Adaptive synchronization of heterogeneous multi-agent systems: A free observer approach

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Abstract

Adaptive synchronization protocols for heterogeneous multi-agent network are investigated. The interaction between each of the agents is carried out through a directed graph. We highlight the lack of communication between agents and the presence of uncertainties in each system among the conventional problems that can arise in cooperative networks. Two methodologies are presented to deal with the uncertainties: A strategy based on robust optimal control and a strategy based on neural networks. Likewise, an input estimation methodology is designed to face the disconnection that any agent may present on the network. These control laws can guarantee synchronization between agents even when there are disturbances or no communication from any agent. Stability and boundary analyzes are performed. Cooperative cruise control simulation results are shown to validate the performance of the proposed control methods.

Introduction

Nowadays, multi-agent system control has a wide variety of applications ranging from mechanical systems like robots synchronization to social behavior for influence analysis [1], [2], [3]. For distributed control systems, problems based on a reference or leader model have been widely considered [4], [5], [6], [7]. Cooperative cruise control has drawn great attention as an application case among the main problems to be tackled [8], [9].

Conventional control techniques for cooperative cruise systems have been used for more than 20 years with effective results [10], [11]. However, the systems are considered without disturbances neither network communication failures, limiting the application of these control methods in practice.

Adaptive control theory is proposed as an effective method for dynamic systems with uncertainty parameters [12], [13], such as Model Reference Adaptive Control (MRAC) for leader–follower models. MRAC allows the online adjustment of the controller parameters through adaptive laws in order to synchronize dynamics with respect to a reference model [14]. For distributed systems, MRAC is extended including matching conditions for both, the reference and the dynamics of neighboring agents [15]. Similarly, as a robust complement, optimal adaptive theory or neural network approach could be included to mitigate input system uncertainties [16], [17].

Likewise on a cooperative practical level, one of the common scenarios to be presented is the communication loss between agents [18]. In the distributed MRAC case, where communication of each agent control input is handled, the lack of communication of this variable is common in practice due to different conditions such as disconnection from the network by physical environment or by pre-established configuration against energy losses. The conventional control strategies present failures in their operation by not considering a lack of communication [19], or handle it as a disturbance but without considering an adaptive law for estimation [20]. The challenge is to build some adaptive protocols to allow an input estimation of uncommunicated agents and also address input uncertainties in the case of a heterogeneous agents network.

In recent works, just few results have been proposed using the MRAC from a robust optimal perspective to handle disturbances in centralized way [13], [21], and some others results have proposed on distributed input estimation, but without covering additional uncertainty parameters [22], [23]. In the distributed control used to synchronize heterogeneous agents, the controller must adjust four sets of parameters: the feedback matching conditions related to the dynamics of the reference agent, the coupling matching conditions related to the dynamics of neighboring agents, the uncertainty optimal parameters for the suppression of disturbances, and the input estimation parameter for the uncommunicated agents input. These parameters should be adjusted for agents that are directly communicated with the reference and those which are not [15], [16].

The main contribution of this paper is threefold, first the development of a control protocol that allows the suppression of uncertainty parameters, second, the development of a law for estimating the input in cases of communication failure, and third the conjunction of these theories into a general control protocol. The validation of established control laws is presented through a boundary analysis using Lyapunov’s theory. In particular, a third order cooperative cruise control simulation case is presented to show the improvement in the temporal response of the implemented control laws.

The rest of the paper is organized as follows. Section 2 presents the formulation of the problem and the mathematical preliminaries, in Section 3 the development of control laws for managing uncertainties through adaptive optimal theory and the use of neural networks are presented. Section 4 presents the development of the control law for estimating input parameters, in Section 5 the simulation results under the cooperative cruise control study case are presented, and finally Section 6 presents the conclusions of the work done and the projections of future work.

Section snippets

Problem formulation and mathematical preliminaries

This section shows a contextualization of the heterogeneous agents synchronization problem and the basic notations to be used throughout the paper.

Consider a heterogeneous network with N agents and a reference model. Communication presented in the network is defined by a graph G=(V,E), where V={1,2,,N} is the set of nodes or agents in the network and EV×V is the link set of G. To determine communication, if there is a link between agent i and agent j then (i,j)E, which means that i and j are

Adaptive control laws

In this section, the solutions to the proposed problems are tackled in two directions: the first approach is a robust optimal approximation called adaptive optimal control modification; the second approach is an approximation of disturbances by neural networks.

Input estimation

In this section, we present the case where some neighboring agent j cannot communicate the input value to its neighborhood. The definition of a control law that allows the estimation of neighbors inputs in order to avoid failures in the proposed control laws due to the communication is presented. The control law to employ is āui=ākijxi+kmiΞij+āuˆjiθiϕi,The adaptive laws associated with the MRAC are taken from (12), validating that the law krij is no longer used due to the isolation of the

Simulation results

This section presents the study case of cooperative cruise control as an application of proposed Theorem 1, Theorem 2, Theorem 3 and the simulation results obtained.

Conclusions

In this work, adaptive control laws based on robust models are presented in the case of cooperative cruise control study. An adaptive optimal control law and a neural network based approach are proposed for the suppression of each agent input uncertainty parameters. Likewise, an estimation law is used for its application in the case of disconnected agents. For the adaptive control laws the use of matching conditions allows a synchronization of the agents with the reference and its neighbors. In

CRediT authorship contribution statement

Miguel F. Arevalo-Castiblanco: Acquisition of data, Analysis, Interpretation of data, Drafting the manuscript. Duvan Tellez-Castro: Conception, Design of study, Analysis, Interpretation of data. Jorge Sofrony: Conception, Design of study. Eduardo Mojica-Nava: Conception, Design of study.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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    Duvan Tellez-Castro was supported by Colombian Administrative National Department of Science, Technology, and Innovation (COLCIENCIAS) under Grant No. 727/2016.

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