Multi‐agent adaptive consensus of networked systems on directed graphs

Abstract

This paper considers adaptive consensus problem on directed graphs of multi-agent systems with unknown control directions. The proposed consensus protocol assumes that each agent receives information about delayed values of state and control signals of respective neighbors. In case of unknown sign of the high-frequency gain of agent dynamics, the proposed algorithm employs Nussbaum-like switching function. The algorithm allows for a designer to select low gain or high gain consensus protocols. Assuming that the underlying graph is strongly connected, it is proved that all agent states converge toward the same value, and the inter-agent coupling parameters are convergent functions. ADAPTIVE CONSENSUS ON DIRECTED GRAPHSThe following theorem examines the stability properties of (27).

Cooperative Control of Multiple Agents With Unknown High-Frequency Gain Signs Under Unbalanced and Switching Topologies

“…for all ν ∈ N + such that T d ℓν ≥ T iς (ǫ), ς ∈ {1, 2 · · · , r}. Using now the triangle inequality with (23) and (28) for ς = m, n we result in |y im (t) − y in (t)| ≤|y im (t) − y im (T d ℓν )| + |y in (t) − y in (T d ℓν )| + |y im (T d ℓν ) − y in (T d ℓν )| ≤ ǫ…”

PI consensus error transformation for adaptive cooperative control of nonlinear multi-agent systems

“…The dynamical systemẋ ag = f ag (x ag ) with augmented state vector x ag := [x 1 , w 1 ,θ 1 , ζ 1 , · · · , x N , w N ,θ N , ζ N ] T defined by (5), (19), (21), (22) has a smooth locally Lipschitz map f ag and therefore a maximal solution exists over some interval [0, t f ) [36]. From (24) and Lemma 1 we have that z i ,θ i , ζ i , [36].…”

“…Chen et al [20] considered the adaptive consensus of first-order and second-order agents with unknown identical control directions using a novel Nussbaum function. The consensus control problem with unknown identical control directions was also addressed later in [21] using delayed inputs and switching functions, in [22] for higher-order integrators and in [23] for nonlinear systems. The unknown identical control directions assumption was relaxed in [24] and [25] for agent networks having a leader.…”

Tracking control for nonlinear time‐delay multiagent systems with input saturation

“…Over the past decades, the multiagent systems (MASs) have been extensively researched owing to its impacts on militaries and civilian facilities. [1][2][3][4][5] As one of the most significant problems in the research of MASs, the tracking control problem has emerged as a popular topic and received lots of attention in the realm of control. A lot of achievements have been obtained in tracking control problem of linear MASs.…”