Two-Layer Distributed Formation-Containment Control of Multiple Euler-Lagrange Systems by Output Feedback

Bionic Swarm Control Based on Second-Order Communication Topology

In this article, we propose bionic swarm control based on second-order communication topology (SOCT) inspired by the migration of birds, which solves the difficulty in constructing communication topologies and high-computational complexity in controlling large-scale swarm systems. To realize bionic swarm control, there are three problems supposed to be solved. First, the adjacency matrix and the Laplacian matrix in traditional methods cannot be applied to SOCT directly, which should be redesigned. Second, sub-swarm systems formed based on 2-order communication topology (2-OCT) and independently distributed with each other also need to be put forward to reduce computational complexity. At last, the followers in 1-order communication topology (1-OCT) are set as the leaders of sub-swarm systems in 2-OCT. As a result, coupling in large-scale swarm systems would be reduced. The bionic swarm controller is designed through the backstepping method. In this case, the stability of bionic swarm controller is proven by the designed Lyapunov function. The simulations show the efficiency of the designed bionic swarm controller. And the tracking-containment control based on SOCT with 42 swarm members is realized.

Resilient exponential tracking for disturbed systems with communication links faults

Resilience is to appraise the ability of disturbed systems to recover cooperative performance after suffering from failures or disturbances. In this paper, the improvement on the exponential tracking resilience for disturbed Euler-Lagrange systems is explored by settling the unknown time-variant faults imposed on the communication interaction between agents. First, we transform the resilient exponential tracking problem into designing the trajectory and velocity observers for leaders, and showcase that the proposed observers are resilient to communication interaction malfunctions. Second, a disturbance observer is manifested to estimate disturbances precisely, which is needless to know the upper bound of disturbance. The reliable observers and estimator are incorporated into the resilient tracking control frame. Further, the global exponential stabilization of the tracking systems is performed by utilizing the Lyapunov theory. Moreover, benefiting from feasible and reliable observation and estimation results, the proposed control framework enables to realize a satisfactory resilient exponential tracking performance even in the case of communication links faults (CLFs) and disturbances. Comprehensive studies are executed on a group of satellite systems, and the simulations results verify the effectiveness of the proposed resilient approaches in a time-variant tracking case.

Leader-following output-feedback consensus for second order multiagent systems with arbitrary convergence time and prescribed performance

This paper investigates the prescribed-time leader-following output-feedback consensus problem for second order multiagent systems without velocity measurement. Firstly, by introducing a time-scaling function, novel prescribed-time state observers are designed to estimate the second-order states of the agents. Then, a distributed output-feedback scheme is proposed to achieve leader-following consensus, where the transient performance, including the convergence rate and the overshoot, can be offline pre-assigned. It should be noted that the singularity-like problem is solved for the system under measurement errors by adopting a form of piecewise functions. Moreover, the control strategy is modified by introducing an auxiliary system when taking the common saturation problem into account. Finally, the efficiency of the proposed schemes is illustrated by numerical simulation examples.

Adaptive neural networks-based fixed-time fault-tolerant consensus tracking for uncertain multiple Euler-Lagrange systems

This article addresses the fixed-time fault-tolerant consensus tracking (FTCT) problem for uncertain multiple Euler-Lagrange systems (MELS) with the digraph and actuator faults. Firstly, a fixed-time distributed observer (DO) is built to estimate the states of leader. Then, the approximation ability of radical basic function neural networks (RBFNN) is exploited to deal with the system uncertainties. By using backstepping technique, the novel fault-tolerant local control protocol (FTLCP) and updating laws are designed to ensure that error variables converge to the small adjacent area of zero within fixed-time. Eventually, the effectiveness and practicality of the presented method are demonstrated through a typical MELS simulation.

Spherical Formation Tracking Control of Nonlinear Second-Order Agents With Adaptive Neural Flow Estimate

This article addresses the spherical formation tracking control problem of nonlinear second-order vehicles moving in flowfields under both undirected networks and directed, strongly connected networks. Different from the previous adaptive estimate of the time-invariant parameters of flowfields, the flowfields under our consideration are spatial and absolutely unknown dynamics. Adaptive neural networks (ANNs) with the novel cooperative adaptive algorithms are proposed to approximate the flowfield acting on the channel of each vehicle's velocity (i.e., the mismatched flowfield) and the flowfield pushing the acceleration (i.e., the matched flowfield), respectively. For the purpose of avoiding the complex derivation derived from backstepping, the novel first-order filters are generated by dynamic surface based on barrier functions and relative positions of neighbors. The proposed control algorithms and adaptive upgrade law are fully distributed without using any global information of the graph. The uniform boundedness is analyzed in the Lyapunov sense. Simulation results are given to verify the theoretical analysis.

Time-Varying Group Formation-Containment Tracking Control for General Linear Multiagent Systems With Unknown Inputs

Time-varying group formation-containment tracking problems for general linear multiagent systems with unknown control input are investigated. Agents are classified into tracking leaders, formation leaders, and followers and assigned in groups. Tracking leaders with unknown control inputs provide unpredictable trajectories as macroscopic moving references. Formation leaders accomplish desired subformations while following the trails of tracking leaders. At the same time, followers converge into different convex hulls spanned by formation leaders. First, formation-containment tracking protocols are designed with neighboring relative information and effects of unknown input of tracking leaders. Then, the design of group division is analyzed by adjusting the properties in Laplacian matrices, which represent interaction relationships. An algorithm to determine the parameters in control protocols is proposed, and the formation tracking feasible constraint is presented. Next, it is proved that the general linear multiagent system can achieve time-varying group formation-containment control effectively with errors uniformly asymptotically converging to zero under designed protocols. Finally, a numerical simulation is given to verify the effectiveness of obtained theoretical results.

Optimal Bounded Ellipsoid Identification With Deterministic and Bounded Learning Gains: Design and Application to Euler-Lagrange Systems

This article proposes an effective optimal bounded ellipsoid (OBE) identification algorithm for neural networks to reconstruct the dynamics of the uncertain Euler-Lagrange systems. To address the problem of unbounded growth or vanishing of the learning gain matrix in classical OBE algorithms, we propose a modified OBE algorithm to ensure that the learning gain matrix has deterministic upper and lower bounds (i.e., the bounds are independent of the unpredictable excitation levels in different regressor channels and, therefore, are capable of being predetermined a priori). Such properties are generally unavailable in the existing OBE algorithms. The upper bound prevents blow-up in cases of insufficient excitations, and the lower bound ensures good identification performance for time-varying parameters. Based on the proposed OBE identification algorithm, we developed a closed-loop controller for the Euler-Lagrange system and proved the practical asymptotic stability of the closed-loop system via the Lyapunov stability theory. Furthermore, we showed that inertial matrix inversion and noisy acceleration signals are not required in the controller. Comparative studies confirmed the validity of the proposed approach.

Distributed Fractional-Order Intelligent Adaptive Fault-Tolerant Formation-Containment Control of Two-Layer Networked Unmanned Airships for Safe Observation of a Smart City

This article investigates a distributed fractional-order fault-tolerant formation-containment control (FOFTFCC) scheme for networked unmanned airships (UAs) to achieve safe observation of a smart city. In the proposed control method, an interval type-2 fuzzy neural network (IT2FNN) is first developed for each UA to approximate the unknown term associated with the loss-of-effectiveness faults in the distributed error dynamics, and then a disturbance observer (DO) is proposed to compensate for the approximation error and bias fault encountered by each UA, such that the composite learning strategy composed of the IT2FNN and the DO is obtained for each UA. Moreover, fractional-order (FO) calculus is incorporated into the control scheme to provide an extra degree of freedom for the parameter adjustments. The salient feature of the proposed control scheme is that the composite learning algorithm and FO calculus are integrated to achieve a satisfactory fault-tolerant formation-containment control performance even when a portion of leader/follower UAs is subjected to the actuator faults in a distributed communication network. Furthermore, it is shown by Lyapunov stability analysis that all leader UAs can track the virtual leader UA with time-varying offset vectors, and all follower UAs can converge into the convex hull spanned by the leader UAs. Finally, comparative hardware-in-the-loop (HIL) experimental results are presented to show the effectiveness and superiority of the proposed method.

Necessary and Sufficient Conditions of Formation-Containment Control of High-Order Multiagent Systems With Observer-Type Protocols

The analysis and design problems of formation-containment control for high-order linear time-invariant (LTI) multiagent systems (MASs) on directed graphs with observer-based output-feedback protocols are given in this work. To expand the feasibility of state formation configuration, two well-structured compensation signals are introduced for the leaders and followers in the protocols, respectively. Benefitting from the compensation signal of followers, the decoupling between formation control of leaders and containment control of followers is achieved. Thus, a necessary and sufficient condition is first established such that the formation-containment control for high-order LTI MASs can be achieved. Moreover, a heuristic iterative algorithm is developed to compute the controller gains, observer gains, as well as the compensation signals. Finally, two numerical examples are implemented to illustrate the time-varying formation-containment control of high-order MASs, which shows the validity and practicability of the theoretical results and algorithm.

Formation-Containment Control of Euler-Lagrange Systems of Leaders With Bounded Unknown Inputs

Motivated by the promising applications of multiple Euler-Lagrange (EL) systems, we study, in this article, the formation-containment (FC) control problem for multiple EL systems of leaders with bounded unknown control inputs and with communication among each other over directed topologies, which can cooperatively generate safe trajectories to avoid obstacles. Given the FC shapes, an algorithm is first proposed to obtain the stress matrix while satisfying certain conditions, based on which a novel adaptive distributed observer to the convex hull is proposed for every follower. An adaptive updating gain is applied to make the observer fully distributed without using the global information of the graph, and a continuous function is designed to restrain the influence of the inputs of the leaders. Then, a local control law using the adaptive distributed observer is presented to accomplish the FC control of EL systems. Based on the Lyapunov stability theory, it is proved that the FC error can be designed as small as possible by adjusting some parameters in the observer.

Adaptive Coordinated Formation Control of Heterogeneous Vertical Takeoff and Landing UAVs Subject to Parametric Uncertainties

This article focuses on the solution to the coordinated formation problem of heterogeneous vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs) in the presence of parametric uncertainties. In particular, their inertial parameters are distinct and unavailable. For the sake of the accomplishment of the coordinated formation objective of multiple underactuated VTOL UAVs through local information exchange, an adaptive distributed control algorithm is developed under a cascaded structure. Specifically, by introducing an immersion and invariance (I&I) adaption strategy for the exponential mass estimation, a distributed command force is first synthesized in the position loop. Next, an applied torque with adaption is synthesized for the attitude tracking to a command attitude. This command attitude, as well as the applied thrust, is extracted from the synthesized command force without singularity. It is shown in terms of the Lyapunov theory that driven by the proposed adaptive distributed control algorithm, the concerned coordinated formation control of multiple VTOL UAVs is achieved asymptotically. Finally, an illustrative example is simulated to validate the effectiveness of the proposed control algorithm.

Distributed Formation Control of Multiple Euler-Lagrange Systems: A Multilayer Framework

In this technical correspondence, a multilayer formation (MLF) control problem is considered and solved by a unified framework. The agents in each layer present a sort of hierarchical distinction: receive information from former layers, communicate inside the current layer, and send information to subsequent layers. With an arbitrary number of layers, we extend the previous result from undirected graphs to directed ones. The proposed controller achieves MLF without using the distributed estimators and the acceleration information. This removes the induced discontinuities and alleviates the system complexity. It is then proved that the closed-loop errors are semiglobally uniformly ultimately bounded. Simulations are presented to illustrate the effectiveness of this approach.

Micro Flapping-Wing Vehicles Formation Control With Attitude Estimation

This article addresses the formation control problem of flapping-wing vehicles (FWVs) under the model uncertainty and the measurement inaccuracy. A two-layer formation strategy is adopted, which consists of a formation control layer for the leaders, and a containment control layer for the followers. In both layers, attitudes and positions are required by the formation geometry. A formation state estimation algorithm is designed to achieve the desired formation states from local neighborhoods. In FWVs, attitude angles are usually achieved from angular velocities, whose measurement error accumulates during integration and leads to divergence of the system. In order to solve this problem, we explore the coupling property between the translational motion and the rotational motion of FWVs, and design a coupling-based estimation method for attitude angles. To compensate for the model uncertainty, the measurement error, and the estimation error, adaptive neural networks are developed together with the control algorithm. The stability of both the control algorithm and the estimation algorithm is guaranteed based on the Lyapunov stability theory. Simulations are conducted to validate our method, and the results illustrate its effectiveness.

Model-Independent Formation Tracking of Multiple Euler-Lagrange Systems via Bounded Inputs

This article addresses two kinds of formation tracking problems, namely: 1) the practical formation tracking (PFT) problem and 2) the zero-error formation tracking (ZEFT) problem for multiple Euler-Lagrange systems with input disturbances and unknown models. In these problems, the bounded input constraint, which can be possibly caused by actuator saturation and power limitations, is taken into consideration. Then, the two classes of model-independent distributed control approaches, in which the prior information (i.e., the structures and features) of the system model is not used, are proposed correspondingly. Based on the nonsmooth analysis and Lyapunov stability theory, several novel criteria for achieving PFT and ZEFT of multiple Euler-Lagrange systems are derived. Finally, numerical simulations and comparisons are presented to verify the validity and effectiveness of the proposed control approaches.

Time-varying formation control of multiple quad-rotors based on ellipsoid

Time-varying formation control problem for a group of multiple quad-rotors has been considered in this article with the help of ellipsoid. Firstly, an elliptic equation with time-varying parameters has been firstly introduced to describe the desired formation patterns for multiple quad-rotors in three-dimensional space. Then position controller and attitude controller are constructed using the method of sliding model control, respectively. Through tuning parameters of the elliptic equation, time-varying formation control of multiple quad-rotors has been realized using the controllers proposed in this article where smoothing transition between rigid formations has been guaranteed. Simulation results for formation control of quad-rotors that perform translation, scaling, and rotating actions have illustrated effectiveness of the time-varying formation controller that proposed in this article.

Cooperative Circumnavigation Control of Networked Microsatellites

This paper addresses the trajectory analysis, mission design, and control law for multiple microsatellites to cooperatively circumnavigate a host spacecraft. This cooperative circumnavigation (CCN) problem is defined to drive a group of networked microsatellites to a predefined planar ellipse concerning a host spacecraft while maintaining a geometric formation configuration. We first design several potential functions to guide the microsatellites to the given planar elliptical orbit with a proper radius. Next, the affine Laplacian matrix is introduced to characterize the desired formation shape of microsatellites. Based on the potential functions and the Laplacian matrix, a CCN control law is finally proposed. Then, the simulation results of eight microsatellites with earth-orbiting mission scenarios are given, where the natural trajectory motion is incorporated which consumes nearly zero-fuel.

Ultra-Wideband and Odometry-Based Cooperative Relative Localization With Application to Multi-UAV Formation Control

This puts forth an infrastructure-free cooperative relative localization (RL) for unmanned aerial vehicles (UAVs) in global positioning system (GPS)-denied environments. Instead of estimating relative coordinates with vision-based methods, an onboard ultra-wideband (UWB) ranging and communication (RCM) network is adopted to both sense the inter-UAV distance and exchange information for RL estimation in 2-D spaces. Without any external infrastructures prepositioned, each agent cooperatively performs a consensus-based fusion, which fuses the obtained direct and indirect RL estimates, to generate the relative positions to its neighbors in real time despite the fact that some UAVs may not have direct range measurements to their neighbors. The proposed RL estimation is then applied to formation control. Extensive simulations and real-world flight tests corroborate the merits of the developed RL algorithm.

Three-Variable Chaotic Oscillatory System Based on DNA Strand Displacement and Its Coupling Combination Synchronization

The synchronization control of two chaotic oscillatory systems is designed based on DNA strand displacement in the present work. Thus, combination synchronization of three 3-variable chaotic oscillatory systems is proposed based on DNA strand displacement. Firstly, five chemical reaction modules of double, displacement, adjustment, catalysis and degradation are designed. Based on these five modules, a 3-variable chaotic oscillatory system is designed. Secondly, based on the design principle of coupling terms and theory of stability, synchronization modules and coupling terms are added to three chaotic oscillatory systems to design combination synchronization of three 3-variable chaotic oscillatory systems based on DNA strand displacement. Modules and systems are implemented and tested using visual DSD and Matlab, and the simulation results are presented to demonstrate the effectiveness and correctness of the chemical reaction modules and systems. The combination synchronization of three 3-variable chaotic oscillatory systems is proposed based on DNA strand displacement, which may be extended to the reaction networks of DNA strand displacement and to the combination synchronization of multivariable chaotic oscillatory systems based on DNA strand displacement.

Velocity Free Platoon Formation Control for Unmanned Surface Vehicles with Output Constraints and Model Uncertainties

This paper studies the velocity free platoon formation control for unmanned surface vehicles (USVs) with the model uncertainties and output constraints. Firstly, a reconstruction module is designed to estimate the velocity of the leader, which will be completed in finite time and will reduce the communication burden. Along with this, the model-based control combined with the symmetric barrier Lyapunov functions (BLF) method is designed to guarantee the output constraints. Then, the model uncertainties of the USV are approximated by the neural networks (NNs) and the NN BLF control is developed. To achieve the desired formation pattern, the constraints, including collision avoidance and communication distance, are under consideration. Finally, we proved that our system is semiglobally uniformly ultimately bounded (SGUUB) and verified the effectiveness of this approach by simulations.

Neural Network-Based Adaptive Consensus Control for a Class of Nonaffine Nonlinear Multiagent Systems With Actuator Faults

In this paper, the consensus problem is investigated for a class of nonaffine nonlinear multiagent systems (MASs) with actuator faults of partial loss of effectiveness fault and biased fault. To deal with the control difficulty caused by the nonaffine dynamics, a neural network (NN)-based adaptive consensus protocol is developed based on the Lyapunov analysis. The neuron input of the NN uses both the state information and the consensus error information. In addition, the negative feedback term of the NN weight update law is multiplied by an absolute value of the consensus error, which is helpful in improving the consensus accuracy. With the developed adaptive NN consensus protocol, semiglobal consensus with a bounded residual consensus error of the MAS is achieved, and the bounded NN weight matrix is guaranteed. Finally, simulation results show that the developed adaptive NN consensus protocol has advantages of fast convergence rate and good consensus accuracy and has the capability of rapid response with respect to the actuator faults.

Output Containment Control for Heterogeneous Linear Multiagent Systems With Fixed and Switching Topologies

In this paper, we investigate the output containment control problem for a network of heterogeneous linear multiagent systems. The control target is to drive the outputs of the followers into the convex hull spanned by the leaders. To this end, we first derive a necessary condition imposed on both system dynamics and network topology from the viewpoint of internal model principle. Then, based on the necessary condition, we utilize a dynamic controller to drive the outputs of the leaders and followers to track the reference trajectories to achieve containment exponentially. We consider a general network topology which only contains a united spanning tree. Both fixed and dynamic network topologies are taken into consideration. Then, the optimal control problem for containment is further studied. An optimal control law is constructed from an algebraic Riccati equation, which is proved to be a stabilizing one as well. Finally, a reinforcement learning algorithm is introduced to solve the optimal control problem on line without the knowledge the system dynamics. Simulations are given at last to validate our theoretical findings.