Optimal UAV Formation Tracking Control with Dynamic Leading Velocity and Network-Induced Delays

With the rapid development of UAV technology, the research of optimal UAV formation tracking has been extensively studied. However, the high maneuverability and dynamic network topology of UAVs make formation tracking control much more difficult. In this paper, considering the highly dynamic features of uncertain time-varying leader velocity and network-induced delays, the optimal formation control algorithms for both near-equilibrium and general dynamic control cases are developed. First, the discrete-time error dynamics of UAV leader–follower models are analyzed. Next, a linear quadratic optimization problem is formulated with the objective of minimizing the errors between the desired and actual states consisting of velocity and position information of the follower. The optimal formation tracking problem of near-equilibrium cases is addressed by using a backward recursion method, and then the results are further extended to the general dynamic case where the leader moves at an uncertain time-varying velocity. Additionally, angle deviations are investigated, and it is proved that the similar state dynamics to the general case can be derived and the principle of control strategy design can be maintained. By using actual real-world data, numerical experiments verify the effectiveness of the proposed optimal UAV formation-tracking algorithm in both near-equilibrium and dynamic control cases in the presence of network-induced delays.     

Leader-following formation control of multi-agent networks based on distributed observers

To investigate the leader-following formation control, in this paper we present the design problem of control protocols and distributed observers under which the agents can achieve and maintain the desired formation from any initial states, while the velocity converges to that of the virtual leader whose velocity cannot be measured by agents in real time. The two cases of switching topologies without communication delay and fixed topology with time-varying communication delay are both considered for multi-agent networks. By using the Lyapunov stability theory, the issue of stability is analysed for multi-agent systems with switching topologies. Then, by considering the time-varying communication delay, the sufficient condition is proposed for the multi-agent systems with fixed topology. Finally, two numerical examples are given to illustrate the effectiveness of the proposed leader-following formation control protocols.     

Distance-based formation tracking control of multi-agent systems with double-integrator dynamics

This paper addresses the distance-based formation tracking problem for a double-integrator modeled multi-agent system(MAS) in the presence of a moving leader in d-dimensional space. Under the assumption that the state of leader can be obtained over fixed graphs, a distributed distance-based control protocol is designed for each double-integrator follower agent. The protocol consists of three terms: a gradient function term, a velocity consensus term, and a leader tracking term.Different shape stabilizing functions proposed in the literature can be applied to the gradient function term. The proposed controller allows all agents to both achieve the desired shape and reach the same velocity with moving leader by controlling the distances and velocity. Finally, we analyze the local asymptotic stability of the equilibrium set with center manifold theory. We validate the effectiveness of our approach through two examples.     

Tracking Consensus for Second-Order Multi-Agent Systems with Nonlinear Dynamics in Noisy Environments

This paper investigates the leader-following tracking consensus problem for second-order multi-agent systems with time delays and nonlinear dynamics in noisy environments on the conditions of fixed and switching directed topologies. Based on a novel velocity decomposition technique and stochastic analysis, a measurement-based distributed tracking control protocol is proposed, under which all agents can track the leader in mean square. Simulation results are also given to illustrate the effectiveness of the proposed protocol.     

Distributed formation control for a multi-agent system with dynamic and static obstacle avoidances

Formation control and obstacle avoidance for multi-agent systems have attracted more and more attention. In this paper, the problems of formation control and obstacle avoidance are investigated by means of a consensus algorithm. A novel distributed control model is proposed for the multi-agent system to form the anticipated formation as well as achieve obstacle avoidance. Based on the consensus algorithm, a distributed control function consisting of three terms(formation control term, velocity matching term, and obstacle avoidance term) is presented. By establishing a novel formation control matrix, a formation control term is constructed such that the agents can converge to consensus and reach the anticipated formation. A new obstacle avoidance function is developed by using the modified potential field approach to make sure that obstacle avoidance can be achieved whether the obstacle is in a dynamic state or a stationary state. A velocity matching term is also put forward to guarantee that the velocities of all agents converge to the same value. Furthermore, stability of the control model is proven. Simulation results are provided to demonstrate the effectiveness of the proposed control.     

Tracking consensus for nonlinear heterogeneous multi-agent systems subject to unknown disturbances via sliding mode control

We investigate the tracking control for a class of nonlinear heterogeneous leader-follower multi-agent systems(MAS)with unknown external disturbances. Firstly, the neighbor-based distributed finite-time observers are proposed for the followers to estimate the position and velocity of the leader. Then, two novel distributed adaptive control laws are designed by means of linear sliding mode(LSM) as well as nonsingular terminal sliding mode(NTSM), respectively. One can prove that the tracking consensus can be achieved asymptotically under LSM and the tracking error can converge to a quite small neighborhood of the origin in finite time by NTSM in spite of uncertainties and disturbances. Finally, a simulation example is given to verify the effectiveness of the obtained theoretical results.     

Flocking in Multi-Agent Systems with Multiple Virtual Leaders Based Only on Position Measurements

Most existing flocking algorithms assume one single virtual leader and rely on information on both relative positions and relative velocities among neighboring agents. In this paper, the problem of controlling a flock of mobile autonomous agents to follow multiple virtual leaders is investigated by using only position information in the sense that agents with the same virtual leader asymptotically attain the same velocity and track the corresponding virtual leader based on only position measurements. A flocking algorithm is proposed under which every agent asymptotically attains its desired velocity, collision between agents can be avoided, and the final tight formation minimizes all agents' global potentials. A simulation example is presented to verify and illustrate the theoretical results.     

Time-varying formation for general linear multi-agent systems via distributed event-triggered control under switching topologies

This paper investigates the time-varying formation problem for general linear multi-agent systems using distributed event-triggered control strategy.Different from the previous works,to achieve the desired time-varying formation,a distributed control scheme is designed in an event-triggered way,in which for each agent the controller is triggered only at its own event times.The interaction topology among agents is assumed to be switching.The common Lyapunov function as well as Riccati inequality is applied to solve the time-varying formation problem.Moreover,the Zeno behavior of triggering time sequences can be excluded for each agent.Finally,a simulation example is presented to illustrate the effectiveness of the theoretical results.     

Design of exponential state estimators for neural networks with mixed time delays

In this Letter, the state estimation problem is dealt with for a class of recurrent neural networks (RNNs) with mixed discrete and distributed delays. The activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. We aim at designing a state estimator to estimate the neuron states, through available output measurements, such that the dynamics of the estimation error is globally exponentially stable in the presence of mixed time delays. By using the Laypunov–Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions to guarantee the existence of the state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.     

Output regulation for linear multi-agent systems with unmeasurable nodes

The output regulation of linear multi-agent systems with partial unmeasurable agents is investigated in this paper. All the agents except the exosystem can be classified into two groups. Agents in the first group can be measured by themselves and their neighbors. State variables are not fully accessible for direct communication and full order Luenberger observers are constructed for the unmeasurable agents. We give a state feedback control law to solve the output regulation problem under the communication topologies based on both measurable and unmeasurable agents. The heterogeneous agents’ synchronization problem is a general case of our results. Finally, examples are utilized to show the effectiveness of the obtained results.     

一种线性速度估计器在光电跟踪系统伺服控制中的应用

高性能的伺服控制除了需要高质量的控制器,还需要高质量的反馈信息。对于光电跟踪系统,通过位置和电流传感器可以提供位置和电流信息,而速度信息则需要通过处理测量信息得到。传统的差分方法会放大位置信息中的量化噪声,从而降低光电跟踪系统的精度。介绍了全维状态观测器及其基本原理,结合伺服控制系统电机模型架构,设计了一种线性速度估计器,并讨论了其参数选择问题。采用抗积分饱和PI控制器和积分分离PI控制器作为三环控制回路的控制器,在某型号光电跟踪系统对该算法进行了实验。实验结果证明,采用该算法的伺服控制系统基本无超调,上升时间0．43s,稳定时间0．65s,跟踪精度为1．78″,完全满足实际工程要求。     

Finite-time consensus of second-order leader-following multi-agent systems without velocity measurements

This Letter investigates the finite-time consensus problems of second-order multi-agent systems in the presence of one and multiple leaders under a directed graph. Specifically, we propose two bounded control laws, which are independent of velocity information, to deal with the finite-time consensus tracking problem with one leader and the finite-time containment control problem with multiple leaders, respectively. With the aid of homogeneous theory, some sufficient conditions are established for the achievement of the finite-time tracking control problem of second-order multi-agent systems. Numerical examples are finally provided to illustrate the theoretical results.     

Antagonistic formation motion of cooperative agents

This paper investigates a new formation motion problem of a class of first-order multi-agent systems with antagonistic interactions.A distributed formation control algorithm is proposed for each agent to realize the antagonistic formation motion.A sufficient condition is derived to ensure that all of the agents make an antagonistic formation motion in a distributed manner.It is shown that all of the agents can be spontaneously divided into several groups and that agents in the same group collaborate while agents in different groups compete.Finally,a numerical simulation is included to demonstrate our theoretical results.     

智能群体环绕运动控制

自然界中,鸟类迁徙、鱼类群游等群体智能运动具有一定的规律.例如,鸟类迁徙以领导者和跟随者模式的直线运动为主,鱼类中以环绕运动为主.自然界的这种群体直线运动与环绕运动具有十分重要的理论研究价值和广泛的工程应用前景.本文针对群体环绕运动进行研究,考虑个体只能获取局部目标信息这一特性,设计均值估计器进行群体目标状态估计,建立环绕运动算法,确保实现群体圆形编队且保持队形.通过李雅普诺夫理论分析,证明每个个体在有限时间内能获取所有目标平均位置信息,且能基于群体圆形编队队形进行目标环绕和追踪,队形随目标状态变化.有关结果通过仿真得到进一步验证.     

Collective composite-rotating consensus of multi-agent systems

This paper investigates a distributed composite-rotating consensus problem of second-order multi-agent systems, where all agents move in a nested circular orbit. A distributed control law is proposed which contains two parts： the local state feedback that guarantees the circular motion and the distributed relative state feedback that guarantees the consensus of all agents. A sufficient condition is derived to drive all agents as well as ensure their circle centers make circular motion in a distributed manner. Finally, a numerical simulation is included to demonstrate our theoretical results.     

随机系统的概率密度函数形状调节

针对受高斯白噪声激励的非线性随机系统,提出了使状态响应的概率密度函数形状跟踪期望形状的调节方法.首先,确立了非线性随机系统的多项式反馈机制,同时对系统中的非线性部分进行多项式展开;然后,以Fokker-Planck-Kolmogorov方程为工具,导出了与控制增益相关的各阶矩递推方程,并根据跟踪问题的要求,构造了矩逼近优化问题,用梯度搜索法求解该优化问题,获得了调节函数;再依据特征函数与概率密度函数构成Fourier对的关系,对状态响应的概率密度函数进行重构;最后,通过两个例子仿真,验证了本文方法的有效性.     

光电跟踪系统计算机辅助控制实现

建立了基于数值微分的目标运动状态滤波预测模型,用s-函数实现了卡尔曼滤波预测算法。利用目标位置拟合方法给出角位置信息,并以此为观测信息通过卡尔曼滤波预测出当前角位置和角速度信息,将其引入跟踪控制系统中以克服脱靶量滞后问题,同时也实现了系统的等效复合控制。仿真结果表明,基于数值微分的模型适用于角度跟踪,滤波预测具有较好的鲁棒性。通过对两个不同等效正弦输入的验证,可知角位置合成精度对共轴跟踪影响较大,在脱靶量和跟踪架角位置采样匹配对应时,跟踪仿真精度较高,而对等效复合控制跟踪误差影响较小,输入信号角频率增大时误差增大。     

基于Huber的高阶容积卡尔曼跟踪算法

为改善高阶容积卡尔曼滤波算法的滤波精度和鲁棒性, 提出了一种新的基于Huber的高阶容积卡尔曼滤波算法. 在采用统计线性回归模型近似非线性量测模型的基础上, 利用Huber M 估计算法实现状态的量测更新. 进一步结合高阶球面-径向容积准则的状态预测模块构成基于 Huber的高阶容积卡尔曼跟踪算法. 重点分析了Huber代价函数的调节因子对算法跟踪性能的影响. 通过对纯方位目标跟踪和再入飞行器跟踪两个实例验证了所提算法的跟踪性能优于传统高阶容积卡尔曼滤波算法.     

Inverse estimation of the pulse parameters of a time-varying laser pulse to obtain desired temperature at the material surface

A proper selection of the pulse parameters is essential to achieve desired temperature at the material surface. This leads to obtain the required metallurgical changes in the surface vicinity when a time-varying laser pulse is used in a heating process such as surface modification. In this paper, the conjugate gradient method (CGM) for parameter estimation is successfully applied to estimate the unknown laser pulse parameters for those purposes during laser heating process. The determination of the pulse parameters is treated as a one-dimensional, transient, non-linear inverse heat conduction problem (IHCP). Based on a sensitivity analysis, the inverse problem is solved as an optimization problem comparing a desired temperature at the surface and a calculated one where the objective function is minimized by CGM. The method has been applied to a test case of a heating process on steel, appropriate pulse parameters and desired temperature distribution can also be returned.     

Tracking problem under a time-varying topology

This paper studies the multi-agent tracking problem of a third-order maneuvering target under uncertain communication environments. Each tracking agent is assumed to be a third-order system and can only use its own and neighbors＇ position, velocity, and acceleration information to design its control input. In this work, the uncertain communication environments are modelled by a finite number of constant Laplacian matrices together with their corresponding scheduling functions. Sufficient conditions for the existence of a tracking strategy have been expressed in terms of the solvability of linear matrix inequalities. Finally, a numerical example is employed to demonstrate the effectiveness of the proposed tracking strategy.