Abstract
This article 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. Prescribed-time 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 high-order 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.
Highlights
Cooperative control of Multi-Agent Systems (MASs) is a broad topic involving many different related research problems, such as consensus, formation control, flocking, coverage control, among others; attracting considerable attention over the last decades due to their broad applications in different research areas ( [1], [2])
Our setup consists of a multi-agent system (MAS) formed by a collection of N agents named followers whose dynamics are described by nonlinear systems with relative degree n, an agent named leader, and a communication graph G with N + 1 vertices, each one associated to a different agent
Since the results are similar for the unperturbed case, in this subsection, we show the performance of the proposed robust prescribed-time time base generators (TBGs) controller (21) considering disturbances ρi(t) = αi(1 + 1 sin(5t)), with αi randomly selected in (0, 1)
Summary
Cooperative control of Multi-Agent Systems (MASs) is a broad topic involving many different related research problems, such as consensus, formation control, flocking, coverage control, among others; attracting considerable attention over the last decades due to their broad applications in different research areas ( [1], [2]). We address the problem of designing a distributed control protocol to achieve consensus tracking of a leader in prescribed time for high-order MASs with nonlinear dynamics affected by disturbances. The references are characterized by time base generators (TBGs), which are continuous time-dependent polynomial functions that converge to zero in a specified time ( [20], [21]) Once these time-varying functions are designed, one of the main difficulties to solve the defined problem is to guarantee robust tracking of the reference signals defined for high-order systems to achieve accurate convergence of the consensus error in a preset time regardless of the interaction between agents and disturbances. An additional advantage of our approach is that the proposed control protocols do not use information about the network’s connectivity, as used by other consensus approaches, which represents a robustness property that allows our protocols to work properly for either small or large number of agents without readjusting controller parameters
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