Containment control of high‐order multi‐agent systems with heterogeneous uncertainties, dynamic leaders, and time delay

Abstract

This paper deals with containment control of multi‐agent systems where high‐order canonical controllable linear systems with heterogeneous uncertainties are considered as the agents' dynamics. The leaders are dynamic with polynomial‐type trajectories. In this paper, the control protocol is smooth and it is constructed from a flexible combination of local state feedback controller and a PI‐type protocol. Utilizing this protocol, containment without suffering from chattering phenomena and consideration of any bound on the agents' states is achieved. In addition, the flexibility of this protocol helps the designer to reduce or even discard the inter‐agent communication. Recalling the significant effects of time delay on the performance and stability of multi‐agent systems, in this paper input time delay is also considered. Following a Lyapunov‐Krasovskii stability approach, two linear matrix inequalities (LMIs) are derived, and then solving the LMIs' gains of the protocol are attained such that asymptotic stability of the multi‐agent system under switching graph topology is guaranteed. Finally, the feasibility of the LMIs and the validity of the theoretical results are demonstrated through some numerical examples.

Scalable Formation of Heterogeneous Agents considering Unknown Disturbances

“…Following is the main result of this paper: Theorem 1. Given system of N agents of (2)(3) with control input of u i (t) given by (8), auxiliary state dynamics given by ( 6) (7) where the communication graph (t) is directed leader-follower where ∈ Z N is the leader node, reference-output i,re (t) given by (5), and dynamic compensator given by (9). Further, let d be the desired scaling factor of the formation.…”

“…In recent years, the problem of cooperative control of MASs have received great attention from the research community. Problems studied in cooperative control of MASs include but not limited to consensus or synchronization where the objective is to reach agreement among agents [1][2][3][4], containment control where the objective is such that the states of agents asymptotically converge to the convex hull of the leader agents' states [5][6][7], and multi-agent formation where the objective is such that asymptotically agents' states or output differs by a predefined vector or desired formation pattern [8][9][10][11][12].…”

Observer‐based adaptive neural network dynamic surface bipartite containment control for switched fractional order multi‐agent systems

“…In recent years, many achievements have been made regarding MAS containment control technology. Many research results of MASs containment control have been reported in the field of integer order control, such as sliding mode control (SMC), 15 adaptive control, 16,17 feedback control, 18,19 optimal control, 20 linear matrix inequalities (LMIs), 21,22 and so on. However, the challenging problem of fractional order bipartite containment control has been considerably less studied.…”

Switched Fractional Order Multiagent Systems Containment Control with Event-Triggered Mechanism and Input Quantization

“…Further study of the cooperative control problem of multiagent systems, extending the consensus control of a single leader, considers multiagent cooperative control in the case of multiple leaders, and designs a controller to make the followers converge to a convex hull composed of multiple leaders, which is called containment control. As a special case of cooperative control, many research results of MASs containment control have been reported in the field of integer order control, such as adaptive control [12,13], feedback control [14,15], linear matrix inequalities (LMIs) [16,17], sliding mode control [18], and so on.…”