Distributed Global Output-Feedback Control for a Class of Euler–Lagrange Systems

Abstract

This paper investigates the distributed tracking control problem for a class of Euler-Lagrange multi-agent systems when the agents can only measure the positions. In this case, the lack of the separation principle and the strong nonlinearity in unmeasurable states pose severe technical challenges to global output-feedback control design. To overcome these difficulties, a global nonsingular coordinate transformation matrix in the upper triangular form is firstly proposed such that the nonlinear dynamic model can be partially linearized with respect to the unmeasurable states. And, a new type of velocity observers is designed to estimate the unmeasurable velocities for each system. Then, based on the outputs of the velocity observers, we propose distributed control laws that enable the coordinated tracking control system to achieve uniform global exponential stability (UGES). Both theoretical analysis and numerical simulations are presented to validate the effectiveness of the proposed control scheme.

Adaptive Fault-Tolerant Guaranteed Performance Control for Euler-Lagrange Systems With Its Application to a 2-Link Robotic Manipulator

“…A robust autopilot controller is designed for a generic missile without consideration of the actuator nonlinearities, angle of attack constraint, and mismatched uncertainties by applying the barrier Lyapunov function and dynamic surface control techniques in [9]. As for the cooperative control of the multiple EL systems, a dis-tributed output tracking control scheme is devised for a class of EL multiagent systems with only using the measurable position information in [10]. To solve the actuator saturation problem, a dynamic auxiliary system is introduced for each EL agent system to obtain some auxiliary variables.…”

Consensus of multiagent systems with nonlinear dynamics and time‐varying communication delays

“…Therefore, the communication delays should be modeled in consensus of multiagent systems. Currently, some works have been done to eliminate the negative effect of time delays on the multiagent systems . Taylor expansion was firstly introduced in the work of Yu et al to address the consensus of multiagent systems, and based on graph theory, some stability conditions were derived by constructing Lyapunov functional and applying Free‐matrix–based inequality method.…”

“…Currently, some works have been done to eliminate the negative effect of time delays on the multiagent systems. [22][23][24][25][26][27][28][29][30][31][32][33] Taylor expansion was firstly introduced in the work of Yu et al 23 to address the consensus of multiagent systems, and based on graph theory, some stability conditions were derived by constructing Lyapunov functional and applying Free-matrix-based inequality method. In the work of Wang et al, 24 the consensus for the multiagent systems with time-varying delays was investigated under jointly connected communication topologies, and some stability conditions of the control algorithms were proposed based on Lyapunov theory and integral inequality.…”

Distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays

“…However, the tracking errors were only locally but not globally convergent to zero. To achieve the global convergence for the tracking errors, a novel distributed tracking control algorithm was proposed in the work of Yang et al for multiple EL systems, where only the position information of the agents could be measured. By utilizing observers to estimate the velocities, the systems could achieve uniform global exponential stability.…”

“…A second‐order sliding‐mode observer was designed to estimate the velocity information of the systems. When multiple leaders exist, the control strategies in the works of Bouteraa et al, Yang et al, Yang et al, and Zhao et alare not available. In these cases, all the followers should move into the convex hull formed by the leaders, which can be named as containment control.…”