Adaptive Neural Network Fixed-Time Leader-Follower Consensus for Multiagent Systems With Constraints and Disturbances

Fixed-Time Collision-Free Fault-Tolerant Formation Control of Multi-UAVs Under Actuator Faults

When cooperating through an intensive formation, the safe distancing of unmanned aerial vehicles (UAVs) is a delicate issue, especially if UAVs are subjected to actuator faults that cause rapid maneuvers. This article investigates the fixed-time fault-tolerant formation control of multiple quadrotor UAVs under actuator faults, which considers the collision avoidance among UAVs when faults occur, and the convenience of engineering application. First, an augmented fixed-time observer with measurement noise oppression is adopted to estimate and compensate actuator faults and disturbance in rotational and translational dynamics. Then, a baseline attitude controller, a command filter, and a velocity controller are proposed for each quadrotor UAV to track the desired velocity within a fixed time. Next, a distributed fixed-time sliding-mode controller that integrates the gradient of repulsive potential function into the sliding manifold is designed to achieve leader-follower formation control and collision avoidance simultaneously. The control scheme is proven to be fixed-time convergent via Lyapunov stability analysis and is normalized in accordance with the compatibility of hardware implementation. Finally, the designed algorithm is embedded into PX4 architecture to illustrate the effectiveness and practicality of the control strategy.

Distributed Adaptive Fixed-Time Fault-Tolerant Formation Control for Heterogeneous Multiagent Systems With a Leader of Unknown Input

In this article, the distributed adaptive fixed-time output time-varying formation tracking issue of heterogeneous multiagent systems (MASs) with actuator faults is addressed, in which the followers suffer from loss-of-effectiveness actuator faults, and the leader has unknown bounded input. To solve the above issue, a distributed fixed-time observer is constructed with the leader's unknown input, by which each follower can obtain the leader's states in a predesigned time. Then, based on the observer and the desired formation vector, a local adaptive fixed-time fault-tolerant formation control algorithm is proposed for each follower with the help of time-varying gains to make up for the influence of actuator faults. Furthermore, it is proven that the designed controller can satisfactorily accomplish the considered task of the heterogeneous MASs by using the Lyapunov stability theory. Specifically, the obtained upper bound of the convergence time only depends on a few controller parameters. Finally, a simulation example is implemented to validate the efficiency of the analytical results.

Adaptive Neural Network Event-Triggered Output-Feedback Containment Control for Nonlinear MASs With Input Quantization

This article investigates the adaptive neural network (NN) event-triggered containment control problem for a class of nonlinear multiagent systems (MASs). Since the considered nonlinear MASs contain unknown nonlinear dynamics, immeasurable states, and quantized input signals, the NNs are adopted to model unknown agents, and an NN state observer is established by using the intermittent output signal. Subsequently, a novel event-triggered mechanism consisting of both the sensor-to-controller and controller-to-actuator channels are established. By decomposing quantized input signals into the sum of two bounded nonlinear functions and based on the adaptive backstepping control and first-order filter design theories, an adaptive NN event-triggered output-feedback containment control scheme is formulated. It is proved that the controlled system is semi-globally uniformly ultimately bounded (SGUUB) and the followers are within a convex hull formed by the leaders. Finally, a simulation example is given to validate the effectiveness of the presented NN containment control scheme.

Nonsingular Practical Fixed-Time Adaptive Output Feedback Control of MIMO Nonlinear Systems

This article studies the nonsingular fixed-time control problem of multiple-input multiple-output (MIMO) nonlinear systems with unmeasured states for the first time. A state observer is designed to solve the problem that system states cannot be measured. Due to the existence of the unknown system nonlinear dynamics, neural networks (NNs) are introduced to approximate them. Then, through the combination of adaptive backstepping recursive technology and adding power integration technology, a nonsingular fixed-time adaptive output feedback control algorithm is proposed, which introduces a filter to avoid the complicated derivation process of the virtual control function. According to the fixed-time Lyapunov stability theory, the practical fixed-time stability of the closed-loop system is proven, which means that all signals of the closed-loop system remain bounded in a fixed time under the proposed algorithm. Finally, the effectiveness of the proposed algorithm is verified by the numerical simulation and practical simulation.

Distributed convex optimization of bipartite containment control for high-order nonlinear uncertain multi-agent systems with state constraints

This article investigates a penalty-based distributed optimization algorithm of bipartite containment control for high-order nonlinear uncertain multi-agent systems with state constraints. The proposed method addresses the distributed optimization problem by designing a penalty function in the form of a quadratic function, which is the sum of the global objective function and the consensus constraint. Moreover, the observer is presented to address the unmeasurable state of each agent. Radial basis function neural networks (RBFNN) are employed to approximate the unknown nonlinear functions. Then, by integrating RBFNN and dynamic surface control (DSC) techniques, an adaptive backstepping controller based on the barrier Lyapunov function (BLF) is proposed. Finally, the effectiveness of the suggested control strategy is verified under the condition that the state constraints are not broken. Simulation results indicate that the output trajectories of all agents remain within the upper and lower boundaries, converging asymptotically to the global optimal signal.

Fixed-time connectivity-preserving consensus of periodically disturbed nonlinear multi-agent systems with limited communication ranges

This paper concentrates on the fixed-time consensus control problem with preserved connectivity for periodically disturbed nonlinear multi-agent systems with limited communication ranges. The dynamics model of the considered multi-agent systems is general, in which the periodically time-varying disturbance appears in the unknown system function in a nonlinear fashion. The Fourier series expansion-radial basis function neural network-based approximator is incorporated to describe the unknown disturbed functions. In consideration of the limited communication ranges, a unified error transformation is utilized to preserve the initial connectivity. Then, via the backstepping method, a consensus control scheme is recursively constructed to guarantee that the consensus errors fall into a small region around the origin in fixed time, and the connectivity preservation is ensured simultaneously. In simulation part, the consensus trajectories, consensus errors and the results of connectivity preservation are provided. The simulation results demonstrate the capability of the proposed control strategy in achieving connectivity-preserving consensus in fixed time.

NN event-triggered finite-time consensus control for uncertain nonlinear Multi-Agent Systems with dead-zone input and actuator failures

This paper develops a Neural Network (NN) event-triggered finite-time consensus control method for uncertain nonlinear Multi-Agent Systems (MASs) with dead-zone input and actuator failures. In practical applications, actuator failures would inevitably arise in MASs. And the time, pattern, and value of the failures are unknown. Besides, the actuators of MASs also suffer from dead-zone nonlinearity. No matter actuator failures or dead-zone input would dramatically affect the performance and stability of MASs. To address these issues, finite-time adaptive controllers capable of simultaneously compensating for actuator failures and dead-zone input are constructed by adopting the backstepping technology. Meanwhile, the NN control scheme is adopted to handle the unknown nonlinear dynamics of each agent. Furthermore, an event-triggered control mechanism is established that no longer requires continuous communication on the control network. Under the proposed control method, all followers achieve finite-time synchronization, irrespective of the presence of limited bandwidth, unknown failures, and dead-zone input. These results are demonstrated by simulations.

Neural Adaptive Fixed-Time Control for Nonlinear Systems With Full-State Constraints

This article aims at this problem of adaptive neural tracking control for state-constrained systems. A general fixed-time stability criterion is first presented, by which an adaptive neural control algorithm is developed. Under the action of the proposed adaptive neural tracking controller, the tracking error converges into a small neighborhood around the origin in fixed time; meanwhile, all system states abide by the corresponding state constraints for all the time. The main difference between the present research and the previous control schemes for state-constrained systems is that this article proposes a novel and feasible approach to ensure that the constructed virtual control signals satisfy the state constraints on the corresponding states viewed as the virtual control inputs. Such an approach guarantees theoretically that all the system states cannot violate their constrained requirements at any time. Finally, two simulation examples provide support to the proposed results.

Deterministic learning-based neural network control with adaptive phase compensation

Under the persistent excitation (PE) condition, the real dynamics of the nonlinear system can be obtained through the deterministic learning-based radial basis function neural network (RBFNN) control. However, in this scheme, the learning speed and accuracy are limited by the tradeoff between the PE levels and the approximation capabilities of the neural network (NN). Inspired by the frequency domain phase compensation of linear time-invariant (LTI) systems, this paper presents an adaptive phase compensator employing the pure time delay to improve the performance of the deterministic learning-based adaptive feedforward control with the reference input known a priori. When the adaptive phase compensation is applied to the hidden layer of the RBFNN, the nonlinear approximation capability of the RBFNN is effectively improved such that both the learning performance (learning speed and accuracy) and the control performance of the deterministic learning-based control scheme are improved. Theoretical analysis is conducted to prove the stability of the proposed learning control scheme for a class of systems which are affine in the control. Simulation studies demonstrate the effectiveness of the proposed phase compensation method.

Roto-Translation Invariant Formation of Multiple Underactuated Planar Rigid Bodies

This article investigates the roto-translation invariant (RTI) formation of multiple underactuated planar rigid bodies, which are established under the framework of matrix Lie groups. The main contribution is that we define the RTI and pseudo RTI (P-RTI) formation of planar rigid bodies. Different from the common formation given in the earth-fixed frame, the RTI formation is defined in the body-fixed frame so that it possesses a rigid-body motion obtained by composing rotation and translation simultaneously. Moreover, regarding fully actuated planar rigid bodies, we propose the velocity and force requirements to maintain the RTI formation, which are derived based on the kinematic and dynamic model, respectively. Another contribution of this article is that the RTI formation feasibility is investigated for underactuated planar rigid bodies subject to nonholonomic constraints on velocities and accelerations. To be more specific, we study the occasions when wheeled mobile robots and underactuated surface vessels can maintain the RTI or P-RTI formation. Finally, the results of the simulation and experiment are presented so as to exhibit the RTI and P-RTI formation intuitively.

A Comment on and Correction to: Opinion Dynamics in the Presence of Increasing Agreement Pressure

We identify counterexamples to the consensus result given in Semonsen et al. (2018). We resolve the counterexamples by replacing Lemma 5 in the given reference with a novel variation of the Banach fixed-point theorem, which explains both the numerical results in the reference and the counterexample(s) in this note and provides a sufficient condition for consensus in systems with increasing peer-pressure. This work is relevant for other papers that have used the proof technique from Semonsen et al. and establishes the veracity of their claims assuming the new sufficient condition.

Neural-Network-Based Adaptive Event-Triggered Asymptotically Consensus Tracking Control for Nonlinear Nonstrict-Feedback MASs: An Improved Dynamic Surface Approach

In this article, the asymptotic tracking control problem for a class of nonlinear multi-agent systems (MASs) is researched by the combination of radial basis function neural networks (RBF NNs) and an improved dynamic surface control (DSC) technology. It's important to emphasize that the MASs studied in this article are nonlinear and nonstrict-feedback systems, where the nonlinear functions are unknown. In order to satisfy the requirement that all items in the controller must be available, the unknown nonlinearities in the system are flexibly approximated by utilizing RBF NNs technique. Moreover, the issue of ``complexity explosion'' in the backstepping procedure is handled by improving the traditional DSC technology, and meanwhile, the influences of the boundary layers caused by the filters in the DSC procedure are eliminated skillfully through the compensation terms. In addition, the relative threshold event-triggered strategy is developed for the designed controllers to reduce the waste of communication resources, where Zeno phenomenon is successfully avoided. It is observed that the new presented control strategy ensures that all the closed-loop systems variables are uniformly ultimately bounded (UUB), and furthermore all the outputs of followers are able to track the output of the leader with zero tracking errors. Finally, the simulation results are presented to show the effectiveness of the obtained design scheme.

Neuro-adaptive augmented distributed nonlinear dynamic inversion for consensus of nonlinear agents with unknown external disturbance

This paper presents a novel neuro-adaptive augmented distributed nonlinear dynamic inversion (N-DNDI) controller for consensus of nonlinear multi-agent systems in the presence of unknown external disturbance. N-DNDI is a blending of neural network and distributed nonlinear dynamic inversion (DNDI), a new consensus control technique that inherits the features of Nonlinear Dynamic Inversion (NDI) and is capable of handling the unknown external disturbance. The implementation of NDI based consensus control along with neural networks is unique in the context of multi-agent consensus. The mathematical details provided in this paper show the solid theoretical base, and simulation results prove the effectiveness of the proposed scheme.