Consensus control of output‐constrained multiagent systems with unknown control directions under a directed graph

Abstract

Summary This paper presents a novel distributed adaptive control algorithm for uncertain higher‐order nonlinear multiagent systems subject to output constraints and unknown control directions. Regarding the latter, a generic class of cases is considered, allowing completely unknown and even nonidentical control directions. Furthermore, the communication topology is only required to contain a fixed directed spanning tree. To guarantee the output constraints and address the asymmetric directed communication topology, a new reference output using the transformation strategy is introduced for each agent, benefiting from which the consensus problem of the multiagent system is recast as local tracking control problems of single agents. Then, the distributed control algorithm is recursively established based on the backstepping technique and the Nussbaum‐type function. By leveraging the unique properties of the Laplacian matrix on directed graphs and matrix theory, it is shown that, under the proposed distributed algorithm, uniform boundedness of all closed‐loop signals can be ensured, and asymptotic consensus is achieved without violation of the output constraints. Finally, simulation studies on the angle control of single‐link robots are given to verify the effectiveness of the proposed algorithm.

A Data-Driven Distributed Adaptive Control Approach for Nonlinear Multi-Agent Systems

“…Note that the proposed CFDL-DAC can be extended to deal with the leaderless control problems [34], [35] since it is applicable as long as the local measurement information can be described, which is demonstrated by (3). However, the results in [34], [35] are obtained for continues-time multiagent systems with unknown control directions, and this paper considers discrete-time multi-agent systems where the control directions are known. Therefore, the two obstacles are required to be tackled before utilizing the proposed approach.…”

Consensus Control of Position-Constrained Multi-Agent Systems Without the Velocity Information of Neighbors

“…. , 2(n − 1) + 1},L is the related Laplacian matrix, and the edge setĒ can be deduced from (16). Since rank(c 1 ) = n − 1 and rank(c 2 (I n−1 −Ā n−1 )) = rank(L n−1 ) = n − 1, we obtain rank(L 2(n−1) ) = 2(n − 1).…”

“…Since rank(c 1 ) = n − 1 and rank(c 2 (I n−1 −Ā n−1 )) = rank(L n−1 ) = n − 1, we obtain rank(L 2(n−1) ) = 2(n − 1). By (16), it can be obtained rank(L) = 2(n − 1). Proceeding in a fashion similar to C1, it can be concluded that each closed-loop signal remains bounded, lim t→∞ (p i (t)−p j (t)) = 0, and L < p i (t) < U for all t ≥ 0, for all i, j = 1, .…”

“…In addition, the results have been extended to higher-order multi-agents with output limitations and unknown control directions under an undirected graph [15]. With the further development of the directed graph in [16], a desired output is presented using a transformation strategy, and a consensus control law is obtained in the backstepping framework.…”

“…(3) Different from the position-constrained consensus controller under the undirected graph [14], [15], this innovative distributed method is able to address the consensus issue and the position-constrained issue under the directed topology condition. In addition, neighbors' velocity measurement required in [16] is unnecessary.…”