This article presents a novel design algorithm for the cooperative source-seeking problem using a group of quadrotors equipped with sensors for source scalar field measurement with limited communications. The main objective is to drive the average position state of quadrotors to the optimal point of a given scalar field function while maintaining the desired formation, based on the field value measured by each quadrotor. To achieve this objective, the formation-based source-seeking algorithm is proposed with a cascade structure and the consensus filter, which is composed of a formation controller and a gradient-free optimization algorithm: the formation controller implements the desired formation and provides optimization direction information for the optimization algorithm, while the optimization algorithm generates a movement direction to guide the average position state of quadrotors collectively moving toward the source without estimating gradient, and the consensus filters estimate the centralized quantities. The Lyapunov stability analysis and invariancelike theorem are applied to establish the convergence and robustness of quadrotors’ positions and velocities to the formation and the average position to the optimal point. Finally, the effectiveness of the proposed method is illustrated by a physical experiment and a numerical simulation.

In this study, the self-triggered distributed formation control problem is considered for a group of fixed-wing unmanned aerial vehicles (UAVs) under unknown wind disturbances subject to velocity and overload constraints. A more general kinematic model of UAVs involving the position, velocity, velocity yaw angle, velocity pitch angle, velocity roll angle, acceleration, overload, and wind disturbances is employed. Based on the sampled local relative position information, a novel distributed control scheme with an inner-outer loop structure and a self-triggered sampling mechanism are developed. Velocities and overloads of the controlled fixed-wing UAVs are maintained within desired ranges by introducing appropriate saturations to the loops. The nonlinear small-gain method and differential inclusion theories are used as fundamental tools to establish the stability of the closed-loop system. It is shown that the formation control objective can be achieved if a spanning tree condition is satisfied by the interconnection topology. Finally, the effectiveness and superiority of the proposed method are illustrated by simulation and experimental studies with subsonic UAVs. Note to Practitioners —This study is motivated by the emerging need for the self-triggered distributed formation control of fixed-wing UAVs. The inherent difficulty of distributed formation control for a group of fix-wing UAVs with unknown wind disturbances subject to various constraints (e.g., velocity constraints, overload constraints) is intensified by a large number of communication resources and coupling constraints. Based on the constructed kinematic model of UAVs, the presented self-triggered distributed control strategy with an inner-outer loop structure and a self-triggered sampling mechanism can achieve the formation control objective and reduce the use of communication resources, making a trade-off between formation performances and communication resources. The proposed strategy is universal and versatile, as it can be applied to different UAVs formation control frameworks and also implemented in heterogeneous multi-agent systems. Preliminary experiment tests suggest that this approach is feasible and the model does consider unknown wind disturbances. In future research, our modeling approach will integrate dynamic uncertainty to improve the proposed strategy.

This article presents a composite fuzzy distributed control law to solve a cooperative control problem of fuzzy multiagent systems with a nonlinear leader system based on the distributed observer. The contributions of this article are three-fold. First, the small-gain theorem is extended to fuzzy systems, and input-to-output stability (IOS) and output-Lagrange input-to-output stability (OL-IOS) fuzzy small-gain theorem are proposed for fuzzy systems. Second, the OL-IOS small-gain theorem of fuzzy systems with multiple loop is given. Third, based on fuzzy small-gain theorem, the fuzzy distributed control law is composed of a purely fuzzy distributed control law and a distributed observer for the leader system. Finally, the effectiveness of the proposed method is illustrated by using a numerical example and the leader-following consensus problem of the quadrotor.

This article studies the feedback optimization problem for nonlinear systems. In particular, we assume that the controlled plant admits a global asymptotic stable equilibrium corresponding to each fixed reference input and consider a modified gradient-flow optimizer augmented with a nonlinear perturbation function. With the output map of the controlled plant satisfying a linear growth condition, this article proves the existence of a perturbation function such that the resulting feedback optimization system is globally asymptotically stable at the desired equilibrium. The proof is based on the seamless integration of tools from the singular perturbation theory, input-to-state stability, and the nonlinear small-gain theorem. The possibility of extending the proposed approach to other optimizers is also discussed. Three numerical examples are employed to verify the effectiveness of the proposed method.

Based on the framework of distributed optimization algorithms, this brief studies distributed optimal formation behaviors of multi-agent systems modeled as a group of uncertain Euler-Lagrange systems with collision avoidance. Assume that each agent can only obtain measured position-based gradient value of a local objective function. By integrating a modified distributed optimization algorithm and an adaptive control law, the proposed distributed optimal formation controllers can lead the positions of agents asymptotically converging to the optimal solution to the total objective function with collision avoidance. The proposed design is verified by a numerical example of mobile relays for communication.

The distributed optimization problem (DOP) of Takagi–Sugeno (T–S) fuzzy cyber–physical systems is studied under the framework of weight-balanced graphs and quasistrongly connected characteristics. The objective is to drive the outputs of all agents to the optimal solution of a given global objective function regarded as the desired output, based on the partial information of the local objective functions. To this end, distributed optimal coordinators (DOCs) are used to generate optimal solutions of local objective functions that converge to the desired output, and fuzzy reference-tracking controllers are designed to ensure that all agents can track the optimal solutions. As novel technical results, two Lyapunov-based fuzzy input-to-state stability (ISS) small-gain theorems are proposed for the T–S fuzzy interconnected system. Thus, the overall closed-loop system is an interconnected system involving the modules of optimal coordinators and fuzzy tracking controllers with T–S fuzzy subsystems. The fuzzy ISS cyclic-small-gain theorem is applied to analyze the system stability. The DOP of T–S fuzzy cyber–physical systems is solved using the DOCs and fuzzy reference-tracking controllers through the fuzzy small-gain approach. A numerical example is presented to demonstrate the effectiveness and superiority of the proposed method.