Continuous-time Linear Multi-agent Systems Research Articles

Optimal Consensus Control for Continuous-Time Linear Multiagent Systems: A Dynamic Event-Triggered Approach.

This article investigates the optimal consensus problem for general linear multiagent systems (MASs) via a dynamic event-triggered approach. First, a modified interaction-related cost function is proposed. Second, a dynamic event-triggered approach is developed by constructing a new distributed dynamic triggering function and a new distributed event-triggered consensus protocol. Consequently, the modified interaction-related cost function can be minimized by applying the distributed control laws, which overcomes the difficulty in the optimal consensus problem that seeking the interaction-related cost function needs all agents' information. Then, some sufficient conditions are obtained to guarantee optimality. It is shown that the developed optimal consensus gain matrices are only related to the designed triggering parameters and the desirable modified interaction-related cost function, relaxing the constraint that the controller design requires the knowledge of system dynamics, initial states, and network scale. Meanwhile, the tradeoff between optimal consensus performance and event-triggered behavior is also considered. Finally, a simulation example is provided to verify the validity of the designed distributed event-triggered optimal controller.

A DDPG-based solution for optimal consensus of continuous-time linear multi-agent systems

A DDPG-based solution for optimal consensus of continuous-time linear multi-agent systems

Parametric Dynamic Distributed Containment Control of Continuous-Time Linear Multi-Agent Systems with Specified Convergence Speed

This paper focuses on the distributed containment control of continuous-time linear multi-agent systems (MASs) with multiple leaders over fixed topology. A parametric dynamic compensated distributed control protocol is proposed in which both the information from the observer in the virtual layer and actual adjacent agents are employed. The necessary and sufficient conditions of the distributed containment control are derived based on the standard linear quadratic regulator (LQR). On this basis, the dominant poles are configured by using the modified linear quadratic regulator (MLQR) optimal control and Geršgorin's circle criterion, hence the containment control with specified convergence speed of the MAS is achieved. Another main advantage of the proposed design is, in the case of virtual layer failure, by adjusting parameters the dynamic control protocol reduces to static, and the convergence speed can still be specified through the dominant pole assignment method combined with inverse optimal control. Finally, typical numerical examples are presented to demonstrate the effectiveness of theoretical results.

Global Cooperative Output Regulation of Linear Multiagent Systems With Limited Bandwidth

This article investigates the global cooperative output regulation problem of continuous-time linear multiagent systems (MASs), under the communication constraint of limited bandwidth. With a novel scaling function strategy, a distributed protocol based on the sampled and quantized data is designed to solve this problem. Compared with the existing works on quantized control of MASs, not only the boundedness assumption on initial conditions is removed, but also the communication graph is not restricted to be balanced or strongly connected. Moreover, the proposed quantized cooperative output regulation protocol does not rely on any global information of the communication graph. A simulation example is finally presented to illustrate the effectiveness of the proposed quantized cooperative output regulation protocol.

Learning Distributed Stabilizing Controllers for Multi-Agent Systems

We address model-free distributed stabilization of heterogeneous continuous-time linear multi-agent systems using reinforcement learning (RL). Two algorithms are developed. The first algorithm solves a centralized linear quadratic regulator (LQR) problem without knowing any initial stabilizing gain in advance. The second algorithm builds upon the results of the first algorithm, and extends it to distributed stabilization of multi-agent systems with predefined interaction graphs. Rigorous proofs are provided to show that the proposed algorithms achieve guaranteed convergence if specific conditions hold. A simulation example is presented to demonstrate the theoretical results.

Formation Static Output Control of Linear Multi-Agent Systems With Hidden Markov Switching Network Topologies

This paper addresses the $\mathcal {H}_{2}$ , $\mathcal {H}_\infty $ and mixed $\mathcal {H}_{2}/\mathcal {H}_\infty $ formation static output control of continuous-time linear multi-agent systems with Markovian switching network topologies. It is assumed that the operation mode of the network topology cannot be directly measured but, instead, can be estimated by an imperfect detector. To model this problem, we consider a continuous-time hidden Markov model, in which the hidden component represents the real operation mode of the network topology while the observed component represents the information emitted from the detector and available for the controller. It is also assumed that only a partial information from the state variables of the multi-agent systems is available. By using an LMI (linear matrix inequality) formulation, a distributed static output controller which switches according to the detector information is designed to guarantee the stability in the mean square sense of the closed loop system, as well as an upper-bound for an index performance. Three situations are considered for the performance criteria: the $\mathcal {H}_{2}$ norm, the $\mathcal {H}_\infty $ norm, and the mixed $\mathcal {H}_{2}/\mathcal {H}_\infty $ norms. The paper is concluded with a numerical example to illustrate the effectiveness of the theoretical results.

Consensus of Continuous-Time Linear Multiagent Systems With Discrete Measurements.

This article concerns the robust consensus problem of continuous-time linear multiagent systems (MASs) with uncertainty and discrete-time measurement information, where the output measurement information is in the data-sampled form. Distributed output-feedback protocol with or without controller interaction is proposed for each agent. Specifically, the output-feedback protocol runs in continuous time with an output error correction term mixed with the discrete-time measurement information. The concrete algorithm is given for the construction of the feedback matrices. Then, by using the delay-input approach, sufficient conditions are provided for the robust consensus of this kind of MASs interacting over networks described by the directed graphs. Finally, numerical simulations are given to illustrate the theoretical results.

Bounded consensus control for stochastic multi-agent systems with additive noises

This paper considers bounded consensus problem of continuous-time linear multi-agent systems with both additive system and communication noises under an undirected communication topology. Owning to the coexistence of the additive system and communication noises, the exact consensus cannot reach. Hence, the distributed controller is to be designed such that all the agents can reach to a collection behavior to some degree. It is supposed that each agent can obtain full state of itself and receive its neighbors’ state with additive noises. For each agent, the consensus protocol is designed based on the error between the estimated state of its neighbors’ and full state of itself. By means of Kalman filtering and matrix analysis, the bound of consensus is given via the solution of a Lyapunov equation. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed control strategy.

Output consensus of high‐order linear multi‐agent systems with time‐varying delays

In this study, the problem of output consensus control for high-order continuous-time linear multi-agent systems with interval time-varying delays is investigated. The observability decomposition technique is employed to design the output consensus protocols which are the collections of delayed output information from neighbouring agents. On the basis of invertible transformations, output consensus for the concerned dynamical agents is transformed into the problem of asymptotical stability analysis for some lower dimensional subsystems. By introducing the prescribed convergence rate scalar into the constructed delay-dependent Lyapunov functionals, the framework for output consensus analysis is theoretically derived. Benefitting from the method of slack matrix variables, sufficient conditions are obtained in terms of linear matrix inequalities to design the protocol gain matrices which can guarantee the property of output consensus. Moreover, the output consensus function determined merely by the initial states of dynamic agents and consensus protocol is presented without the influences of time-varying delays. Numerical examples are exploited to illustrate the effectiveness of the derived results.

An approach to quantized consensus of continuous-time linear multi-agent systems

This paper investigates the consensus problem of continuous-time linear multi-agent systems (MASs), under the communication constraint of limited bandwidth. By constructing a novel dynamic quantizer, a distributed protocol via sampled and quantized data is designed to solve this problem. It is shown that the required number of the quantization levels of the new quantizer remains to be small even if the number of the agents in the MAS is large. A simulation example is given to illustrate the effectiveness of the proposed consensus protocol.

Consensus of linear multi-agent systems via reduced-order observer

This paper is concerned with the consensus problem for continuous time linear multi-agent systems with directed communication topology. An estimation error dynamic is proposed to design the reduced-order observer for dealing with unknown coefficient matrices. To guarantee the consensus, control protocols based on the reduced-order observer are designed to utilize the relative outputs of neighboring agents whose communication topology contains a directed spanning tree. Then the algorithms are extended to the model reference consensus case, where the case of zero control input for reference node is not assumed. Numerical examples are given to illustrate the effectiveness of proposed approaches.

Consensus of High-Order Linear Multiagent Systems with Multitype Switching Topologies Based on the Dynamic Dwell Time Approach

This paper investigates the consensus problem of high-order continuous-time linear multiagent systems (LMASs) with multitype switching topologies which include both consensusable and unconsensusable communication topologies. A linear transformation is introduced, which equivalently transforms the consensus problem into the stability problem of a corresponding switched system, along with a necessary and sufficient condition to analyze the consensus problem. This paper is aimed at studying the impact of a switching rule on communication topologies for consensus of LMASs. Based on the dynamic dwell time method, a sufficient condition is derived for consensus of LMASs. It is shown that, with switching signals that satisfy this switching rule, LMASs can achieve consensus under directed switching communication topologies. A numerical example is provided to illustrate the effectiveness of the theoretical results.

Containment control of continuous-time linear multi-agent systems with aperiodic sampling

In this paper, the containment control problem of continuous-time linear multi-agent systems is investigated. An aperiodic sampled-data based protocol is induced by using neighboring information with uncertainly time-varying sampling intervals. By utilizing the proposed protocol and properties of Laplacian matrix, the containment control problem of continuous-time linear multi-agent systems is equivalently transformed into a stability problem of discrete-time linear systems. The stability analysis is based on the robustness of related discrete-time systems against perturbation caused by the variation of sampling intervals. By using small-gain theorem, sufficient conditions are obtained to guarantee the stability of uncertain discrete-time systems. Furthermore, two special cases are given to illustrate the method proposed in this paper. The theoretical results are verified by some simulations.

Periodic event/self‐triggered consensus for general continuous‐time linear multi‐agent systems under general directed graphs

This study considers the decentralised periodic event-triggered consensus problem for continuous-time linear multi-agent systems (MASs) under general directed graphs. The authors discretise the continuous-time MASs based on zero-order hold, and propose an event-triggered consensus control (ETCC) algorithm rendering the states of agents reach consensus. They prove that under the proposed ETCC implemented in multiple steps, there is no Zeno-like behaviour exhibited in the sense of sampling. To relax the requirement of the periodic monitoring in the ETCC, it is further proposed a self-triggered consensus control algorithm, where the next triggering instant is predetermined by each agent at the previous triggering instant. For the case where the states of MASs are unavailable, the authors further propose an observer-based ETCC algorithm. Simulation results are given to illustrate the theoretical results.