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.
Highlights
Recent years have witnessed the great development of distributed cooperative control based on multi-agent systems (MASs) with the aim at solving the large variety of consensus problems commonly arising in different application fields, such as, for example, synchronization, leader-tracking, containment, formation-containment, rendezvous [7]
As the cooperative control theory went improving, more complex and realistic scenarios have been treated bringing to the birth of the so-called heterogeneous MASs [12,43], where each agent acts according to its own dynamics
Based on the above facts, in this work, we propose a fully distributed adaptive PID protocol for heterogeneous nonlinear and unknown high-order multiagent systems, able to ensure leader-tracking in the presence of parameter uncertainties, arising from the unavoidable simplifications occurring during the modeling phase, from the not-complete knowledge of the system dynamics and from the presence of external disturbances
Summary
Recent years have witnessed the great development of distributed cooperative control based on multi-agent systems (MASs) with the aim at solving the large variety of consensus problems commonly arising in different application fields (e.g., physics, economic sciences, biology, engineering, and robotics), such as, for example, synchronization, leader-tracking, containment, formation-containment, rendezvous [7]. For example, in [34], where authors propose a distributed PI control strategy able to track only a constant leading behavior under the main hypothesis that the input matrix of each agent (follower) is structured in order to guarantee that there exists a specific control action for each state variables, limiting by this way the applicability of the approach to a specific system category Some of these drawbacks have been very recently overcome for heterogeneous, but linear, MASs in [32], where an optimal distributed PID protocol is proposed, able to solve both leader-tracking and output containment problems (i.e., when more leaders are present), without requiring restrictive assumptions on the agents matrix structures.
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