Fuzzy Adaptive Finite-Time Cooperative Control With Input Saturation for Nonlinear Multiagent Systems and its Application

Abstract

In this paper, the fuzzy adaptive finite-time cooperative control with input saturation (FAFTCCIS) is designed to quickly accomplish the cooperation of nonlinear multiagent systems (MASs) without the risk of bumping among agents. At least one agent must communicate with the leader and the information of neighborhood agents is required to accomplish the assigned task. Each agent, including the leader and the followers, is first approximated by N fuzzy-based linear subsystems. To accomplish the null cooperation error in finite time, the proposed adaptive control possesses the switching surface with fraction order, a time-varying switching gain, and an on-line learning of the upper bound of the uncertainties in each fuzzy subsystem of agent j. The stability of all the cooperative uncertain systems is then verified by the Lyapunov stability theory. Finally, the application to the cooperative control of intelligent chef is presented to confirm the effectiveness, robustness and feasibility of the proposed FAFTCCIS. INDEX TERMS Adaptive law, Cooperative tracking control, Finite-time control, Fuzzy model, Intelligent chef, Lyapunov stability theory, Switching surface with fraction order, Time-varying switching gain. I. INTRODUCTION Recently, many consensus, containment or cooperative controls of multiagent systems (MASs) are published [1]-[33]. These typical studies are briefly discussed in the next three paragraphs. Afterwards, their features are summarized to lead to the motivations, objectives, and contributions of this paper. Based on local information that is measured or received from its neighbors and itself, a distributed consensus controller for each follower agent is designed by the fuzzy approximations of unknown nonlinear functions and one adaptive parameter to decay the effect of external disturbances [1]. Under a weighted undirected topology, the robust fixed-time consensus control for nonlinear MASs with uncertainties is investigated [2]. In [3], a multiagent collision avoidance problem is formulated by differential game to steer each agent from its initial position to a desired goal while avoiding collisions with obstacles and other agents. Despite unknown nonaffine dynamics and mismatched uncertainties, a distributed neural adaptive control for containment achieves the dynamic containment in finite time with sufficient accuracy [4]. In [5], a distributed adaptive containment control for nonlinear MASs with input quantization is developed by employing a matrix factorization and normalization technique. In [6], the output consensus problem of the heterogeneous stochastic nonlinear MASs with directed communication topologies is developed by the fuzzy approximation of the unknown nonlinear functions of agents. Under the directed communication topology, the distributed adaptive output feedback consensus problem for linear MASs with the matched nonlinear functions and actuator bias faults is designed [7]. In [8], a joint objective of the distributed formation tracking control and learning/identification of the

Cooperative multiple elastic‐joint arms control using the (p, q)‐analogue of Bernstein operators as the uncertainty approximator

“…where 𝜙 i ( q i ) ∈ ℜ n indicates the forward kinematic. By differentiating (20), the below equation is obtained.…”

“…The system stability is also assured. The fuzzy adaptive control addressed in Reference 20 is applied to accomplish a task that needs the cooperation of planar robots, lacking the collision risk. The aim of Reference 21 is to provide a distributed control strategy for the networked manipulators, which cooperatively move an un‐modeled object in the absence of force measuring requirement.…”

Adaptive control of cooperative robots in the presence of disturbances and uncertainties: A Bernstein–Chlodowsky approach

“…By known F o , and based on Assumptions 2 and 4, the force F e , satisfying (14), is decomposed into two parts. These parts are orthogonal and correspond to the internal force production and the object transportation as (15) [32,33].…”

“…This study also assured the system's stability. A fuzzy adaptive controller was suggested in Hwang et al [15] to carry out a job that needed the cooperation of robots without collision possibility. This study suggested the control/approximation scheme to confront lumped uncertainties and confirm cooperative tasks efficiently.…”

Recurrent Neural Network With Fractional Learning-Based Fixed-Time Formation Tracking Constrained Control for a Group of Quadrotors

“…In this article, the advantageous features of nonlinear filtering error with dynamic fraction order include the easy trajectory planning for formation change, the linear dynamics and dynamic fraction order of formation error to shape the frequency response and to achieve fixed-time formation tracking ability [45]- [47]. As the nonlinear filtering error is in the neighborhood of zero, not only the time-varying switching gain increases to accomplish its fixed time convergence but also the fractional learning continues providing the innovative compensation to ensure zero fixed-time formation error in uncertain environments.…”