In this article, an input-constrained visual servoing formation controller is proposed for multiple quadrotor systems operating without intervehicle communication or relative position measurements. The aerial formation control is achieved by formulating image-based leader-follower dynamics using a virtual camera framework and sphere-based image moments. An adaptive velocity observer is developed for the follower quadrotor to estimate the relative velocity with respect to the leader quadrotor in communication-free environments. Input-constrained visual servoing and attitude controllers are proposed using an off-policy reinforcement learning (RL) algorithm to handle visibility and attitude constraints, without relying on accurate system model parameters. The stability of the closed-loop system is theoretically analyzed, and the effectiveness of the proposed controller is demonstrated through case studies.

This article studies the robust optimal formation control problem of networked fixed-wing unmanned aerial vehicles (UAVs) under communication uncertainties and external disturbances. A learning-based observer–feedforward–feedback control framework is constructed. A resilient self-triggered (ST) observer is designed to estimate reference data while enabling intermittent communication under communication uncertainties. By integrating reference estimation with a backstepping technique, the cooperative formation control problem is reformulated as a robust optimal regulation problem. The robust optimal feedforward control law is learned via an off-policy reinforcement learning (RL) algorithm that exploits the collected internal system data and external disturbance inputs. The stability of the constructed closed-loop control system is guaranteed, and Zeno behavior in the ST rule is avoided. The effectiveness of the proposed approach is demonstrated through an experimental study of multiple fixed-wing UAVs.

In this article, the security formation control problem is investigated for underactuated quadrotors involving nonlinear coupled dynamics, subject to denial-of-service (DoS) attacks and uncertain communication faults. A security formation control method is proposed, including a distributed resilient observer and a hierarchical data-driven controller. The observer with an adaptive event-triggered mechanism is developed to restrain the influence of DoS and communication faults on interaction information among quadrotors, and Zeno behavior of all observers can be avoided. The optimal control laws are learned iteratively based on observation data and system data by utilizing reinforcement learning without knowledge of system dynamics. The stability of the constructed closed-loop control system is proven, and sufficient conditions are established for the unreliable network. Simulation results demonstrate the advantages of the proposed security control method.

In this paper, a robust optimal three-dimensional cooperative guidance law with input saturation is proposed for intelligent aerial vehicles to intercept an unknown maneuvering target. The problem of cooperative interception is formulated as a leader-follower optimal tracking control problem based on the differential graphical game subject to a nonautonomous leading vehicle with bounded control inputs. Utilizing the backstepping method, the guidance law is divided into a feedforward part for generating the desired state signals and compensates for the impact of input saturation, and a data-driven feedback part based on the differential graphical game that regulates tracking errors due to unknown target maneuvers while optimizing interactive performance indices. The uniform ultimate bounded property of the tracking errors in the closed-loop system can be guaranteed and the predefined interactive cost function can be optimized by the proposed guidance law. Simulation examples of cooperative interception are provided to validate the effectiveness of the proposed approach.

This paper investigates the robust intelligent control problem of multi-line re-entrant manufacturing plants. The control system is designed with a hierarchical architecture, where a nonlinear stochastic hyperbolic partial differential equation (PDE) is used to describe the system dynamics and a robust controller is designed to exponentially drive the manufacturing plants to a desired operation mode with steady feeding and production rates. The developed robust control scheme is shown to be practically implementable through convex optimization techniques. Numerical experiments are presented to demonstrate the feasibility and advantages of the proposed approach.Note to Practitioners—The motivation of this work originates from the need to develop an intelligent robust control strategy for a class of practical complex re-entrant manufacturing plants, for instance, the semiconductor wafer factory and the chemical production lines with numerous process procedures. Discrete-model-based algorithms have been extensively employed in this field due to their excellent convenience and great accuracy. However, when dealing with coupled multi-line re-entrant manufacturing plants with nonlinearities, traditional discrete-model-based methods lack rigorous theoretical analysis and, more importantly, suffer from the curse of dimensionality in many cases. To equip the re-entrant manufacturing plant with a desired operation mode that enjoys significant robustness against stochastic noises, we propose a continuum-model-based intelligent robust control strategy. The proposed method is practically useful in the sense that it can be conveniently applied to various industrial scenarios with re-entrant characteristics and the control design problem can be well solved via available convex optimization algorithms.

This article proposes an optimal controller for a team of underactuated quadrotors with multiple active leaders in containment control tasks. The quadrotor dynamics are underactuated, nonlinear, uncertain, and subject to external disturbances. The active team leaders have control inputs to enhance the maneuverability of the containment system. The proposed controller consists of a position control law to guarantee the achievement of position containment and an attitude control law to regulate the rotational motion, which are learned via off-policy reinforcement learning using historical data from quadrotor trajectories. The closed-loop system stability can be guaranteed by theoretical analysis. Simulation results of cooperative transportation missions with multiple active leaders demonstrate the effectiveness of the proposed controller.

This paper investigates the optimal formation control of a heterogeneous multiagent system consisting of multiple quadrotors and ground vehicles via reinforcement learning to achieve the time-varying formation under switching topologies. A distributed observer is firstly constructed to generate references using local information for each vehicle to form time-varying formation and the convergence of the observer under switching topologies is proven. Then, reinforcement learning methods are provided for the heterogeneous vehicle group to realize the optimal tracking control without information of vehicle dynamical model. Simulation tests are given to confirm the effectiveness of the proposed method.

This paper investigates the coordination control problem for a special nonlinear heterogeneous multi-agent system consisting of tail-sitter unmanned aerial vehicles and unmanned ground vehicles with uncertainties and disturbances. A robust hierarchical pinning control scheme is proposed for the heterogeneous multi-agent system to restrain the uncertainties and disturbances and achieve coordination scenarios. The heterogeneous multi-agent system can realize coordination tasks by selecting proper pinning nodes and estimating coupling strength. The robustness of the whole system is proven utilizing the Lyapunov stability theorem. The effectiveness of the robust hierarchical pining control method is validated by simulation scenarios.

In this article, the data-driven optimal formation control problem is addressed for a heterogeneous quadrotor team with a virtual leader. Each quadrotor is considered as a highly nonlinear system with six degrees of freedom and the accurate dynamic information of the quadrotor is difficult to obtain in practical applications. An optimal cascade formation controller, including a position controller and an attitude controller, is proposed to track a virtual leader and form a predesigned formation. By using the reinforcement learning (RL) approach, the optimal formation controller is learned from the quadrotor system data without any knowledge of dynamic information of the quadrotors. Simulation results of a heterogeneous multiquadrotor system in a formation flight are given to show the effectiveness of the proposed controllers.

This article considers the practical fixed-time self-triggered consensus tracking problem of delayed multiagent networks (MANs) subject to external disturbances under undirected topology and directed topology. The fixed-time consensus implies that the consensus is reached in a finite time and the convergence time is independent of initial conditions under the nonlinear consensus protocols. A self-triggered control (STC) strategy is developed based on the event-triggered control (ETC) strategy. For the ETC strategy, the nonlinear controllers and the measurement errors are designed based on the hyperbolic tangent function to avoid a nondifferential problem and Zeno behavior. To avoid continuous monitoring, the STC strategy is presented. Furthermore, the minimal interevent interval is strictly positive, which implies that no Zeno behavior occurs in the STC strategy. Finally, a numerical example is presented to verify the availability of the algorithms.

In this paper, a model-free optimal synchronization controller is designed to achieve the aggressive attitude synchronization for multiple heterogeneous quadrotor systems with highly nonlinear and coupled dynamics by using a reinforcement learning (RL) approach. A distributed observer is first designed for each following quadrotor to estimate the states of a virtual leader. A performance function is then utilized for each quadrotor to penalize the observed synchronization error and the control effort. An RL approach is finally employed to learn the optimal control law without any knowledge of the dynamic model information of the followers. The control law depends on the quadrotor states and the observer states, and guarantees that the attitude synchronization error converges to zero for all quadrotors, under aggressive maneuvers. Simulation results are provided to verify the effectiveness of the proposed controller.

The robust time-varying formation control problem for a group of satellites is addressed. By the static state feedback control strategy and the disturbance estimation theory, a formation flying controller is proposed for the satellite group to form desired time-varying formation patterns and trajectories, and achieve the satellite attitude consensus. The dynamics of each satellite is subject to nonlinearities, parametric perturbations, and external disturbances. Robustness analysis shows that the trajectory and attitude tracking errors of the global closed-loop control system can converge into a given neighborhood of the origin in a finite time. The numerical simulation results validate the effectiveness and advantages of the proposed formation flying controller.

In this article, the model-free robust formation control problem is addressed for cooperative underactuated quadrotors involving unknown nonlinear dynamics and disturbances. Based on the hierarchical control scheme and the reinforcement learning theory, a robust controller is proposed without knowledge of each quadrotor dynamics, consisting of a distributed observer to estimate the position state of the leader, a position controller to achieve the desired formation, and an attitude controller to control the rotational motion. Simulation results on the multiquadrotor system confirm the effectiveness of the proposed model-free robust formation control method.

This paper mainly addresses the formation control problem for a group of tail-sitters in transition flight between forward and vertical flight. A robust formation control method is proposed to achieve the aggressive time-varying formation subject to nonlinear dynamics and uncertainties. For each tail-sitter, the proposed control method results in a composite controller that includes a trajectory tracking controller and an attitude controller to achieve the translational and rotational motion control, respectively. It is proven that tracking errors of the proposed global closed-loop system can converge to a given neighborhood around the origin in a finite time. Finally, the simulation studies for multiple tail-sitters to accomplish the time-varying formation in transition flight are presented to show the effectiveness of the proposed control strategy.

The formation of unmanned underwater vehicles (UUVs) has wide potential for applications in various marine activities. This paper studies the robust formation protocol design problem for multiple UUVs, whose dynamics are subject to nonlinearity, parametric uncertainties, and external disturbances. A robust distributed formation control scheme is proposed, which yields a control structure involving a position loop and an attitude loop to govern the translational motion and rotational motion, respectively. Theoretical analysis is given to show the robustness properties of the global closed-loop control system. Simulation results are provided to validate the effectiveness of the proposed formation control method.

In this paper, the robust formation control problem is investigated for a group of quadrotors. Each quadrotor dynamics exhibits the features of underactuation, high nonlinearities and couplings, and disturbances in both the translational and rotational motions. A distributed robust controller is developed, which consists of a position controller to govern the translational motion for the desired formation and an attitude controller to control the rotational motion of each quadrotor. Theoretical analysis and simulation studies of a formation of multiple uncertain quadrotors are presented to validate the effectiveness of the proposed formation control scheme.

In this paper, the fault-tolerant time-varying formation control problem for a group of tail-sitters with multiple actuator faults and uncertainties is studied. A robust distributed fault-tolerant formation control strategy is developed to achieve aggressive time-varying formation flying in flight mode transitions. For each tail-sitter, the designed controller can be divided into an inner attitude controller and an outer position controller to govern the rotational and translational motions, respectively. The information of the actuator faults does not need to be identified online and the tracking errors of the global closed-loop control system can converge into a given neighborhood of the origin in a finite time. Simulation results are presented to show the effectiveness of the proposed control strategy.

The guaranteed-performance consensualization for high-order linear and nonlinear multiagent systems with switching topologies is respectively realized in a completely distributed manner in the sense that consensus design criteria are independent of interaction topologies and switching motions. This paper first proposes an adaptive consensus protocol with guaranteed-performance constraints and switching topologies, where interaction weights among neighboring agents are adaptively adjusted and state errors among all agents can be regulated. Then, a new translation-adaptive strategy is shown to realize completely distributed guaranteed-performance consensus control and an adaptive guaranteed-performance consensualization criterion is given on the basis of the Riccati inequality. Furthermore, an approach to regulate the consensus control gain and the guaranteed-performance cost is proposed in terms of linear matrix inequalities. Moreover, main conclusions for linear multiagent systems are extended to Lipschitz nonlinear cases. Finally, two numerical examples are provided to demonstrate theoretical results.

A robust nonlinear attitude control method is proposed for uncertain robotic quadrotors. The proposed controller is developed based on a nonlinear model with the quaternion representation and subject to parameter uncertainties, nonlinearities, and external disturbances. A new state feedback controller is proposed to restrain the effects of nonlinearities and uncertainties on the closed-loop control system. These uncertainties are considered as input equivalent disturbances and their effects are guaranteed to be attenuated. Experimental results are given to show good steady-state and dynamic tracking performance of the closed-loop system by the proposed robust control method compared with other nonlinear control methods.