensus functions is presented. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.

<p>The consensus tracking problem of leader-follower multi-agent systems (MASs) with singular structures on jointly connected topology is studied in this paper. To achieve the objective of consensus tracking, a distributed adaptive control protocol is formulated to adjust the coupling weights among the agents using the adaptive rate, where the adaptive protocol can be implemented by each agent in a fully distributed manner without using any global information. A fuzzy logic system method is used to deal with the nonlinear terms in response to the limitations of nonlinear system analysis. The consensus tracking problem is transformed into an error system stability analysis, and two sufficient conditions are provided to guarantee the control objective based on Lyapunov stability theory and singular system theory. Finally, the effectiveness of this method is verified through a simulation example.</p>

This paper studies the controllability of two-time-scale continuous-time multi-agent systems with switching topology. The definition of controllability of continuous-time leader-follower multi-agent systems with two-time-scale feature connected by switching topology is proposed for the first time. To avoid the ill-posed problem caused by the singular perturbation parameter, firstly, the singular perturbation method based on iterative approximation is used to decompose the two-time-scale multi-agent systems into fast-time-scale and slow-time-scale subsystems. Then, according to the concepts of invariant subspace and controllable state set, a criterion of controllability is given. Finally, the simulation is used to illustrate the correctness of the theoretical results.KeywordsMulti-agent systemsControllabilityTwo-time-scaleSwitching topology

ABSTRACTThis study concerns the admissible consensus problem for networked singular multi-agent systems with communication delays and agents described by general singular systems. Only the information of outputs is available through the network. An observer-based networked predictive control scheme (NPCS) is employed to compensate for the communication delays actively. Based on NPCS and dynamic compensator (dynamic output feedback), a novel protocol is proposed. Based on graph, algebra and singular system theory, the necessary and sufficient conditions are given to guarantee existence of the proposed protocol. The conditions depend on the topologies of singular multi-agent systems and the structure properties of each agent dynamics. Moreover, a consensus algorithm is provided to design the predictive protocol. A numerical example demonstrates the effectiveness of compensation for networked delays.

Consensus of Singular Multi-agent Systems Based on Networked Predictive Control

This chapter introduces some basic definitions and results on graph theory, consensus decomposition of linear space theory, matrix theory, linear system theory, and singular system theory, which will be used in the following chapters. First, the definitions of directed graph, spanning tree, and Laplacian matrix, etc. are given, and properties of Laplacian matrix are addressed. Then the concepts of consensus subspace, complement consensus subspace, and state/output space decomposition are defined. Third, the properties of Kronecker product and Schur complement lemma are introduced. Moreover, the definitions and criteria for controllability, observability, and stability of linear time-invariant systems are summarized, and some results on partial stability of linear systems are also given. Finally, the definitions and results on the regularity, equivalent form, admissibility, and controllability of singular systems are introduced.

SummaryThis paper is concerned with the time‐varying formation control problem for singular multiagent systems with switching topologies. First, in order to eliminate the pulse solution of singular systems and extend the formation function set, the distributed formation controller has been formulated based on the output information of the agents. Then, the explicit expression of formation position function is presented based on the impulse free and the equivalent transformation of singular multiagent systems. Next, the sufficient and necessary conditions of the feasibility of the formation function are provided. Moreover, the sufficient conditions of formation control of singular multiagent systems with switching topologies are presented and the algorithm is designed to solve the distributed controller. Finally, the validity of the proposed approaches is verified by numerical simulation in this paper.

In this paper sufficient conditions for both practical and finite time stability of linear singular continuous time delay systems were introduced. The singular and singular time delay systems can be mathematically described as and , respectively. Analyzing finite time stability, the new delay independent and delay dependent conditions were derived using the approaches based on Lyapunov-like functions and their properties on the subspace of consistent initial conditions. These functions do not need to be positive on the whole state space and to have negative derivatives along the system trajectories. When the practical stability was analyzed, the approach was combined with classical Lyapunov technique to guarantee the attractivity property of the system behavior. Furthermore, an LMI approach was applied to obtain less conservative stability conditions. The proposed methodology was applied and tested on a medical robotic system. The system was designed for different insertion tasks playing important roles in automatic drug delivery, biopsy or radioactive seeds delivery. In this paper we have summarized different techniques for adequate modeling, control and stability analysis of the medical robots. The model of the robotic system, with the tasks described above, the entire system can be decomposed to the robotic subsystem and the environment subsystem. Modeling of the system by the method mentioned has been proved to be suitable when the force appears as a result of the interaction of the two subsystems. The mathematical model of the system has a singular characteristic. The singular system theory could be applied to the case described. It is well known that all mechanical systems have some delay. In that case a theory of singular systems with delayed states may be applied, as well. For the second phase in which there is no interaction, the dynamic behavior can be analyzed by the classic theory.

This study deals with the H ∞ filtering problem for a class of singular biological systems with stochastic exogenous disturbance. Singular system theory is utilised to build a stochastic singular food chain system. The authors’ purpose is to estimate the unmeasurable state variables of the food chain system by the available measurements. The general condition is established for a class of non‐linear singular systems to achieve input‐to‐state stable in mean and the prescribed H ∞ performance level. A sufficient condition of the solvability of filtering problem is proposed for the singular food chain system. Simulation example is provided to illustrate the effectiveness of the proposed filtering approach developed in this study.

In this paper sufficient conditions for both practical and finite time stability of linear singular continuous time delay systems were introduced. The singular and singular time delay systems can be mathematically described as and , respectively. Analyzing finite time stability, the new delay independent and delay dependent conditions were derived using the approaches based on Lyapunov-like functions and their properties on the subspace of consistent initial conditions. These functions do not need to be positive on the whole state space and to have negative derivatives along the system trajectories. When the practical stability was analyzed, the approach was combined with classical Lyapunov technique to guarantee the attractivity property of the system behavior. Furthermore, an LMI approach was applied to obtain less conservative stability conditions. The proposed methodology was applied and tested on a medical robotic system. The system was designed for different insertion tasks playing important roles in automatic drug delivery, biopsy or radioactive seeds delivery. In this paper we have summarized different techniques for adequate modeling, control and stability analysis of the medical robots. The model of the robotic system, with the tasks described above, the entire system can be decomposed to the robotic subsystem and the environment subsystem. Modeling of the system by the method mentioned has been proved to be suitable when the force appears as a result of the interaction of the two subsystems. The mathematical model of the system has a singular characteristic. The singular system theory could be applied to the case described. It is well known that all mechanical systems have some delay. In that case a theory of singular systems with delayed states may be applied, as well. For the second phase in which there is no interaction, the dynamic behavior can be analyzed by the classic theory.

In this paper, the modelling and analysis problem of a planar quadruped walking robot with eight degrees of freedom using singular system theory is investigated. First, a brief description about singular system is given and then, the singular model of the quadruped robot is derived. Because of the complexity of the singular model of the robot, we linearized it around the contact point of the leg and the ground, and based on this model it is shown that impulses are generated in the force which exists between leg and ground in the contact points.

In this paper, the discrete- and continuous time dynamic input-output control models, the consumption-tracking models, are considered. Generally, these models are described by the linear-quadratic singular systems. So this paper, by using the singular system theory, investigates the optimal regulation problems of these models. The optimal controls of both discrete- and continuous-time linear-quadratic singular systems we derived.

In this paper, according to the fractional factor derivative method, we study the Lie symmetry theory of fractional nonconservative singular Lagrange systems in a configuration space. First, fractional calculus is calculated by using the fractional factor, and the fractional equations of motion are derived by using the differential variational principle. Second, the determining equations and the limiting equations of Lie symmetry under an infinitesimal group transformation are obtained. Furthermore, the fractional conserved quantity form of singular Lagrange systems caused by Lie symmetry is obtained by constructing a gauge‐generating function that fulfills the structural equation, which conforms to the Noether criterion equation. Finally, we present an example of a calculation. The results show that the Lie symmetry condition of nonconservative singular Lagrange systems is more strict than conservative singular systems, but because of increased invariance restriction, the nonconservative forces do not change the form of conserved quantity; meanwhile, the fractional factor method has high natural consistency with the integral calculus, so the theory of integer‐order singular systems can be easily extended to fractional singular Lagrange systems.