Consensus problems in discrete-time multiagent systems with fixed topology

In this paper, we study the consensus problems in discrete-time multiagent systems with fixed topology. A necessary and sufficient condition for a system that solves a consensus problem is established, and the structure of consensus functions is characterized. Based on them, we introduce the standard topologies (graphs) of information flow, with which the systems can be viewed as single-leader-multi-follower systems. Moreover, the convex combination of these topologies can create a system that solves any predeterminate consensus problem. Additionally, we characterize the structural decomposition—the leaders-followers decomposition of a multiagent system, and establish a necessary and sufficient condition for an agent to be a leader.     

Consensus of second-order and high-order discrete-time multi-agent systems with random networks

This paper studies the convergence and convergence speed for the second-order and the high-order discrete-time multi-agent systems with random networks and arbitrary weights. Random networks mean that the existence of any edge is probabilistic and independent of any other edge. By introducing the agreement set, velocity control gain and high-order state control gain, some consensus protocols are provided for the discrete-time random networks. Moreover, the per-step and asymptotic convergence factors are proposed to measure the convergence and convergence speed. Some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.     

Formation control for second-order multi-agent systems with time-varying delays under directed topology

In this paper, we investigate a formation control problem for second-order multi-agent systems with directed graph interconnection topologies that contain time-varying coupling delays. By using a special multiple leaders’ framework, sufficient conditions are obtained for both time-invariant and time-varying formations as well as for time-varying formations for trajectory tracking, which guarantees the attainment of the formations is at exponentially converging speeds. Some numerical simulations are also conducted to validate the theoretical results.     

Consensus of the second-order multi-agent systems with an active leader and coupling time delay

This article investigates the consensus problem of the second-order multi-agent systems with an active leader and coupling time delay in direct graph. One decentralized state control rule is constructed for each agent to track the active leader and it is proved that the proposed control scheme enables the consensus to be obtained when the adjacency topology is fixed/switched. Simulation results show effectiveness of the proposed theoretical analysis.     

Impulsive consensus problem of second-order multi-agent systems with switching topologies

The paper proposes an impulsive consensus protocol to solve the consensus problem of the second-order multi-agent systems with fixed and switching topologies. Some sufficient conditions are obtained for the states of follower agents converging to the state of leader asymptotically. Two numerical simulations are also given to verify the effectiveness of the theoretical analysis.     

Consensus of heterogeneous multi-agent systems with linear and nonlinear dynamics

In this paper, we perform an in-depth study about the consensus problem of heterogeneous multi-agent systems with linear and nonlinear dynamics.Specifically, this system is composed of two classes of agents respectively described by linear and nonlinear dynamics. By the aid of the adaptive method and Lyapunov stability theory, the mean consensus problem is realized in the framework of first-order case and second-order case under undirected and connected networks.Still, an meaningful example is provided to verify the effectiveness of the gained theoretical results. Our study is expected to establish a more realistic model and provide a better understanding of consensus problem in the multi-agent system.     

Consensus seeking in multi-agent systems via hybrid protocols with impulse delays

This paper studies the consensus problem of multi-agent systems with both fixed and switching topologies. A hybrid consensus protocol is proposed to take into consideration of continuous-time communications among agents and delayed instant information exchanges on a sequence of discrete times. Based on the proposed algorithms, the multi-agent systems with the hybrid consensus protocols are described in the form of impulsive systems or impulsive switching systems. By employing results from matrix theory and algebraic graph theory, some sufficient conditions for the consensus of multi-agent systems with fixed and switching topologies are established, respectively. Our results show that, for small impulse delays, the hybrid consensus protocols can solve the consensus problem if the union of continuous-time and impulsive-time interaction digraphs contains a spanning tree frequently enough. Simulations are provided to demonstrate the effectiveness of the proposed consensus protocols.     

Necessary and sufficient conditions for consensus of third-order discrete-time multi-agent systems in directed networks

This paper studies consensus of third-order discrete-time multi-agent systems in directed networks. When each agent can only receive its neighbor’s position information, necessary and sufficient conditions for consensus of the system are established. Compared with the preceding work, we not only answer what consensus value the system eventually achieves, but also clearly show the equivalent relationship between consensus, scaling parameters and nonzero eigenvalues of the involved Laplacian matrix. Illustrative examples are also given to demonstrate the effectiveness of the obtained theoretical results.     

Filtering of discrete-time systems hidden in discrete-time random measures

This paper is concerned with the filtering problem of a discrete-time signal hidden in discrete-time random measures. Using measure change techniques as discussed in [1], recursive estimates of the signal are obtained. Also, a finite-state signal is discussed and filters of functionals of the signals are derived.     

Analysis of discrete-time queueing systems with priority jumps

This text is a summary of the author’s PhD thesis supervised by Herwig Bruneel and Joris Walraevens, and defended on 5 March 2009 at Ghent University. The thesis is written in English and is available from the author upon request. The work deals with several priority scheduling disciplines with so-called priority jumps. An efficient priority scheduling discipline is of great importance in modern telecommunication devices. Static priority scheduling achieves maximum service differentiation between different types of traffic, but may have a too severe impact on the performance of lower-priority traffic. Introducing priority jumps aims for a more gradual service differentiation. In the thesis, we propose several (types of) jumping mechanisms, and we analyse their effect on the performance of a discrete-time queueing system.     

Edge agreement of second-order multi-agent system with dynamic quantization via the directed edge Laplacian

This work explores the edge agreement problem of second-order multi-agent systems with dynamic quantization under directed communication. To begin with, by virtue of the directed edge Laplacian, we propose a model reduction representation of the closed-loop multi-agent system depending on the spanning tree subgraph. Considering the limitations of the finite bandwidth channels, the quantization effects of second-order multi-agent systems under directed graph are considered. The static quantizers generally contain a fixed quantization interval and infinite quantization level, which are, to some extent, inefficient and impractical. To further reduce the bit depth (number of bits available) and to obtain better precision, the dynamic quantized communication strategy referring to zooming in-zooming out scheme is required. Based on the reduced model associated with the essential edge Laplacian, the asymptotic stability of second-order multi-agent systems under dynamic quantized effects with only finite quantization level can be guaranteed. Finally, the simulation of altitude alignment of micro air vehicles is provided to verify the theoretical results.     

Balancing singular discrete-time systems

In this work, we deal with normalizable-balanced singular systems, that is, singular systems where the obtained closed-loop system is balanced by an appropriate feedback. In the invariant case, we use a proportional and derivative feedback to obtain systems without infinite poles. In addition, the existence and construction of state-feedbacks to obtain normalizable-balanced N-periodic singular systems is analyzed.     

Non-linear second-order periodic systems with non-smooth potential

In this paper we study second order non-linear periodic systems driven by the ordinary vectorp-Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth conditions on the potential function. Then we establish the existence of non-trivial homoclinic (to zero) solutions. Our theorem appears to be the first such result (even for smooth problems) for systems monitored by thep-Laplacian. In the last section of the paper we examine the scalar non-linear and semilinear problem. Our approach uses a generalized Landesman-Lazer type condition which generalizes previous ones used in the literature. Also for the semilinear case the problem is at resonance at any eigenvalue.     

Hybrid consensus for multi-agent systems with time-driven jumps

In this paper, the behavior of scalar multi-agent systems over networks subject to time-driven jumps. Assuming that all agents communicate through distinct communication digraphs at jump and flow times, the asymptotic multi-consensus behavior of the hybrid network is explicitly characterized. The hybrid multi-consensus is shown to be associated with a suitable partition that is almost equitable for both the jump and flow communication digraphs. In doing so, no assumption on the underlying digraphs is introduced. Finally, the coupling rules making the multi-consensus subspace attractive are established. Several simulation examples illustrate the theoretical results.     

On consensus speed of multi-agent systems with double-integrator dynamics

The performance of multi-agent systems is an important issue. In this paper, it is focused on consensus speed for multi-agent systems with double-integrator dynamics and fixed undirected graphes under a kind of consensus protocols. It is revealed that, under some conditions, the maximum consensus speed is determined by the largest and the smallest nonzero eigenvalues of the Laplacian matrix of the undirected connected graph. Based on the mentioned results, arbitrary desired consensus speed can be achieved by choosing suitable feedback gains. Numerical simulations are given to illustrate the main results.     

Stabilization analysis for discrete-time systems with time delay

The stabilization problem for a class of discrete-time systems with time-varying delay is investigated. By constructing an augmented Lyapunov function, some sufficient conditions guaranteeing exponential stabilization are established in forms of linear matrix inequality (LMI) technique. When norm-bounded parameter uncertainties appear in the delayed discrete-time system, a delay-dependent robust exponential stabilization criterion is also presented. All of the criteria obtained in this paper are strict linear matrix inequality conditions, which make the controller gain matrix can be solved directly. Three numerical examples are provided to demonstrate the effectiveness and improvement of the derived results.