Decentralized state feedback consensus of linear multi-agent systems with input saturation

This paper investigates the problem of leader-following consensus of a linear multi-agent system on a switching network. The input of each agent is subject to saturation. Low gain feedback based distributed consensus protocols are developed. It is established that, under the assumptions that each agent is asymptotically null controllable with bounded controls and that the network is connected or jointly connected, semi-global leader-following consensus of the multi-agent system can be achieved. Numerical examples are presented to illustrate this result.

This paper investigates the consensus problem for multiagent systems with time-varying delays. The bounded delays can be arbitrarily fast time-varying. The communication topology is assumed to be undirected and fixed. With general linear dynamics under average state feedback protocols, the consensus problem is then transformed into the robust control problem. Further, sufficient frequency domain criteria are established in terms of small gain theorem by analyzing the delay dependent gains for both continuous-time and discrete-time systems. The controller synthesis problems can be solved by applying the frequency domain design methods. Numerical examples are demonstrated to verify the effectiveness of the proposed approaches.

Consensus conditions for heterogeneous multi-agent sampled-data control systems with nonlinearities and inter-agent communication delay.

In this work, stochastic consensus of linear multi-agent systems with multiplicative measurement noises is investigated under undirected graphs. Based on the algebraic graph theory and the matrix theory, the consensus problem is converted into the stochastic stability problem of stochastic differential equations (SDEs) driven by multiplicative noises. Then by stochastic stability theorem for SDEs, the stochastic consensus conditions are given for the multi-agent systems. For the general linear multi-agent systems, the sufficient conditions for the mean square and the almost sure consensus are obtained based on the solution to an algebraic Riccati equation, where the consentability condition on the algebraic connectivity and the channel uncertainties is revealed. For the case of second-order integrator dynamics, by choosing some appropriate Lyapunov functions, the sufficient conditions for the mean square and the almost sure consensus, and the necessary conditions for the mean square consensus are derived. Moreover, it is shown that for any bounded noise intensities, the mean square and the almost sure consensus can be achieved by carefully choosing the control gain.

In this manuscript, the stability and consensus problem of the leader-following multi-agent system is studied. The state information of the leader is only available to the dynamics of all the followers, while the communication among the agents occurs at sampling instant. The innovative part of this paper is to reach the consensus and attain the stability for prescribed MASs with interval time varying delay using impulsive control in the presence of leader. The interaction between the agent is illustrated by an undirected graph. A class of distributed impulsive protocol relying on sampling information is suggested to reach the leader following consensus. The consensus is critically relying on the sampling period, control gains. By performing the similar procedures, the consensus problem of multi-agent system is converted to stability problem of the error system. By utilizing the stability theory of impulsive systems, algebraic graph theory, sufficient conditions are derived to guarantee the leader-following consensus of the multi-agent system. Terminally, a numerical example is given to show an efficacy of this presented approach and the sureness of theoretical analysis.

As a new area of research, consensus problems for multi-agent systems have been studied extensively in the literature. It is usually assumed that all agents share a common one-dimensional state space. The authors of this study concentrate on the consensus problems of multi-agent systems in the framework of high-dimensional state space. As a basis for the analysis, a general model is first introduced by presenting two typical examples along with some necessary and sufficient conditions for the system to solve a consensus problem. Then the structures of consensus functions are investigated and some algebraic characterisations are given. Finally, a class of switched multi-agent systems are discussed and some sufficient conditions for the possession of the consensus property are provided. Several examples to illustrate the effectiveness of theoretical results are given.

This paper examines the event-triggered consensus problem of the multi-agent system on signed networks. An event-based distributed control protocol is proposed for multiagent networks where the dynamics of each agent is characterized by a controllable linear time-invariant system ( $A, B$ ). By exploring the Gauge transformation between Laplacian matrix and signed Laplacian matrix, we show that the bipartite consensus and trivial consensus can be achieved, respectively, in terms of the structural balance of the underlying signed network. Furthermore, the Zeno phenomenon of the closed-loop system is shown to be non-existed when employing the proposed event-based control protocol. Simulation results are finally provided to demonstrate our results.

In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function approach and the decomposition method, the design problem of a distributed controller is solved in terms of convex optimization. The interplay among the allowable bound of the sampling interval, the probability of random packet losses, and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions. The obtained criteria are closely related to the maximum eigenvalue of the Laplacian matrix versus the second minimum eigenvalue of the Laplacian matrix, which reveals the intrinsic effect of communication topologies on consensus performance. Finally, simulations are given to show the effectiveness of the proposed results.In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function approach and the decomposition method, the design problem of a distributed controller is solved in terms of convex optimization. The interplay among the allowable bound of the sampling interval, the probability of random packet losses, and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions. The obtained criteria are closely related to the maximum eigenvalue of the Laplacian matrix versus the second minimum eigenvalue of the Laplacian matrix, which reveals the intrinsic effect of communication topologies on consensus performance. Finally, simulations are given to show the effectiveness of the proposed results.

Markovian jumping systems have arisen naturally in the mathematical modeling of phenomena spanning disciplines in the social sciences, natural sciences, and engineering. This kind of stochastic dynamical systems can be employed to model the dynamics when parameters are subject to random abrupt changes due to sudden environment changes, subsystem switching, system noises, executor faults, and so forth. Much attention has been given to modeling, optimization, and real applications of such stochastic dynamical systems in the literature in recent years. As the advanced control and optimization will provide a basis for the design and application of such stochastic systems, these advanced techniques would result in substantial and sustainable benefits. The accepted papers in this special issue include stochastic stability, stabilization, stochastic control optimization, system modeling and identification methods, predictive control, signal processing, robust filtering, multiagent systems, networked control systems, time-delayed systems, neural networks, the Takagi-Sugeno fuzzy systems, simulated annealing, and fault detection methods.

This paper considers bipartite consensus of linear multi-agent systems over signed directed graphs, where both collaboration and competition coexist. The agent dynamics are distinct and can all have different dimensions. The communication graph can be time-varying and need not to be connected at each time. A distributed control law is proposed which enables the group to split into two disjoint subgroups, and the outputs of all agents within each subgroup achieve consensus, but the two subgroups move oppositely towards each other. Rigorous analysis and a simulation example are provided.

This paper investigates the leaderless <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> consensus problem of multi-agent systems with higher-order Lipschitz dynamics and external disturbance. The topology is assumed to be directed. Distributed controllers using only relative outputs information of the adjacent agents are constructed. In order to deal with the non-symmetric property of the associated Laplacian matrix of directed topology, some properties of Laplacian matrix are introduced. By introducing an appropriate state transformation, the <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> consensus problem is converted to a low-dimensional system stability problem which is solved using Lyapunov stability analysis method. The effectiveness of the proposed control design is demonstrated through simulation examples.

This paper investigates the event-triggered consensus problem of multi-agent systems with uncertainties and input saturation. First, a fully distributed robust consensus low-gain feedback control strategy is proposed, in which some global information, such as the communication graph and the scale of network, is not needed. Then, by defining an internal dynamic variable to memory the past state, an adaptive dynamic event-triggering mechanism is proposed, which contributes to reducing the usage of communication resources and also does not rely on any global information. Furthermore, Lyapunov-based consensus analysis results are presented, and it is also formally shown that Zeno behavior can be excluded with the proposed consensus protocols. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.

The event-based leader-following consensus problem for multi-agent systems with input saturation is studied in this paper. The control input update is event-driven, and the triggering function is linear, under the given trigger function and trigger condition. At first, a sufficient condition of the leader-following consensus for multi-agent systems without input saturation is presented. Furthermore, under the constraint of input saturation and communication time delay, the leader-following consensus control is achieved through designing control protocol and choosing suitable parameters of control input. Lyapunov function in combination with S-procedure method is adopted to prove the consensus stability for multi-agent systems with input saturation and communication time delay. Moreover, the Zeno-behavior is excluded for the triggering time sequence. Finally, simulations are present to illustrate the effectiveness of the proposed consensus control protocols.

This article investigates the double dynamic event-triggered consensus of linear multiagent systems with periodic sampled-data via a novel decentralized output feedback stabilization approach. A novel dynamic event-triggered strategy based on periodic sampled-data is proposed for the sensor-to-controller channel and controller-to-actuator channel, respectively. This strategy can further reduce the number of triggers without affecting the system’s performance. We use a state linear transformation based on a directed spanning tree of the communication topology to equivalently transform the consensus problem into the decentralized output feedback stabilization problem of the corresponding edge-state system and propose a decentralized pole assignment approach to design the gain matrix for the consensus protocol. Then, by employing the Lyapunov function combined with the lossless S-procedure, we derive consensus criteria containing matrix inequalities. Finally, numerical examples are provided to verify the effectiveness of the proposed approach.

&lt;abstract&gt;&lt;p&gt;This article considers a consensus problem of multiagent systems with double integrator dynamics under nonuniform sampling. In the considered problem, the maximum sampling time can be selected arbitrarily. Moreover, the communication graph can change to any possible topology as long as its associated graph Laplacian has eigenvalues in an arbitrarily selected region. Existence of a controller that ensures consensus in this setting is shown when the changing topology graphs are undirected and have a spanning tree. Also, explicit bounds for controller parameters are given. A sufficient condition is given to solve the consensus problem based on making the closed loop system matrix a contraction using a particular coordinate system for general linear dynamics. It is shown that the given condition immediately generalizes to changing topology in the case of undirected topology graphs. This condition is applied to double integrator dynamics to obtain explicit bounds on the controller.&lt;/p&gt;&lt;/abstract&gt;