Guaranteed Performance Consensus Research Articles

Guaranteed-performance consensus for multi-agent systems with Lipschitz nonlinearity

This paper mainly addresses the guaranteed-performance consensus problem of multi-agent systems (MASs), under the energy constraints and Lipschitz nonlinear dynamics. First, to reach consensus under energy constraints, the consensus protocol and the quadratic performance function are proposed. Afterward, by using the properties of nonsingular transformation matrix and Lipschitz’s nonlinear representation, the consensus function conditions are expressed. Moreover, considering the guaranteed-performance cost, this paper designs the quadratic performance function derived from the Riccati inequality and Lyapunov–Krasovskii theorem. Eventually, numerical simulations are implemented to validate the theoretical results.

Leader-following Adaptive Guaranteed-performance Consensus Control for Multi-agent Systems With Exogenous Disturbance

Leader-following Adaptive Guaranteed-performance Consensus Control for Multi-agent Systems With Exogenous Disturbance

Guaranteed-performance consensus control for multi-agent systems with external disturbances via event-triggered strategy

In this paper, we investigate the leader-following guaranteed performance consensus problem for multi-agent systems(MASs) controlled by event-triggered under external disturbances. First, a disturbance observer is designed for each follower, which can be used to efficiently estimate external disturbances. Second, to reduce the waste of communication resources, a new distributed event-triggered strategy based on the state estimation of neighboring agents is presented, which does not need continuous communication among agents. And the growing estimation error is reset by communication updates. The analysis illustrates that Zeno behavior can be effectively averted by formulating a lower bound on the number of normals for the minimum inter-event interval. Also, based on the above proposed state feedback consensus protocol with guaranteed performance, sufficient conditions are derived to guarantee that a MASs can achieve leader-following consensus. In addition, the consensus criterion with guaranteed performance is put forward in the form of a linear matrix inequality. The cost of guaranteed performance with leader-following structural properties is also established. At last, an example of numerical simulation is presented to confirm the derived analytical solution.

Guaranteed‐performance consensus tracking for one‐sided Lipschitz non‐linear multi‐agent systems with switching communication topologies

The guaranteed-performance consensus tracking (GPCT) for non-linear multi-agent systems (MASs) with switching communication topologies is presented. Different from the existing work, the non-linear range of one-sided Lipschitz non-linear MASs is wider than the Lipschitz ones, and the upper bound of the tracking performance is given while achieving the consensus tracking. First, a guaranteed-performance tracking control protocol is proposed, where consensus tracking regulation performance is involved. Then, by the linear matrix inequality (LMI), sufficient conditions are provided to achieve the GPCT under the one-sided Lipschitz and quadratic inner bounded conditions. It is worth noting that a special LMI structure is directly constructed by introducing these two conditions to simplify the complexity of the derivation. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed results.

Guaranteed-performance consensus for descriptor nonlinear multi-agent systems based on distributed nonlinear consensus protocol

In this paper, guaranteed-performance consensus (GPC) for descriptor nonlinear multi-agent systems (DNMASs) with a leader is studied. The interactions among followers are bidirectional for leader-following DNMASs. Firstly, one designs a novel distributed nonlinear consensus protocol based on state feedback to reach consensus for DNMASs. The performance function is constructed by state errors among agents, which is time integration of quadratic function. Secondly, not only are sufficient conditions presented for guaranteed-performance consensus to ensure the scalability of DNMASs based on the Riccati inequality, but also an upper bound of the cost function is derived. It is shown that the guaranteed-performance costs are dependent on initial states of agents. Moreover, the conclusions are extended to achieve the leaderless GPC. Finally, simulation examples are presented to demonstrate the effectiveness of theoretical results.

Adaptive Guaranteed-Performance Consensus Control for Multi-Agent Systems with an Adjustable Convergence Speed

In this paper, adaptive guaranteed-performance consensus control problems for multiagent systems with an adjustable convergence speed are investigated. A novel adaptive guaranteed-performance consensus protocol is proposed, where the communication weights can be adaptively regulated. By the state space decomposition method and the stability theory, sufficient conditions for guaranteed-performance consensus are obtained and the guaranteed-performance cost is determined. Moreover, the lower bound of the convergence coefficient for multiagent systems is deduced, which is linearly adjustable approximately by changing the adaptive control gain. Finally, simulation examples are introduced to demonstrate theoretical results.

Completely Distributed Guaranteed-Performance Consensualization for High-Order Multiagent Systems With Switching Topologies

The guaranteed-performance consensualization for high-order linear and nonlinear multiagent systems with switching topologies is respectively realized in a completely distributed manner in the sense that consensus design criteria are independent of interaction topologies and switching motions. This paper first proposes an adaptive consensus protocol with guaranteed-performance constraints and switching topologies, where interaction weights among neighboring agents are adaptively adjusted and state errors among all agents can be regulated. Then, a new translation-adaptive strategy is shown to realize completely distributed guaranteed-performance consensus control and an adaptive guaranteed-performance consensualization criterion is given on the basis of the Riccati inequality. Furthermore, an approach to regulate the consensus control gain and the guaranteed-performance cost is proposed in terms of linear matrix inequalities. Moreover, main conclusions for linear multiagent systems are extended to Lipschitz nonlinear cases. Finally, two numerical examples are provided to demonstrate theoretical results.

Guaranteed-performance Consensualization for High-order Multi-agent Systems with Intermittent Communications

The current paper studies the guaranteed-performance consensualization for general high-order multi-agent systems with intermittent communications. Firstly, a new consensus protocol is constructed by using only intermittent local information, and the corresponding performance function is given to guarantee the consensus regulation performance among neighboring agents. Then, linear matrix inequality conditions for guaranteed-performance consensus and consensualization are respectively provided and a guaranteed-performance cost of multi-agent systems is determined meanwhile. Furthermore, the whole motion mode of the multi-agent system can be described by deriving a precise expression of the consensus function. If the nominal converge rate is larger than a positive threshold, then multi-agent systems can achieve guaranteed-performance consensus by determining the gain matrix when intermittent communications are involved, and the performance function is less than the guaranteed-performance cost. Finally, a simulation example is shown to demonstrate the effectiveness of the proposed theorems.

Leader‐following guaranteed performance consensus for second‐order multi‐agent systems with and without communication delays

The leader-following guaranteed-performance consensus problems for second-order multi-agent systems with and without communication time delays are investigated, where a guaranteed performance function is proposed to consider the consensus regulation performance. For the case without the time delay, the coupling gain and pinning strength are carefully considered. When the time delays exist in the communication, we find that the inequality (Seuret and Gouaisbaut) cannot be used to investigate the consensus problems proposed in the study since the obtained conditions cannot be satisfied. Therefore, Jensen's inequality and Newton–Leibniz formula, which can solve this issue well, are introduced. By using the state space decomposition approach, linear matrix inequality and Lyapunov stability theory, some sufficient conditions are derived for achieving the guaranteed performance consensus. Moreover, the upper bound of the performance function is determined. Finally, two examples are shown to verify the validity of the theoretical results.

Adaptive guaranteed-performance consensus design for high-order multiagent systems

The current paper investigates the distributed guaranteed-performance consensus design problems for high-order linear multiagent systems with leaderless and leader-follower structures, respectively. The information about the Laplacian matrix of the interaction topology or its minimum nonzero eigenvalue is usually required in existing works on the guaranteed-performance consensus, which means that their conclusions are not completely distributed. A new translation-adaptive strategy is proposed to realize the completely distributed guaranteed-performance consensus control by the structure feature of a complete graph in the current paper. For the leaderless case, an adaptive guaranteed-performance consensualization criterion is given in terms of Riccati inequalities and a regulation approach of the consensus control gain is presented by linear matrix inequalities. Extensions to the leader-follower cases are further investigated. Especially, the guaranteed-performance costs for leaderless and leader-follower cases are determined, respectively, which are associated with the intrinsic structure feature of the interaction topologies. Finally, two numerical examples are provided to demonstrate theoretical results.

Guaranteed performance consensus problems for nonlinear multi-agent systems with directed topologies

ABSTRACTThe guaranteed performance consensus problem for multi-agent systems with Lipschitz nonlinear dynamics is investigated, where the interaction topology is directed. Both switching and fixed interaction topologies are considered. By the matrix transformation method, the guaranteed performance consensus problems are transferred into guaranteed performance stabilisation problems. Then, the criteria of guaranteed performance consensus for nonlinear multi-agent systems with switching and fixed interaction topologies are obtained, respectively. For the introduced performance function, an upper bound is given. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed results.

Leader-following guaranteed-performance consensus design for singular multi-agent systems with Lipschitz nonlinear dynamics

Leader-following guaranteed-performance consensus problems for singular multi-agent systems with Lipschitz nonlinear dynamics are investigated. To obtain leader-following guaranteed-performance consensus, the consensus protocol and quadratic performance function based on state errors are proposed. Then, leader-following consensus problems of a nonlinear singular multi-agent system are transformed into asymptotic stabilization problems of a reduced-order subsystem by a new state decomposition method, and the impacts of the Lipschitz nonlinear dynamics are eliminated by using the structure property of the transformation matrix and the Lipschitz condition. Moreover, a guaranteed-performance consensualization criterion based on the Riccati inequality is given and the guaranteed-performance cost with a new structure is determined. Finally, a numerical simulation is shown to verify the validity of theoretical results.

Guaranteed performance consensus in second-order multi-agent systems with hybrid impulsive control

This paper studies the problem of guaranteed performance consensus in second-order multi-agent systems. Taking advantage of impulsive control, a hybrid cooperative control is presented, and an index function is introduced to assess the performance of agents. It is shown that by synthesizing the coupling weights and the average impulsive intermittence, multi-agent systems can achieve guaranteed performance consensus. A numerical example is given to illustrate the theoretical results.