Synchronisation of high-order MIMO nonlinear systems using distributed neuro-adaptive control

Abstract

This paper addresses synchronisation problem of high-order multi-input/multi-output (MIMO) multi-agent systems. Each agent has unknown nonlinear dynamics and is subject to uncertain external disturbances. The agents must follow a reference trajectory. An adaptive distributed controller based on relative information of neighbours of each agent is designed to solve the problem for any undirected connected communication topology. A radial basis function neural network is used to represent the controller's unknown structure. Lyapunov stability analysis is employed to guarantee stability of the overall system. By the theoretical analysis, the closed-loop control system is shown to be uniformly ultimately bounded. Finally, simulations are provided to show effectiveness of the proposed control method against uncertainty and disturbances.

Distributed adaptive output feedback tracking control for a class of uncertain nonlinear multi-agent systems

“…It also should be pointed out that similar conditions are required in many relevant literatures, e.g. distributed state feedback tracking control problems of nonlinear multi-agent systems (Das & Lewis, 2010;Sarand & Karimi, 2016;Zhang & Lewis, 2012 ) and distributed output feedback tracking control problems of linear multi-agent systems (Sun & Geng, 2015;Zhang et al, 2011). The condition can be easily checked by computing H and G in Equation (2).…”

“…Recently, a series of papers (Cheng, Hou, Tan, Lin, & Zhang, 2010;Das & Lewis, 2010;El-Ferik, Qureshi, & Lewis, 2014;Hou, Cheng, & Tan, 2009;Sarand & Karimi, 2016;Wang, Huang, Wen, & Fan, 2014;Zhang & Lewis, 2012;Zou, Kumar, & Hou, 2013 ) addressed the consensus problem of nonlinear multi-agent systems. For a class of first-order nonlinear multi-agent systems, where nonlinear dynamics was emulated by neural networks, Hou et al (2009) studied the leaderless consensus problem, while Das and Lewis (2010) and Cheng et al (2010) considered the leader-following consensus problem.…”

“…Shi and Shen (2015) developed a distributed adaptive neural-network-based controller for the leader-following consensus of uncertain higher order nonlinear multi-agent systems with unknown controlling effects, in which the Nussbaum-type gain technique is employed to handle the unknown controlling effects. In Sarand and Karimi (2016), an adaptive distributed algorithm was proposed to solve the synchronisation problem of higher order multi-input/multioutput multi-agent systems. One common feature in the aforementioned works is that the proposed distributed consensus protocols require all states of each agent.…”

“…(1) In Zhang and Lewis (2012), El-Ferik et al (2014), Zou et al (2013), Wang et al (2014), Shi and Shen (2015) and Sarand and Karimi (2016), distributed controllers were designed based on a very ideal condition that all relative states between itself and its neighbours are directly measured. However, in this paper, the distributed control law design for each agent does not require relative state information and works with only the relative output information between itself and its neighbours.…”

Robust consensus tracking control of higher‐order uncertain non‐linear systems via cascaded finite‐time estimation of reference states

“…Cooperative control for higher‐order systems is even more challenging. There also have been many works dedicated to higher‐order cooperative control [17–22], under various problem settings. Especially, the works of [20–22] address the cooperative tracking of non‐linear systems with unknown dynamics using the neuro‐adaptive feedback linearisation technique.…”