Distributed adaptive tracking backstepping control in networked nonidentical Lagrange systems

Abstract

In this paper, the problem of adaptive tracking control in networked nonidentical Lagrange systems is investigated via backstepping schemes. Two distributed tracking control algorithms are designed for directed network topology graph with a spanning tree, where both the leader's position and its velocity are assumed to be varying. Some generic criteria for adaptive tracking control algorithms with uncertain external disturbance and parametric uncertainties are presented. It is shown that the proposed algorithms only require a subset of the followers access to leader's position. Furthermore, the adaptive control algorithm for uncertain external disturbance systems is robust, and it can avoid online measurement for neighbors' velocities and efficiently eliminate the chattering during tracking. The results show that all followers can track the leader's dynamics. Two examples and their simulations show the effectiveness of the proposed algorithms.

Pinning Synchronization in Networked Lagrangian Systems

“…Therefore, the above equations exhibit certain fundamental properties due to their Lagrangian dynamics structure. Throughout this paper, we assume that the following properties held : P1. The matrix is skew‐symmetric, implying that and for arbitrary x ∈ R n . P2.…”

“…In addition, the proposed pinning scheme takes into account more challenging nonlinear Lagrangian system although we here consider the networked Lagrangian systems with identical agent's dynamics. However, the design of nonlinear controllers based on linear parameterization property or passivity framework have partly removed dynamics complexity of nonlinear Lagrangian system in the existing literatures [1,6,7,[9][10][11][12][13][14][15][16][17][18].…”

“…Impulsive synchronization motion is discussed in networked systems formulated by Lagrangian dynamics [9,10]. Distributed adaptive controlled synchronization scheme is designed for Lagrangian network with parametric uncertainties [11][12][13][14][15][16][17][18]. For more details on this topic, we can refer to the literature [1,19] and relevant references therein.…”

“…The main contributions of this work can be stated as follows: The novelties of the proposed algorithm compared with the existing works on networked Lagrangian systems include: (i) independence on the knowledge of system models; (ii) explicit consideration of agent's intrinsic complex dynamics; and (iii) simplicity of implementing the procedure in practice. For example, different from the coordinated tracking algorithms for nonlinear Lagrangian systems [5,[8][9][10][11][12][13][14][15][16][17][18], the designed pinning algorithm does not rely on the linear parameterization property, and does not require the prerequisite knowledge of system models, such as the inertial matrix, the Coriolis and centrifugal torques, and the gravitational torque. In contrast to the passivity-based approach for synchronization [1,6,7], the algorithm proposed in this article does not rely on the passivity property of the systems.…”

Synchronization control for robot manipulators driven by induction motors with flux and velocity observers

“…By the treatment of the passivity-based control, undirected graph interconnection is used in Ihle et al (2007) and Chopra and Spong (2006), constant time-delay is included in Nuño et al (2011) and Wang (2013),whereas time-varying delay is covered in Min et al (2011), Yu and Antsaklis (2010), Liu and Chopra (2012) and Abdessameud et al (2014). Multiple control strategies have been applied to synchronization, for example: backstepping in Zhang et al (2014) and Wu et al (2013); cross-coupling in Bouteraa et al (2011) and Bouaziz et al (2013); sliding modes in Mei et al (2011); synchronization through neural networks (NN) in Chen and Lewis (2011), Cui and Yan (2012) and Zhao et al (2014); synchronization owing to a composite nonlinear feedback control in the presence of time delays in Mobayen and Tchier (2017) and Mobayen and Ma (2018); and a pulse-modulated intermittent control is applied to consensus problems of multiagent systems in Liu et al (2017).…”