Semi-global output regulation for linear systems with input saturation by composite nonlinear feedback control

To improve transient performance of output response, this paper applies composite nonlinear feedback (CNF) control technique to investigate semi-global output regulation problems for linear systems with input saturation. Based on a linear state feedback control law for a semi-global output regulation problem, a state feedback CNF control law is constructed by adding a nonlinear feedback part. The extra nonlinear feedback part can be applied to improve the transient performance of the closed-loop system. Moreover, an observer is designed to construct an output feedback CNF control law that also solves the semi-global output regulation problem. The sufficient solvability condition of the semi-global output regulation problem by CNF control is the same as that by linear control, but the CNF control technique can improve the transient performance. The effectiveness of the proposed method is illustrated by a disturbance rejection problem of a translational oscillator with rotational actuator system.     

Cooperative global output regulation of heterogeneous second-order nonlinear uncertain multi-agent systems

In this paper, we study the cooperative global output regulation problem for a class of heterogeneous second order nonlinear uncertain multi-agent systems. We first introduce a type of distributed internal model that converts the cooperative global output regulation problem into the global robust stabilization problem of the so-called augmented multi-agent system. Then we further globally stabilize this augmented multi-agent system via a distributed state feedback control law, thus leading to the solution of the original problem. A special case of our result leads to the solution of the global leader-following consensus problem for the second order nonlinear multi-agent systems without satisfying the global Lipschitz condition.     

Distributed Robust Containment Control of Linear Heterogeneous Multi-Agent Systems: An Output Regulation Approach

In this paper, we consider the robust output containment problem of linear heterogeneous multi-agent systems under fixed directed networks. A distributed dynamic observer based on the leaders’ measurable output was designed to estimate a convex combination of the leaders’ states. First, for the case of followers with identical state dimensions, distributed dynamic state and output feedback control laws were designed based on the state-coupled item and the internal model compensator to drive the uncertain followers into the leaders’ convex hull within the output regulation framework. Subsequently, we extended theoretical results to the case where followers have nonidentical state dimensions. By establishing virtual errors between the dynamic observer and followers, a new distributed dynamic output feedback control law was constructed using only the states of the compensator to solve the robust output containment problem. Finally, two numerical simulations verified the effectiveness of the designed schemes.      

Composite nonlinear feedback control for linear singular systems with input saturation

This paper investigates the composite nonlinear feedback (CNF) control technique for linear singular systems with input saturation. First, a linear feedback control law is designed for the step tracking control problem of linear singular systems subject to input saturation. Then, based on this linear feedback gain, a CNF control law is constructed to improve the transient performance of the closed-loop system. By introducing a generalized Lyapunov equation, this paper develops a design procedure for constructing the CNF control law for linear singular systems with input saturation. After decomposing the closed-loop system into fast subsystem and slow subsystem, it can be shown that the nonlinear part of the CNF control law only relies on slow subsystem. The improvement of transient performance by the proposed design method is demonstrated by an illustrative example.     

Cooperative output regulation with application to multi-agent consensus under switching network

In this paper, we consider the cooperative output regulation of linear multi-agent systems under switching network. The problem can be viewed as a generalization of the leader-following consensus problem of multi-agent systems. Due to the limited information exchanges of different subsystems, the problem cannot be solved by the decentralized approach and is not allowed to be solved by the centralized control. By devising a distributed observer network, we can solve the problem by both dynamic state feedback control and dynamic measurement output feedback control. As an application of our main result, we show that a special case of our results leads to the solution of the leader-following consensus problem of linear multi-agent systems.     

On improvement of transient performance in tracking control for a class of nonlinear systems with input saturation

This paper studies the technique of the composite nonlinear feedback (CNF) control for a class of cascade nonlinear systems with input saturation. The objective of this paper is to improve the transient performance of the closed-loop system by designing a CNF control law such that the output of the system tracks a step input rapidly with small overshoot and at the same time maintains the stability of the whole cascade system. The CNF control law consists of a linear feedback control law and a nonlinear feedback control law. The linear feedback law is designed to yield a closed-loop system with a small damping ratio for a quick response, while the nonlinear feedback law is used to increase the damping ratio of the closed-loop system when the system output approaches the target reference to reduce the overshoot. The result has been successfully demonstrated by numerical and application examples including a flight control system for a fighter aircraft.     

Robust nonlinear integral control

It is well known from linear systems theory that an integral control law is needed for asymptotic set-point regulation under parameter perturbations. The note presents a similar result fur a class of nonlinear systems in the presence of an unknown equilibrium due to uncertain nonlinearities and dynamic uncertainties. Both partial state and output feedback cases are considered. Sufficient small-gain type conditions are identified for existence of linear and nonlinear control laws. A procedure for robust nonlinear integral controller design is presented and illustrated via a practical example of fan speed control     

非线性耦合动态互联系统分布式协作负载均衡控制

针对一类非线性耦合动态互联系统,提出一种分布式协作负载均衡控制方法.借助输入输出反馈线性化技术,构建系统输入输出之间的关系,将耦合互联系统的分布式负载均衡控制设计问题转化为一阶多速率积分器智能体系统的输出一致性跟踪问题.基于最近邻原则设计增益可调的分布式协作负载均衡控制律,在通信拓扑满足相应的连通条件下,通过子系统间的局部交互实现负载均衡的目标.仿真和实验结果表明了所提出控制方法的有效性和可行性.     

Improving transient performance in tracking control for linear multivariable discrete-time systems with input saturation

In this paper, we present a composite nonlinear feedback (CNF) control technique for linear discrete-time multivariable systems with actuator saturation. The CNF control law serves to improve the transient performance of the closed-loop system by adding an additional nonlinear feedback. The linear feedback can be designed to yield a quick response at the initial stage, then the nonlinear feedback is introduced to smooth out overshoots when the system output approaches the target reference. As such, the resulting closed-loop system typically has very fast transient response and small overshoots. The goal of this work is to complete the theory for general discrete-time systems. The technique is applied to a magnetic-tape-drive servo system design and yields a huge improvement in settling time compared to that of a purely linear controller.     

Containment control of a class of heterogeneous nonlinear multi-agent systems

This paper studies the containment control of a class of heterogeneous nonlinear multi-agent systems under general directed graph. Every follower agent is a nonlinear system in the output feedback form with the same relative degree. The authors’ goal is to design a distributed dynamic controller such that the outputs of followers enter the convex hull spanned by the outputs of leaders. To this end, the containment problem is converted into a cooperative output regulation problem, a distributed adaptive recursive procedure and the internal model are employed to design the distributed controller.     

Cooperative output regulation of heterogeneous multi-agent systems based on passivity

This paper investigates the problem of cooperative output regulation of heterogeneous linear multi-agent systems. A passive framework is presented for the stabilisation analysis of cooperative output regulation, which can overcome the difficulty caused by the fact that the global dynamics of heterogeneous multi-agent systems depends on the global communication structure. An adaptive distributed observer is proposed to estimate the state of the exosystem, and the proposed distributed observer is independent of any global information of the communication graph. Based on passivity design and adaptive distributed observer, both a distributed state feedback and a distributed output feedback protocol are designed for output synchronisation of heterogeneous multi-agent systems. The gain matrices of the distributed protocols and observers are obtained by a Riccati equation design approach. Furthermore, sufficient local conditions for solving the problem of cooperative output regulation of heterogeneous multi-agent systems are presented. Finally, numerical simulation results are given to illustrate the effectiveness of the proposed distributed control schemes.     

Cooperative semi-global robust output regulation for a class of nonlinear uncertain multi-agent systems

In this paper, we study the cooperative semi-global robust output regulation problem for a class of minimum phase nonlinear uncertain multi-agent systems. This problem is a generalization of the leader-following tracking problem in the sense that it further addresses such issues as disturbance rejection, robustness with respect to parameter uncertainties. To solve this problem, we first introduce a type of distributed internal model that converts the cooperative semi-global robust output regulation problem into a cooperative semi-global robust stabilization problem of the so-called augmented system. We then solve the semi-global stabilization problem via distributed dynamic output control law by utilizing and combining a block semi-global backstepping technique, a simultaneous high gain feedback control technique, and a distributed high gain observer technique.     

Distributed output regulation for linear multi-agent systems with communication delays

In this paper, a distributed output regulation approach is presented for the cooperative control of linear multi-agent systems in the presence of communication delays. Both dynamic state and output feedback control laws are designed for achieving the property of output regulation. Sufficient conditions for the existence of these control laws are provided in terms of linear matrix inequalities. Simulation results are given to support the efficiency of the proposed distributed output regulation approach.     

Cooperative Containment Formation for Discrete-time Heterogeneous Networks by Double Compensators

In this paper, two practical distributed observers are constructed to solve the cooperative robust containment formation problem for discrete-time linear multi-agent systems. The dynamics of the systems contain uncertain parts. A containment error is presented to guarantee all the outputs of followers converge to the convex hull spanned by the outputs of the leaders. There are two compensators in this paper, we first present a distributed compensator to estimate the information of convex hull, and use an internal compensator to solve the problem of uncertain parts in dynamics. Further more, based on the both compensators, a distributed dynamic output feedback controller is designed to solve the containment control problem for the discrete-time multi-agent systems. Finally, a numerical example is given to verify the effectiveness of the main results.     

A self-tuning adaptive distributed observer approach to the cooperative output regulation problem for networked multi-agent systems

In this paper, we first propose a self-tuning distributed observer for a multi-agent system, which is capable of providing the estimation of the leader's signal to various followers without assuming all the followers know the system matrix of the leader. We then further develop a novel adaptive distributed control law to solve the cooperative output regulation problem for linear heterogeneous multi-agent systems. This control law offers two advantages in that it makes less use of the information of the network as well as the information of the leader and external disturbances, and it avoids calculating the observer gain.     

Cooperative linear output regulation for networked systems by dynamic measurement output feedback

This paper investigates the cooperative linear output regulation problem of a class of heterogeneous networked systems with a common reference input but with different disturbances for individual nodes. A novel distributed control law is presented based on dynamic measurement output feedback. It is shown that the overall networked closed-loop control system is asymptotically stable and the output regulation errors asymptotically approach zero as time goes to infinity under a sufficient and necessary condition. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed control law.     

Composite nonlinear feedback control for strict-feedback nonlinear systems with input saturation

This paper focuses on composite nonlinear feedback (CNF) controller design for tracking control problem of strict-feedback nonlinear systems with input saturation to address the improvement of transient performance. First, without considering the input saturation, a stabilisation control law is designed by using standard backstepping technique for the nonlinear system, then a feedforward control law is added to the backstepping-based stabilisation control law to construct a tracking control law. The tracking control law is tuned to drive the output of the closed-loop system to track a command input with quick response. Then, an additional nonlinear feedback law is constructed and combined with the tracking control law to obtain a CNF control law. The role of this additional nonlinear feedback law is to smoothly change the damping ratio of the closed-loop system while the system output approaches the command input, and to reduce overshoot caused by the tracking control law. It is shown that the extra-adding nonlinear feedback part does not cause the loss of stability of the closed-loop system in its attractive basin.     

Cooperative learning neural network output feedback control of uncertain nonlinear multi-agent systems under directed topologies

Without assuming that the communication topologies among the neural network (NN) weights are to be undirected and the states of each agent are measurable, the cooperative learning NN output feedback control is addressed for uncertain nonlinear multi-agent systems with identical structures in strict-feedback form. By establishing directed communication topologies among NN weights to share their learned knowledge, NNs with cooperative learning laws are employed to identify the uncertainties. By designing NN-based κ-filter observers to estimate the unmeasurable states, a new cooperative learning output feedback control scheme is proposed to guarantee that the system outputs can track nonidentical reference signals with bounded tracking errors. A simulation example is given to demonstrate the effectiveness of the theoretical results.     

拓扑切换下IT2 T-S模糊非线性多智能体系统全局逆最优控制

针对连续非线性多智能体系统的全局最优协同控制问题,本文提出了模糊输出反馈和逆最优方法的分布式一致性最优控制律和相应的控制策略.首先,通过一种区间2型T-S (interval type 2 Takagi-Sugeno IT2 T-S)模糊模型将非线性系统等价转化为线性系统.其次,基于逆最优方法设计了全局最优协同控制律和相应的模糊输出反馈控制策略,智能体间仅仅通过局部通信,即可实现拓扑切换下非线性多智能体系统的二次性能全局最优控制,且系统的收敛速度大大提高.基于局部稳定性理论给出了全局逆最优控制的充要条件.最后,通过MATLAB算例验证所提方法的正确性和可行性.     

Structural design of composite nonlinear feedback control for linear systems with actuator constraint

The performance of the composite nonlinear feedback (CNF) control law relies on the selection of the linear feedback gain and the nonlinear function. However, it is a tough task to select an appropriate linear feedback gain and appropriate parameters of the nonlinear function because the general design procedure of CNF control just gives some simple guidelines for the selections. This paper proposes an operational design procedure based on the structural decomposition of the linear systems with input saturation. The linear feedback gain is constructed by two linear gains which are designed independently to stabilize the unstable zero dynamics part and the pure integration part of the system respectively. By investigating the influence of these two linear gains on transient performance, it is flexible and efficient to design a satisfactory linear feedback gain for the CNF control law. Moreover, the parameters of the nonlinear function are tuned automatically by solving a minimization problem. The proposed design procedure is illustrated by applying it to design a tracking control law for the inverted pendulum on a cart system. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society