事件触发控制下二阶多智能体的量化一致性

针对多智能体系统网络通信过程中信息需要量化的情况,研究了二阶多智能体系统在事件触发控制下的量化一致性。基于事件触发控制策略,提出一致性协议,并采用对数量化器对控制输入进行量化处理。利用Lyapunov稳定性理论,对系统进行一致性分析,得到了多智能体系统渐近趋于一致的充分条件。仿真结果说明了理论分析的有效性。     

基于事件触发控制的二阶多智能体的一致性

研究二阶多智能体系统在固定有向拓扑下的一致性问题。为减少不必要的网络带宽资源的浪费,给出一种基于事件触发控制的一致性算法。该算法基于状态误差对系统中的所有个体建立事件触发函数,使得个体之间的信息通讯和控制信号更新仅在事件触发时刻进行。采用矩阵理论和模型变换思想对系统进行了分析和转化,并利用Lyapunov理论给出了系统达到渐近一致的充分条件。仿真结果验证了理论方案的有效性。     

Robust consensus tracking of second-order nonlinear systems using relative position information by K-filter and disturbance observer based control

This work considers the problem of distributed consensus tracking control of second-order uncertain nonlinear systems under a directed communication graph which contains a spanning tree, where the leader node is the root. It is assumed that the followers receive only the relative positions from the neighbours. For the purpose of consensus tracking controller design, in each follower, a group of K-filters is introduced so that the necessity of velocity estimating is avoided. Then we can express each follower's tracking error dynamics as a second-order system with mismatched uncertainties. And hence we can design a robust consensus tracking controller for each follower by using the combination of the backstepping design and the disturbance observer based control using only relative position information. Theoretical analysis is performed to show that the DOBs' estimation errors can be made to decay to be sufficiently small very quickly before the system states escape from the feasible region. Then we show that all the followers' states track those of the leader with arbitrarily small ultimate error bounds. And simulation examples are provided to demonstrate the performance of the proposed method.     

Global consensus of second-order unknown multi-agent systems: A distributed fuzzy iterative learning scheme

This article focuses on global fuzzy consensus control of unknown second-order nonlinear multi-agent systems based on adaptive iterative learning scheme. In order to achieve global consensus, a replacement idea is introduced, where fuzzy systems are used as feedforward compensators to model unknown nonlinear dynamics relying on tracking signals. Considering that the network communication is distributed, a kind of hybrid control protocol is designed to avoid the complete dependence on the tracking signals. In addition, considering the complexity of the external environment, this article extends the above distributed protocol to the case of unknown control directions to study global consensus. Finally, the feasibility of the proposed protocols is verified by Matlab numerical simulations.     

Distributed adaptive consensus control of Lipschitz nonlinear multi-agent systems using output feedback

This paper addresses output-feedback-based distributed adaptive consensus control of multi-agent systems having Lipschitz nonlinear dynamics. Distributed dynamic protocols are designed based on the relative outputs of neighbouring agents and the adaptive coupling weights, under which consensus is reached between the nonlinear systems for all undirected connected communication topologies. Extension to the case of Lipschitz nonlinear multi-agent systems subjected to external disturbances is further studied, and a robust adaptive fully distributed consensus protocol is suggested. By application of a decoupling technique, necessary and sufficient conditions for the existence of these consensus protocols are provided in terms of linear matrix inequalities. Finally, numerical simulation results are demonstrated to validate the effectiveness of the theoretical results.     

Leader-following consensus for uncertain second-order nonlinear multi-agent systems

This paper studies the leader-following consensus problem for a class of second-order nonlinear multi-agent systems subject to linearly parameterized uncertainty and disturbance. The problem is solved by integrating the adaptive control technique and the adaptive distributed observer method. The design procedure is illustrated by an example with a group of Van der Pol oscillators as the followers and a harmonic system as the leader.     

Robust model predictive control with guaranteed setpoint tracking

In this paper a novel robust model predictive control (RMPC) algorithm is proposed, which is guaranteed to stabilize any linear time-varying system in a given convex uncertainty region while respecting state and input constraints. Moreover, unlike most existing RMPC algorithms, the proposed algorithm is guaranteed to remove steady-state offset in the controlled variables for setpoints (possibly) different from the origin when the system is unknown linear time-invariant. The controller uses a dual-mode paradigm (linear control law plus free control moves to reach an appropriate invariant region), and the key step is the design of a robust linear state feedback controller with integral action and the construction of an appropriate polyhedral invariant region in which this controller is guaranteed to satisfy the process constraints. The proposed algorithm is efficient since the on-line implementation only requires one to solve a convex quadratic program with a number of decision variables that scale linearly with the control horizon. The main features of the new control algorithm are illustrated through an example of the temperature control of an open-loop unstable continuous stirred tank reactor.     

Consensus of second-order multi-agent systems via impulsive control using sampled hetero-information

In this paper, the consensus problem for second-order multi-agent systems using impulsive control with sampled hetero-information is investigated. Necessary and sufficient conditions for sampling interval to achieve consensus for the second-order multi-agent systems are obtained. Analysis for the upper bound of sampling interval, convergence performance, and communication cost of the proposed control protocols are also discussed. Some numerical examples are given to demonstrate the effectiveness of the proposed control protocols.     

具有通信时延的二阶多智能体系统有限时间一致性跟踪控制

针对具有通信时延的二阶多智能体系统的有限时间一致性控制问题,分别研究了具有固定拓扑和切换拓扑网络结构情形下的二阶多智能体系统的有限时间一致性。为使多智能体系统能在有限时间内可以达到一致,引入一致性控制增益矩阵并设计了相应的基于相对位置和相对速度的时延状态误差有限时间一致性控制算法,利用系统模型转换,泛函微分方程稳定性理论和有限时间Lyapunov稳定性定理得到了使系统在有限时间内达到一致跟踪的最大时延上界值。最后,仿真实验结果验证了所得理论的正确性和有效性。     

Leader-following consensus control of second-order nonlinear multi-agent systems with applications to slew rate control

This paper addresses the distributed leader-following consensus control of second-order strict-feedback nonlinear multi-agent systems. By employing mean value theorem, variable separation technique, and backstepping methodology, a fully distributed adaptive control law is designed using only local relative state information. The proposed control law solves the leader-following consensus problem for any directed communication graph that contains a spanning tree with the root node being the leader agent. The application to hovercraft slew rate control system is given to verify the effectiveness of the theoretical results.     

On the estimation of the consensus rate of convergence in graphs with persistent interconnections

The aim of the current article is to establish myriad convergence rate estimates to consensus for time-varying graphs with persistent interaction. Several novel analysis methodologies for consensus protocols employing the notions of persistence of excitation and Lyapunov functions are provided. The estimates are compared with each other and existing literature. Numerical simulations on test examples are illustrated to support the theoretical findings.     

不确定非线性系统的鲁棒耗散性与保性能控制

考虑了不确定仿射非线性系统的鲁棒耗散性与保性能控制问题,不确定性范数有界,不满足匹配条件.基于HJI不等式,设计了状态反馈控制器.当扰动存在时,控制器能使系统达到耗散,当扰动为零时,所设计的控制器使系统对于给定的性能函数具有上界,最后研究了不确定线性系统的保性能与耗散性控制情形.     

Optimisation and adaptation of synchronisation controllers for networked second-order infinite-dimensional systems

ABSTRACT

The adaptation and optimisation of synchronisation control for networked second-order distributed parameter systems are considered. The objective is to design output feedback controllers guaranteeing agreement between the states of the N systems that individually track a reference model. The controller structure involves feedback terms consisting of the pairwise difference of the measurements of the second-order systems as well as coupling terms that enforce consensus. Placing the closed-loop networked systems in aggregate form allows for further optimisation of the synchronisation gains. Using the aggregate systems ‘closed-loop energy’ as a suitable optimisation measure, the search for the synchronisation gains reduces to the minimisation of the optimisation index, which eventually is described by the trace of the solution to a parameterised Lyapunov operator equation. Considering the adaptation of the synchronisation gains offers an alternative to optimisation. The adaptation is based on Lyapunov redesign-methods and utilises a parameter-dependent Lyapunov functional to extract them. Due to its structure, all network topology information is handled at the local level, thereby relaxing the graph topology conditions in the adaptive case. Numerical studies are included to provide an insight on the effects of synchronisation control of networked second-order distributed parameter systems.     

Group consensus tracking of second-order nonlinear multi-agent systems with time-varying reference velocities

This paper investigates group consensus tracking problems with time-varying reference velocities. The multiple agents are described as second-order nonlinear dynamics in directed information exchange settings. For the multi-agent networks formed by finite agent groups, novel distributed protocols with/without time-varying transmission delays are designed to solve the group consensus tracking problems. The problems are first transformed into the asymptotical stability of consensus error systems and the input-to-state stability of tracking error systems, and then sufficient conditions are derived to guarantee the agents realizing the group consensus tracking based on Lyapunov stability theories. Finally, several simulations are given to verify the effectiveness of the theoretical results.     

Distributed robust consensus control of multi-agent systems with heterogeneous matching uncertainties

This paper considers the distributed consensus problem of linear multi-agent systems subject to different matching uncertainties for both the cases without and with a leader of bounded unknown control input. Due to the existence of nonidentical uncertainties, the multi-agent systems discussed in this paper are essentially heterogeneous. For the case where the communication graph is undirected and connected, based on the local state information of neighboring agents, a fully distributed continuous adaptive consensus protocol is designed, under which the consensus error is uniformly ultimately bounded and exponentially converges to a small adjustable bounded set. For the case where there exists a leader whose control input is unknown and bounded, a distributed adaptive consensus protocol is proposed to ensure the boundedness of the consensus error. A sufficient condition for the existence of the proposed protocols is that each agent is stabilizable.     

Asynchronous consensus of multiple second-order agents with partial state information

This article studies the asynchronous consensus problem of multiple second-order agents in a sampled-data setting, where asynchrony means that the sampling period of each agent is independent of the others. It is assumed that each agent can only obtain the information of its positions relative to its neighbours at sampling instants. First, a discrete-time protocol is provided based on velocity estimation, and a sufficient and necessary condition for consensus under this protocol is established in virtue of properties of periodic systems. Second, a continuous-time protocol is presented by the theory of dynamic output feedback control, and a sufficient condition for consensus under this protocol is obtained by applying an input delay approach. Simulations are performed to illustrate the effectiveness of the theoretical results.     

Synchronisation of linear high-order multi-agent systems via event-triggered control with limited communication

In this paper, the synchronisation problems of multi-agent systems with asynchronous and synchronous event-triggered control under a novel event-triggered condition are solved. Our event-triggered control protocols only require each agent to send its state information to its neighbouring agents when an event-triggered condition is satisfied. Such control protocols substantially reduce the cost of communication. It is worth mentioning that the proposed protocols also ensure that the synchronisation of the multi-agent system with asynchronous and synchronous event-triggered can be achieved asymptotically without Zeno-behaviour. Meanwhile, an ultimate synchronisation trajectory is given. Moreover, our results are applied to solve the formation control problem. Some numerical simulations are presented to illustrate the effectiveness of our protocols.     

Distributed adaptive output consensus control of second-order systems containing unknown non-linear control gains

In this paper, we address the output consensus problem of tracking a desired trajectory for a group of second-order agents on a directed graph with a fixed topology. Each agent is modelled by a second-order non-linear system with unknown non-linear dynamics and unknown non-linear control gains. Only a subset of the agents is given access to the desired trajectory information directly. A distributed adaptive consensus protocol driving all agents to track the desired trajectory is presented using the backstepping technique and approximation technique of Fourier series (FSs). The FS structure is taken not only for tracking the non-linear dynamics but also the unknown portion in the controller design procedure, which can avoid virtual controllers containing the uncertain terms. Stability analysis and parameter convergence of the proposed algorithm are conducted based on the Lyapunov theory and the algebraic graph theory. It is also demonstrated that arbitrary small tracking errors can be achieved by appropriately choosing design parameters. Though the proposed work is applicable for second-order non-linear systems containing unknown non-linear control gains, the proposed controller design can be easily extended to higher-order non-linear systems containing unknown non-linear control gains. Simulation results show the effectiveness of the proposed schemes.     

Robust adaptive control of linearizable nonlinear single input systems with guaranteed error bounds

In this paper, a nonlinear robust adaptive control algorithm is designed and analyzed for a class of single-input nonlinear systems with unknown nonlinearities. The controller employs a single layer neural network to estimate the unknown plant nonlinearities on-line. The proposed controller is continuous and guarantees closed-loop semi-global stability and convergence of the tracking error to a small residual set. Furthermore, it handles the situation where the estimated plant becomes uncontrollable without any restrictive assumptions. In contrast to previous work on the same subject, the size of the residual tracking error can be specified a priori and is guaranteed by choosing certain design parameters. A procedure for choosing these parameters is presented. An example is used to demonstrate the performance and properties of the proposed scheme.     

Consensus of second-order multi-agent systems with nonsymmetric interconnection and heterogeneous delays

In this paper, a consensus algorithm of multi-agent second-order dynamical systems with nonsymmetric interconnection and heterogeneous delays is studied. With the hypothesis of directed weighted topology graph with a globally reachable node, decentralized consensus condition is obtained by applying generalized Nyquist criterion. For the systems with both communication and input delays, it is shown that the consensus condition is dependent on input delays but independent of communication delays.