Distributed bearing-based formation control of networked thrust-propelled vehicles

In this paper, the distributed bearing-based formation control problem of networked thrust-propelled vehicles (TPVs) is addressed, in which both the constant and time-varying velocity leaders are considered, respectively. By introducing a reference acceleration and adaptive control scheme for the followers, the mass knowledge is not necessary in contrast to the existing works. Based on the designed reference accelerations, distributed adaptive control laws are proposed for the networked TPVs. Then the stabilization conditions are presented and an inner-bearing prescribed formation can be achieved. Under the proposed control laws, the leader-follower formation maneuver problem for networked TPVs with system uncertainties can be solved. Finally, simulation results are provided to demonstrate the effectiveness of the proposed control laws.     

Distributed RISE control for spacecraft formation reconfiguration with collision avoidance

In this paper, we investigate the distributed formation reconfiguration problem of multiple spacecraft with collision avoidance in the presence of external disturbances. Artificial potential function (APF) based virtual velocity controllers for the spacecraft are firstly constructed, which overcome the local minima problem through introducing auxiliary inputs weighted by bump functions. Then, based on the robust integral of the sign of the error (RISE) control methodology, a distributed continuous asymptotic tracking control protocol is proposed, accomplishing both formation reconfiguration and the collision avoidance among spacecraft and with obstacles. Furthermore, using tools from graph theory, Lyapunov analysis and backstepping technique, we show the stability and collision avoidance performance of the closed-loop multiple spacecraft system. Numerical simulations for a spacecraft formation are finally provided to validate the effectiveness of the proposed algorithm.     

Distributed event-triggered control co-design for large-scale systems via static output feedback

This work investigates the problem of distributed control for large-scale systems, in which a communication network is available to exchange information. To avoid the unnecessary communication, an event-triggered control (ETC) mechanism is introduced, in which the transmission occurs only when a certain event is triggered. Under the assumption that only the output signal is available, the static output feedback (SOF) is considered in this work. The aim of the co-design is to design an SOF controller and an ETC condition simultaneously such that the overall closed-loop system is stabilized with a certain level of performance. To this end, an event-triggering scheme based on output signals is proposed to determine when the event is triggered. Then the closed-loop system is modeled as a linear perturbed system. The distributed control co-design is formulated as a convex optimization problem with linear matrix inequalities (LMIs) constraints. Finally, a numerical example is presented to show the effectiveness of the proposed design method.     

Distributed rotating formation control of second-order leader-following multi-agent systems with nonuniform delays

In this paper, the leader-following rotating formation control problem is investigated for second-order multi-agent systems with nonuniform time-delays. We propose a distributed algorithm to drive all agents to achieve a desired formation and orbit around a common point. By a frequency domain analysis method, the upper bound of the maximum time-delay is obtained. Finally, a numerical simulation is given to illustrate the obtained results.     

Trajectory tracking control of a 6-DOF quadrotor UAV with input saturation via backstepping

In this paper, the trajectory tracking control problem of a six-degree of freedom (6-DOF) quadrotor unmanned aerial vehicle (UAV) with input saturation is studied. Applying a hierarchical control structure, a priori-bounded control thrust and the desired orientations are derived to stabilize the translational subsystem without singularities. By using a backstepping approach with a Nussbaum function, a priori-bounded control torque for the rotational subsystem is designed to track the desired orientations generated by the translational subsystem. With the proposed control scheme, the latent singularities in the attitude extraction process caused by saturation nonlinearities are avoided, and globally uniformly ultimately bounded (UUB) stability of the closed-loop system is achieved. The tracking error bound is further determined which can be made arbitrarily small by tuning certain control gains. Numerical simulation results are provided to show the effectiveness of the proposed control scheme.     

Adaptive data-driven fault-tolerant control for nonlinear systems: Koopman-based virtual actuator approach

This paper proposes an adaptive data-driven fault-tolerant control scheme using the Koopman operator for unknown dynamics subjected to nonlinearities, time-varying loss of effectiveness, and additive actuator faults. The main objective of this method is to design a virtual actuator to hide actuator faults from the view of the system’s nominal controller without having any prior knowledge about the system’s underlying dynamics. The designed virtual actuator is placed between the faulty plant and the nominal controller of the system to keep the dynamical system’s performance consistent before and after the occurrence of actuator faults. Based on the Koopman operator theory, an equivalent Koopman predictor is first obtained using the process data only, without knowing the governing equations of the underlying dynamics. Koopman operator is an infinite-dimensional, linear operator which takes the nonlinear process data into an infinite-dimensional feature space where the dynamic data correlations have linear behavior. Next, based on the approximated system’s Koopman operator, a virtual actuator is designed and implemented without knowing the system’s nominal controller. Needless to use a separate fault detection, isolation, and identification module to perform fault-tolerant control, the current method leverages the adaptive framework to keep the system’s desired performance in facing time-varying additive and loss of effectiveness actuator faults. Finally, the approach’s efficacy is demonstrated using simulation on a two-link manipulator benchmark, and a comparison study is presented.     

Distributed adaptive fault-tolerant formation control for heterogeneous multiagent systems under switching directed topologies

This paper studies the cooperative fault-tolerant formation control problem of tracking a dynamic leader for heterogeneous multiagent systems consisting of multipile unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) with actuator faults under switching directed interaction topologies. Based on local neighborhood formation information, the distributed fault-tolerant formation controllers are constructed to ensure that all follower UAVs and UGVs can accomplish the demanding formation configuration in the state space and track the dynamic leader’s trajectory. By incorporating the sliding mode control and adaptive control technique, the actuator faults and unknown parameters of follower agents can be compensated. Through the theoretical analysis, it is proved that the cooperatively semiglobally uniformly ultimately boundedness of the closed-loop system is guaranteed, and the formation tracking errors converge to a small adjustable neighborhood of the origin. A simulation example is introduced to show the validity of the proposed distributed fault-tolerant formation control algorithm.     

Distributed formation control of double-integrator fractional-order multi-agent systems with relative damping and nonuniform time-delays

In this paper, distributed formation control problems are studied for double-integrator fractional-order multi-agent systems (DIFOMASs) with relative damping and nonuniform time-delays. The required state deviations of a group of multi-agent systems are achieved through a local state information interaction, which means that this group of multi-agent systems achieves formation control. In the context of this paper, the dynamic model is first established and the formation control protocol is designed for distributed formation control of DIFOMASs with relative damping under symmetric time-delays and asymmetric time-delays. Then, some sufficient conditions for achieving distributed formation control of DIFOMASs are acquired with the help of graph theory, matrix theory, stability theory and frequency-domain theory. In the end, two simulation examples are performed to verify the efficacy of our proposed method.     

Specified-time bearing-based formation control of multi-agent systems via a dynamic gain approach

In this paper, the specified-time bearing-based formation control problem is investigated via a dynamic gain approach. Both the leader-follower and leaderless cases for single- and double-integral multi-agent systems are considered with bearing measurement, respectively. By considering the communication graph as bearing rigid, distributed bearing-based controllers with a time-varying gain are designed. By using time transformation method and Lyapunov stability theory, the close-loop systems under the proposed protocols can achieve the target formation within the specified time. Comparing with some existing results, the proposed approaches can make multi-agent systems converge to the desired formation within any preset time without dependence on the initial conditions or system parameters. Finally, some simulations and experiments are presented to demonstrate the effectiveness of the proposed algorithms.     

Distributed formation control for multiple quadrotor UAVs under Markovian switching topologies with partially unknown transition rates

This paper addresses distributed formation control for a group of quadrotor unmanned aerial vehicles (UAVs) under Markovian switching topologies with partially unknown transition rates. Instead of the general stochastic topology, the graph is governed by a set of Markov chains to the edges, which can recover the traditional Markovian switching topologies in line with the practical communication network. Extended high gain observers (EHGOs) are constructed with a two-time-scale format to deal with the issue of nonlinear input coefficients, so that there could be a higher estimation precision of the system uncertainties. To impel multiple quadrotor UAVs to achieve a predesigned formation shape, a modified integral sliding mode (ISM) control protocol is proposed here with a multi-time-scale structure, which allows independent analysis of the dynamics in each time scale. The stability proof for the system state space origin is derived from the singular perturbation method and Lyapunov stability theory. In addition, the introduced ISM controller can deal with the time varying desired references with the bounded accelerations and is robust to the disturbances. Finally, simulations on six quadrotor UAVs are given to verify the effectiveness of the theoretical results.     

Practical constrained output feedback formation control of underactuated vehicles via the autonomous dynamic logic guidance

This paper investigates the practical leader-follower formation control issue of underactuated vehicles. To achieve the waypoints-based formation navigation, the autonomous dynamic logic (ADL) guidance is proposed by incorporating the marine practice into the virtual ship-based formation guidance strategy. In the proposed guidance, only a dominant virtual leader is required for constructing the waypoints-based formation reference framework, which shows the simplicity and the practicability. As for the control part, a constrained output feedback algorithm is developed by means of the linear extended state observer (LESO). By constructing the augmented variable, the model uncertainty and unknown disturbances are integrated to be estimated and compensated together. In addition, a second-order dynamic auxiliary system is designed to handle the problem of actuator saturation, where two additional saturation compensation terms are introduced to stabilize the kinematics and the kinetics error dynamics, respectively, and the smoothness of constrained control signals can be guaranteed owing to the modification of Gaussian error function. Using the Lyapunov direct method, all signals in the closed-loop system are proved to be semi-global uniformly ultimately bounded (SGUUB). Finally, two simulation experiments, including the comparative experiment and the formation navigation experiment in the presence of simulated ocean disturbances, are carried out to illustrate the feasibility and the superiority of proposed scheme.     

Distributed fuzzy learning sliding mode cooperative control for non-affine nonlinear multi-missile guidance systems via a prescribed performance observer

This paper focuses on the distributed fuzzy learning sliding mode cooperative control issue for non-affine nonlinear multi-missile guidance systems. The dynamics of each follower is non-affine form with unknown lumped factor. To estimate the unknown lumped factor, a generalized fuzzy hyperbolic model (GFHM) based prescribed performance observer (PPO) is proposed. Different from the traditional disturbance observers, a residual set of error transient behavior is incorporated additionally so that the peak phenomenon can be avoided. Meanwhile, an auxiliary system is employed to convert the system of each follower to augmented affine form. Then, a distributed fuzzy learning sliding mode cooperative control approach is designed which consists of two parts. The adaptive sliding mode control (SMC) part is designed to force the states to move along the predefined integral sliding surface. For the equivalent sliding dynamics, the distributed optimal control part with GFHM is developed to minimize the cooperative performance function. Thus, the stability and the optimality of the closed-loop system are guaranteed synchronously. Finally, all signals of closed-loop system are rigorously proved bounded and the multi-missile cooperative guidance scenario is applied to verify the effectiveness of proposed method.     

Distributed fixed-Time secondary control for islanded microgrids: Tackling abnormal data

This paper deals with the distributed secondary control problem for multiple distributed generators in an islanded microgrid. A distributed fixed-time secondary controller is designed for each generator using only its neighbors’ information, where saturation functions are introduced to the designed controllers to constrain the adverse influence of abnormal data from neighbors. Several indicator variables are introduced to reformulate the saturation function to reduce conservatism. The objective of this paper is to realize the recovery of the frequency and voltage as well as the active power-sharing within a fixed time. The fixed-time convergence of the proposed distributed control algorithm is analyzed through rigorous analysis. Also, the upper bound of the settling time is derived, which does not depend on the system’s initial state. Finally, a simulation example is utilized to verify the effectiveness of the proposed distributed control scheme by using the MATLAB/SimPowerSystems toolbox.     

On novel trajectory tracking control of quadrotor UAV: A finite-time guaranteed performance approach

In this work, aiming at the trajectory tracking control of the quadrotor UAV subject to external disturbances and model uncertainties, a finite-time approach with preassigned performance guaranteed is proposed. First, the control system is decoupled into translational and rotational subsystems. Then, in both two subsystems, the performance bounds constructed by the newly established appointed-time performance functions are devised for guaranteeing the tracking performance, and the controllers are designed via applying the dynamic surface control technique with integral barrier Lyapunov functions involved. Moreover, finite-time tracking differentiators and finite-time multivariable disturbance observers are exploited to estimate the target signals and the lumped disturbances, respectively. Finally, two examples of simulation are carried out to validate the effectiveness and superiority of the proposed control method.     

Model-based deep reinforcement learning for data-driven motion control of an under-actuated unmanned surface vehicle: Path following and trajectory tracking

Unmanned surface vehicles (USVs) are a promising marine robotic platform for numerous potential applications in ocean space due to their small size, low cost, and high autonomy. Modelling and control of USVs is a challenging task due to their intrinsic nonlinearities, strong couplings, high uncertainty, under-actuation, and multiple constraints. Well designed motion controllers may not be effective when exposed in the complex and dynamic sea environment. The paper presents a fully data-driven learning-based motion control method for an USV based on model-based deep reinforcement learning. Specifically, we first train a data-driven prediction model based on a deep network for the USV by using recorded input and output data. Based on the learned prediction model, model predictive motion controllers are presented for achieving trajectory tracking and path following tasks. It is shown that after learning with random data collected from the USV, the proposed data-driven motion controller is able to follow trajectories or parameterized paths accurately with excellent sample efficiency. Simulation results are given to illustrate the proposed deep reinforcement learning scheme for fully data-driven motion control without any a priori model information of the USV.     

Direct transformation of dinitrogen: synthesis of N-containing organic compounds via N−C bond formation

N-containing organic compounds are of vital importance to lives. Practical synthesis of valuable N-containing organic compounds directly from dinitrogen (N₂), not through ammonia (NH₃), is a holy-grail in chemistry and chemical industry. An essential step for this transformation is the functionalization of the activated N₂ units/ligands to generate N−C bonds. Pioneering works of transition metal-mediated direct conversion of N₂ into organic compounds via N−C bond formation at metal-dinitrogen [N₂-M] complexes have generated diversified coordination modes and laid the foundation of understanding for the N−C bond formation mechanism. This review summarizes those major achievements and is organized by the coordination modes of the [N₂-M] complexes (end-on, side-on, end-on-side-on, etc.) that are involved in the N−C bond formation steps, and each part is arranged in terms of reaction types (N-alkylation, N-acylation, cycloaddition, insertion, etc.) between [N₂-M] complexes and carbon-based substrates. Additionally, earlier works on one-pot synthesis of organic compounds from N₂ via ill-defined intermediates are also briefed. Although almost all of the syntheses of N-containing organic compounds via direct transformation of N₂ so far in the literature are realized in homogeneous stoichiometric thermochemical reaction systems and are discussed here in detail, the sporadically reported syntheses involving photochemical, electrochemical, heterogeneous thermo-catalytic reactions, if any, are also mentioned. This review aims to provide readers with an in-depth understanding of the state-of-the-art and perspectives of future research particularly in direct catalytic and efficient conversion of N₂ into N-containing organic compounds under mild conditions, and to stimulate more research efforts to tackle this long-standing and grand scientific challenge.     

基于演化博弈的区域大气污染联防联控生态补偿机制分析——以京津冀地区为例

为促进建立有效的生态补偿机制为协调区域大气污染联防联控各方主体利益提供保障,依托演化博弈模型,通过分析影响区域联防联控策略的各利益参数的相互关系与作用,探讨中央政府与地方政府两大博弈主体的策略选择与演化方向,并以京津冀地区为例进行仿真验证,继而运用系统动力学模型模拟主要利益参数对博弈系统均衡结果的影响。结果表明,中央政府补偿政策的实施直接影响京津冀地方政府联防联控的执行决策,可通过有效分配补偿金额、减轻地方政府联防联控成本、提高监管效率以及加强地方政府执行政策不积极的惩罚力度等措施,促进地方政府采取大气污染联防联控策略以高效推进治理进程。     

Fixed-time nonlinear homogeneous sliding mode approach for robust tracking control of multirotor aircraft: Experimental validation

This paper presents a robust scheme for fixed-time tracking control of a multirotor system. The aircraft is subjected to matched lumped disturbances, i.e., unmodeled dynamics, parameters uncertainties, and external perturbations besides measurement noise. Firstly, a novel Nonlinear Homogeneous Continuous Terminal Sliding Manifold (NHCTSM) based on the weighted homogeneity theory is presented. The sliding manifold is designed with prescribed dynamics featuring Global Asymptotic Stability (GAS) and fixed-time convergence. Then, a novel Fixed-time Non-switching Homogeneous Nonsingular Terminal Sliding Mode Control (FNHNTSMC) is proposed for the position and attitude loops by employing the developed NHCTSM and an appropriate reaching law. Moreover, the control framework incorporates a disturbance observer to feedforward and compensate for the disturbances. The designed control scheme can drive the states of the system to the desired references in fixed-time irrespective of the values of the Initial Conditions (ICs). Since the existing works on homogeneous controllers rely on the bi-limit homogeneity concept in the convergence proofs, the estimate of the settling-time or its upper-bound cannot be given explicitly. In contrast, this study employs Lyapunov Quadratic Function (LQF) and Algebraic Lyapunov Equation (ALE) in the stability analysis of both controller and observer. Following this method, an expression of the upper-bound of the settling-time is explicitly derived. Furthermore, to assure the Uniform Ultimate Boundedness (UUB) of all signals in the feedback system, the dynamics of the observer and controller are jointly analyzed. Simulations and experiments are conducted to quantify the control performance. The proposed approach achieves superior performance compared with recent literature on fixed-time/finite-time control and a commercially available PID controller. The comparative results witness that the developed control scheme improves the convergence-time, accuracy, and robustness while overcoming the singularity issue and mitigating the chattering effect of conventional SMC.     

Leader-following consensus considering effects of agents on each other via impulsive control: A topology dependent average dwell time approach

This paper intends to investigate the consensus problem of a nonlinear multi-agent system with new nonlinear terms added to the dynamics of each agent in the leader-following framework with impulsive control. The main contribution of this paper is introducing these new terms expressing the effect of each agent on neighbor agents. The new terms called effect terms (ETs) are considered with time-varying delay. Moreover, the communication interactions among all agents are addressed by a set of consensusable and unconsensusable switching topologies. In particular, the topology-dependent average dwell time (TDADT), one of the significant practical analysis methods for switched systems, has been calculated for each topology. The globally uniformly exponentially stability (GUES) for the consensus error dynamics is analyzed by employing algebraic graph theory and a multiple discontinuous Lyapunov function approach (MDLF) regarding separate Lyapunov functions for impulse instants. Furthermore, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure that consensus can be achieved. Finally, the effectiveness of the theoretical analysis is corroborated by a numerical example.     

Lag quasi-synchronization of incommensurate fractional-order memristor-based neural networks with nonidentical characteristics via quantized control: A vector fractional Halanay inequality approach

This work realizes lag quasi-synchronization of incommensurate fractional-order memristor-based neural networks (FMNNs) with nonidentical characteristics via quantized control. The motivations behind this research work are threefold: (1) quantized controllers, which generate discrete control signals, can be more easily realized in computers than non-quantized controllers, and can consume smaller communication capacity; (2) incommensurate orders in a single FMNN and nonidentical characteristics in drive-response FMNNs are inescapable due to the differences among the circuit elements used to implement FMNNs; (3) convergence analysis of delayed incommensurate fractional-order nonlinear systems, which is the basis for the derivation of synchronization criterion, has not been handled perfectly. As an effective tool for convergence analysis of delayed incommensurate fractional-order nonlinear systems, especially for estimation of ultimate state bound, a vector fractional Halanay inequality is established at first. Then, a quantized synchronization controller, in which the dead-zone is introduced into some logarithmic quantizers to avoid chattering phenomenon, is designed. By means of vector Lyapunov function together with the newly derived vector fractional Halanay inequality, the synchronization criterion is proved theoretically. Lastly, numerical simulations supplementarily illustrate the correctness of the synchronization criterion. In contrast with the hypotheses in the relevant literature, the hypotheses in this paper are weaker.