Backstepping in Infinite Dimension for a Class of Parabolic Distributed Parameter Systems

 In this paper a family of stabilizing boundary feedback control laws for a class of linear parabolic PDEs motivated by engineering applications is presented. The design procedure presented here can handle systems with an arbitrary finite number of open-loop unstable eigenvalues and is not restricted to a particular type of boundary actuation. Stabilization is achieved through the design of coordinate transformations that have the form of recursive relationships. The fundamental difficulty of such transformations is that the recursion has an infinite number of iterations. The problem of feedback gains growing unbounded as the grid becomes infinitely fine is resolved by a proper choice of the target system to which the original system is transformed. We show how to design coordinate transformations such that they are sufficiently regular (not continuous but L _∞). We then establish closed-loop stability, regularity of control, and regularity of solutions of the PDE. The result is accompanied by a simulation study for a linearization of a tubular chemical reactor around an unstable steady state. Date received: June 22, 2001. Date revised: January 17, 2002. RID="*" ID="*"This work was supported by grants from AFOSR, ONR, and NSF.     

Distributed formation control of fractional-order multi-agent systems with absolute damping and communication delay

The distributed formation control of fractional-order multi-agent systems is mainly studied under directed interaction topology in this paper. First, the control algorithm with absolute damping and communication delay is proposed to achieve the formation control. Then, some sufficient conditions are derived by using the matrix theory, graph theory and the frequency-domain analysis method. Finally, based on the numerical method of predictor–corrector, several simulations are presented to illustrate the effectiveness of the obtained results.     

Distributed adaptive control for time-varying formation of general linear multi-agent systems

An adaptive gain scheduling technique is investigated to discuss distributed time-varying formation (TVF) control problems for general linear time-invariant multi-agent systems (LTI-MASs), where two types of topologies are considered: (1) the interaction topology is undirected and connected, and (2) the interaction topology is directed. Two fully distributed adaptive TVF control protocols are, respectively proposed, which both assign a time-varying coupling weight to each node in the interaction topology. Two algorithms to design the constructed protocols are presented under the undirected and directed interaction topologies, respectively. A feasible TVF set is provided. The stabilities of two algorithms are, respectively proved based on the Lyapunov functional theory. For both undirected and directed interaction topologies, general LTI-MASs can achieve the given TVF using the designed fully distributed adaptive formation protocol without any global information about the interaction topology when the TVF satisfies the feasible set. Finally, theoretical results are illustrated with numerical simulation examples.     

Finite-time formation control for multi-agent systems

In this paper, we develop a new finite-time formation control framework for multi-agent systems with a large population of members. In this framework, we divide the formation information into two independent parts, namely, the global information and the local information. The global formation information decides the geometric pattern of the desired formation. Furthermore, it is assumed that only a small number of agents, which are responsible for the navigation of the whole team, can obtain the global formation information, and the other agents regulate their positions by the local information in a distributed manner. This approach can greatly reduce the data exchange and can easily realize various kinds of complex formations. As a theoretical preparation, we first propose a class of nonlinear consensus protocols, which ensures that the related states of all agents will reach an agreement in a finite time under suitable conditions. And then we apply these consensus protocols to the formation control, including time-invariant formation, time-varying formation and trajectory tracking, respectively. It is shown that all agents will maintain the expected formation in a finite time. Finally, several simulations are worked out to illustrate the effectiveness of our theoretical results.     

具有时变时滞耦合的二阶多主体系统的编队控制

多主体系统的编队控制是一类重要的网络协同控制问题.研究了在有向连接拓扑结构下,具有时变时滞耦合的二阶多主体系统的编队控制问题.通过一种多层领导机制的框架建模,得到了时不变编队、时变编队和时变轨迹追踪3种编队问题的充分性条件,并证明了各种预期队列是以指数的收敛速度形成的.数值仿真进一步验证了理论结果的正确性,为该理论在实际中应用起到指导作用.     

Finite-time optimal formation control of multi-agent systems on the Lie group SE(3)

This paper investigates the finite-time optimal formation problem of multi-agent systems on the Lie group SE(3), for the situation when the formation time and/or the cost function need to be considered. Under the condition that the formation time is given according to the task requirement, a finite-time optimal formation controller is proposed for the two-agent case to guarantee that the desired formation is achieved at the given time and the corresponding cost function is optimal. For the systems with multiple agents, the obtained finite-time optimal formation control law has second-order approximation accuracy. Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results.     

Time-varying formation control for double-integrator multi-agent systems with jointly connected topologies

Time-varying formation analysis and design problems for double-integrator multi-agent systems with jointly connected topologies are investigated. Different from the previous work on formation control, in this paper, the formation is specified by time-varying piecewise continuously differentiable vectors and the topology can be disconnected at any time instant. First, a distributed formation control protocol is constructed using local neighbour-to-neighbour information. In the case where the switching topology is jointly connected, necessary and sufficient conditions for double-integrator multi-agent systems to achieve time-varying formations are proposed, where the formation feasibility constraint is also derived. To describe the macroscopic movement of the whole formation, explicit expressions of the formation reference are presented, the motion modes of which can be partially assigned. Moreover, an approach to design the formation control protocol is given, which is fully distributed and requires no global information about the topology. Finally, the obtained theoretical results are applied to deal with the time-varying formation control problems of multi-vehicle systems.     

Bearing-based formation manoeuvre control of nonholonomic multi-agent systems

ABSTRACT

This paper concerns on the bearing-based leader–follower formation manoeuvre control problem for two- (2D) and three-dimensional (3D) multi-agent systems with nonholonomic constraint. The target formation is defined by relative-bearing measurements, which, for example, can be obtained from onboard cameras. The contributions of this paper are twofold. Firstly, a distributed formation manoeuvre control law is proposed for 2D nonholonomic agents according to the inter-bearing measurement. The multi-agent systems can achieve the desired formation which is defined by the bearings information. The formation manoeuvre can be achieved by steering at least two leaders. Secondly, the control law is nontrivially extended to 3D nonholonomic multi-agents systems. The leader–follower formation tracking problem can also be solved by the proposed proportional-integral control scheme. Simulation results for 2D and 3D nonholonomic multi-agents systems are presented. Experiments that used ground mobile robots verify the effectiveness of the proposed control laws.     

A new formation control of multiple underactuated surface vessels

This work investigates a new formation control problem of multiple underactuated surface vessels. The controller design is based on input-output linearisation technique, graph theory, consensus idea and some nonlinear tools. The proposed smooth time-varying distributed control law guarantees that the multiple underactuated surface vessels globally exponentially converge to some desired geometric shape, which is especially centred at the initial average position of vessels. Furthermore, the stability analysis of zero dynamics proves that the orientations of vessels tend to some constants that are dependent on the initial values of vessels, and the velocities and control inputs of the vessels decay to zero. All the results are obtained under the communication scenarios of static directed balanced graph with a spanning tree. Effectiveness of the proposed distributed control scheme is demonstrated using a simulation example.     

Adaptive dynamic surface control for linear multivariable systems

In this paper, an output-feedback adaptive control is presented for linear time-invariant multivariable plants. By using the dynamic surface control technique, it is shown that the explosion of complexity problem in multivariable backstepping design can be eliminated. The proposed scheme has the following features: (1) The L_∞ performance of the system’s tracking error can be guaranteed, (2) it has least number of updated parameters in comparison with other multivariable adaptive schemes, and (3) the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.     

Asynchronous decentralised event-triggered control of multi-agent systems

In this paper, the consensus problem of first-order multi-agent systems under linear asynchronous decentralised event-triggered control is investigated. Both undirected and directed topologies are considered. In the analysis, the closed-loop multi-agent systems with the event-triggered control are modelled as switched systems. After proposing the decentralised event-triggered consensus protocols, decentralised state-dependent event conditions are derived, which act as switching signals. The consensus analyses are performed based on graph theory and stability results of switched systems. Under the event-triggered control schemes presented, consensus is reached with enlarged sampling periods and no Zeno behaviour. Simulation examples are given to illustrate the effectiveness of the proposed theoretical results.     

多智能体网络系统的自适应协调控制

为实现多智能体网络系统的协调控制,设计了一种新型的带有自适应协调器的控制器.基于动态图建立了多智能体网络系统的模型,并考虑了系统的非线性互联和不可避免存在的时变时滞.应用分布式控制策略,设计了自适应参数估计的协调器,用于调节智能体之间的互联强度,使网络达到稳定的预设水平.并基于Lyapunov-Kra-sovskii泛函和自适应动态偏差反馈控制技术,根据拉萨尔不变集原理证明了偏差控制系统的渐近收敛性.这种控制方法,可在系统参数不确定的情况下,同时完成参数估计和协调控制.所设计的控制律和自适应律简单,易于实现,仿真示例验证了所提方法的有效性.     

Fault tolerant cooperative control for a class of nonlinear multi-agent systems

This paper studies the target aggregation problem for a class of nonlinear multi-agent systems with the time varying interconnection topology. The general neighboring rule-based linear cooperative protocol is developed and a sufficient aggregation condition is derived. Moreover, it is shown that in the presence of agent faults, the target point is still reached by adjusting some weights of the cooperative protocol without changing the structure of the topology. An unmanned aerial vehicle team example illustrates the efficiency of the proposed approach.     

Sliding mode control for multi-agent systems under a time-varying topology

This paper addresses the tracking problem of a class of multi-agent systems under uncertain communication environments which has been modelled by a finite number of constant Laplacian matrices together with their corresponding scheduling functions. Sliding mode control method is applied to solve this nonlinear tracking problem under a time-varying topology. The controller of each tracking agent has been designed by using only its own and neighbours’ information. Sufficient conditions for the existence of a sliding mode control tracking strategy have been provided by the solvability of linear matrix inequalities. At the end of this work, numerical simulations are employed to demonstrate the effectiveness of the proposed sliding mode control tracking strategy.     

Containment control of switched multi-agent systems

In this paper, we consider the containment control problem for the switched multi-agent system which is composed of continuous-time and discrete-time subsystems. Continuous-time protocol based on the relative state measurements of agents are designed for the switched multi-agent system with multiple stationary and dynamic leaders, respectively. By using graph theory and matrix theory, some necessary and sufficient conditions are obtained for solving the containment control problem under arbitrary switching. When the leaders are dynamic, impulsive protocol are also proposed for the switched multi-agent system. The simulation results are given to verify the effectiveness of the theoretical results.     

Adaptive containment control of nonlinear multi-agent systems with non-identical agents

This paper addresses the containment control problem for a group of non-identical agents, where the dynamics of agents are supposed to be nonlinear with unknown parameters and parameterised by some functions. In controller design approach for each follower, adaptive control and Lyapunov theory are utilised as the main control strategies to guarantee the convergence of all non-identical followers to the dynamic convex hull formed by the leaders. The design of distributed adaptive controllers is based on the exchange of neighbourhood errors among the agents. For analysis of containment control problem, a new formulation has been developed using M-matrices. The validity of theoretical results are demonstrated through an example.     

基于多Agent的微电网电压无功控制系统

将多Agent技术引入微电网的电压无功控制中,并给出了基于多Agent的三级电压无功控制系统结构,重点分析了微网级(二级)电压无功控制。受电气距离思想的启发,提出了以操作优劣距离最短来确定最优操作动作的控制策略。以IEEE—39系统为基础的仿真说明了多Agent电压无功控制对微电网系统的电压无功能起到良好的调节控制作用。     

Practical time-varying formation tracking for high-order nonlinear multi-agent systems based on the distributed extended state observer

Practical time-varying formation tracking analysis and design problems for high-order nonlinear multi-agent systems are investigated, where the time-varying formation tracking error is controlled within an arbitrarily small bound. The states of followers form a predefined time-varying formation while tracking the state of the leader with unknown control input. Besides, the dynamics of each agent has heterogeneous nonlinearity and disturbance. First, a distributed extended state observer is constructed to estimate the follower's nonlinearity and disturbance, and the leader's unknown control input simultaneously. A protocol based on the distributed extended state observer is proposed. Second, sufficient conditions for the multi-agent systems to achieve the practical time-varying formation tracking under the protocol are presented by using the Lyapunov stability theory. Third, an approach is derived to design the proposed protocol by solving a linear matrix inequality. Finally, numerical simulation results are given to illustrate the effectiveness of the theoretical results.     

Connections between H 2 optimal filters and unknown input observers – performance limitations of H 2 optimal filtering

For linear time invariant continuous-time systems with either unknown or white noise input, two well-known filtering problems are considered. These are the unknown input observer problem and the Kalman filtering problem. Most of the available literature on Kalman filtering considers the so-called regular filtering problem. We consider here the general singular filtering problem. We show that such a Kalman filtering problem for a given system can be transformed to the unknown input observer problem for an auxiliary system constructed from the data of the given system. Such transformations between these two filtering problems enable us to study various properties of Kalman filtering, including existence and uniqueness of Kalman filters, computation of performance indices of Kalman filtering, and performance limitations of Kalman filtering as related to the structural properties of the given system.     

Intermittent observer-based consensus control for multi-agent systems with switching topologies

In this paper, we focus on the consensus problem for leaderless and leader–followers multi-agent systems with periodically intermittent control. The dynamics of each agent in the system is a linear system, and the interconnection topology among the agents is assumed to be switching. We assume that each agent can only share the outputs with its neighbours. Therefore, a class of distributed intermittent observer-based consensus protocols are proposed for each agent. First, in order to solve this problem, a parameter-dependent common Lyapunov function is constructed. Using this function, we prove that all agents can access a prescribed value, under the designed intermittent controller and observer, if there are suitable conditions on communication. Second, based on the investigation of the leader-following consensus problem, we design a new distributed intermittent observer-based protocol for each following agent. Finally, we provide an illustrative example to verify the effectiveness of the proposed approach.