Robust Leader-Following Consensus of High-Order Multi-Agent Systems in Prescribed Time

Abstract

This paper addresses the distributed prescribed-time leader-following consensus problem for a class of high-order multi-agent systems (MASs) with perturbed nonlinear agents dynamics and where the topology of the network contains a directed spanning tree, with the leader as the root. Prescribedtime consensus means that an agreement state of the MAS is achieved in a preset time, introduced as a parameter of the control law, and this constant settling time is achieved independently of the agents' initial state. The proposed control method exhibits three main advantages: first, to our best knowledge, it is the first time that prescribed-time convergence in a consensus problem is achieved for agents with highorder nonlinear dynamics, using a robust leader-following protocol, which allows an effective rejection of matched disturbances in the agents' model. Second, the proposed controller provides control signals of lower magnitude than existing approaches. Third, the proposed consensus protocol does not have parameters to be adjusted depending on the connectivity of the considered communication graph. INDEX TERMS Multi-agent systems, distributed protocol, high-order systems, prescribed-time consensus, time base generators (TBGs).

Dynamic Consensus With Prescribed Convergence Time for Multileader Formation Tracking

“…, pi,m (t) ∈ R 3 for p(t) and its first m derivatives respectively. The DVO at robot i ∈ I communicates N a > 0 reals in a vector a i (t) ∈ R N a only to its neighbors through the network G. Moreover, a DVO has a prescribed convergence time [7], [19]…”

“…However, it is important to note that once each agent is equipped with the value of the reference p(t) along with its derivatives as computed from the MDVO, the employment of a wide variety of trajectory tracking controllers for integrator systems is enabled. In particular, it enables the usage of controllers which incorporate barrier functions for collision avoidance as in [21] or to reject disturbances as in [19].…”

“…It is important to note that the example in Section V-A was chosen precisely since it cannot be solved by existing approaches as a whole. The reason is that other leaderfollower approaches [4], [7], [11]- [19], cannot be directly extended to handle the computation of the geometric center of multiple leaders, or to dynamics of order higher than 2. Moreover, note that the same observer structure of MDVO is used in Section V-B for a different problem than in Section V-A, which highlights the versatility of our proposal in contrast to prior work.…”

“…Moreover, note that the same observer structure of MDVO is used in Section V-B for a different problem than in Section V-A, which highlights the versatility of our proposal in contrast to prior work. Another important improvement of MDVO is that the number of numbers shared between agents N a remains the same regardless of the system order m. In contrast, other high-order techniques [4], [12]- [14], [17]- [19] share a vector of a size growing with m.…”

“…The most significant disadvantage of this approach is that a small disturbance easily compromises the system's behavior due to the high gains employed. Moreover, Time Base Generators (TBG) were used as tracking references in [19] achieving convergence before a deadline in a single-leader scenario with agents of high order dynamics. A similar multi-leader problem is tackled in [4].…”