Robust Consensus Tracking Strategy of Heterogeneous Nonlinear Multi-Agent Systems With Time-Varying Input Delays

In this paper, the robust consensus tracking problem is investigated for the heterogeneous nonlinear multi-agent systems (MASs) with weighted communication graph and time-varying input delays. Different from other existing works, the heterogeneous MASs have more general topology graph which contains a spanning tree. Further, the assumption of leader system is relaxed to contain the disturbance term. Hence, the intelligent technologies are used to approximate the unknown quantities from neighbor systems and leader system. To deal with the difficulties caused by the input delays, the compensation system, double integral type and novel constructed exponential type Lyapunov-Krasovskii (L-K) functionals are proposed to design the adaptive controllers. It should be known that the novel constructed exponential type L-K functional is simpler to design, and not only can satisfy the stability requirements but also can counteract the input delay. Besides, the uniform hysteretic quantizer is used to save the communication costs, and the dynamic surface filter is considered to optimize the controller structure for each agent. Under the proposed control protocol, the tracking errors are shown to achieve satisfactory control accuracy. Finally, the numerical example is provided to verify our strategies. Note to Practitioners—This paper considers the consensus tracking problem for the heterogeneous nonlinear MASs with weighted communication graph and time-varying input delay. The model is widely applied in the flocking control field, such as transportation, communication, manufacturing sector and so on. As the delay causes system performance degradation, it is more meaningful for realistic scene to consider the continuous and non-differentiable controller with unknown time-varying delay. Furthermore, the designed controller can keep the control accuracy, and the computation and communication costs are efficiently reduced.

I. Introduction

Consensus tracking problem one of the most important concerns of MASs, it has been drawn more attention and has been applied in sensor networks [1], [2], spacecraft [3], [4], servo motors [5], robots formation [6], [7], flocking control [8], [9] and so on. The states of followers should synchronize with leader’s on the basis of distributed tracking protocols [10]. The leader-following consensus tracking guarantees the direction of consensus control, enhances the communication and saves energy [11]. For the agents themselves, there are two categories: linear systems [12], [13] and nonlinear systems [14], [15], [16], [17], [18]. With the gradual relaxation of nonlinear conditions, the structure of MASs becomes diversified such as homogeneous MASs and heterogeneous MASs [19], [20], [21]. Meanwhile, the topology of communication graph among agents is expanded from balanced graph [22], [23], unbalanced graph [24], [25] to spanning tree contained graph [26]. Furthermore, the topology of communication graph can be unfixed such as switching topology [27], [28].