Leader tracking control for heterogeneous uncertain nonlinear multi-agent systems via a distributed robust adaptive PID strategy

Abstract

This paper addresses the leader tracking control problem for heterogeneous uncertain nonlinear multi-agent systems sharing information via a communication network, modeled as a directed graph. To solve the problem, we propose a novel distributed PID-like control strategy which, enhanced with a Lyapunov-based adaption mechanism for the control parameters, is able to counteract the uncertainties acting on the agents dynamics. The stability analysis analytically proves the effectiveness of the proposed PID protocol in ensuring the leader-tracking as well as the boundedness of the adaptive control gains. Numerical simulations, involving both the synchronization control problem for nonlinear harmonic oscillators and the practical engineering problem of the cooperative driving for autonomous connected vehicles, confirm the theoretical derivation and disclose the capability of the proposed strategy in achieving the control objective.

Analysis and Design of Cooperative Control Solutions for Electrical Systems of Laser CNC Machines

“…At this time, it is necessary to find a more suitable processing method and processing technology, and laser processing is the best choice for this kind of processing. Compared with traditional machine tool processing, laser processing has the following advantages: Lui et al said that laser processing has high production efficiency, reliable workpiece processing quality, and processing accuracy that can reach the order of microns [7]. During the laser processing, there is no contact with the workpiece to be processed, which will not bring about "tool" wear, and at the same time, there is no direct impact on the workpiece, so there is no mechanical deformation; it is suitable for the processing of some metals and nonmetals, especially for high hardness and processing of materials with high brittleness and high melting point; Gupta and Paliwal said that the beam guidance and focusing of the laser are simple in the processing process, which can easily realize the transformation of all directions, which is very suitable for the processing of complex workpieces with the numerical control system [8].…”

Group consensus tracking of second‐order nonlinear multi‐agent systems with time‐varying reference velocities

“…For agent $$$ i $$$, $$$ f\left({g}_i{v}_i(t)\right) $$$ depends on both its velocity $$$ {v}_i(t) $$$ and the coefficient $$$ {g}_i $$$ which varies with different groups. The nonlinear structure is different from heterogeneous high‐order models in Reference 46. Here, we assume that coefficient $$$ {g}_i $$$ is known positive constant which means the cooperation of the groups.…”

“…Reference 8 studied consensus seeking of second‐order nonlinear MASs with a dynamical leader, and a distributed event‐triggered sliding‐mode control law was designed such that the position and the velocity of all the followers eventually track the position and the velocity of the leader. In Reference 46, a distributed robust adaptive PID strategy was presented to solve a tracking problem for heterogeneous uncertain nonlinear MASs. Reference 47 designed distributed adaptive tracking controllers for nonlinear Lipschitz MASs with multiple time‐varying communication delays where both the leader and the followers were first‐order integrator models.…”

Distributed adaptive PI consensus tracking control for output-constrained nonlinear multiagent systems with unknown control directions

“…Recently, the investigation into multiagent systems (MASs) has attracted increasing attention from researchers, among which distributed consensus tracking control of nonlinear MASs is one of the most popular topics due to its potential applications in many areas [1][2][3]. Considering the uncertainties for high-order MASs, adaptive and robust consensus tracking control strategies were proposed in [4][5][6][7][8][9][10], and then the distributed bounded consensus tracking [4][5][6][7] and the distributed asymptotic consensus tracking [8][9][10] were achieved, respectively. Despite these research efforts, the control directions of agents are all required to be known in the above results.…”