Cooperative robust output regulation of a class of heterogeneous linear uncertain multi‐agent systems

The cooperative output regulation of a linear multi‐agent system can be viewed as a generalization of the leader‐following consensus problem and was studied recently for the case where the system uncertain parameters vary in a sufficiently small neighborhood of their nominal value. This case was handled by the internal model design which converts the problem into a simultaneous eigenvalue placement problem of an augmented multi‐agent system. In this paper, we further consider the cooperative robust output regulation problem for a class of minimum phase linear multi‐agent systems in the sense that the controller allows the system uncertain parameters to vary in an arbitrarily prescribed compact subset. For this purpose, we introduce a new type of internal model that allows the cooperative robust output regulation problem of the given plant to be converted into a robust stabilization problem of an augmented multi‐agent system. We then solve our problem by combining a simultaneous high‐gain state feedback control technique and a distributed high‐gain observer technique. A special case of our result leads to the solution of the leader‐following robust consensus problem for a class of uncertain multi‐agent systems. Copyright © 2013 John Wiley & Sons, Ltd.     

Cooperative robust output regulation problem for discrete‐time linear time‐delay multi‐agent systems

In this paper, we study the cooperative robust output regulation problem for discrete‐time linear multi‐agent systems with both communication and input delays by a distributed internal model approach. We first introduce the distributed internal model for discrete‐time multi‐agent systems with both communication and input delays. Then, we define the so‐called auxiliary system and auxiliary augmented system. Finally, we solve our problem by showing, under some standard assumptions, that if a distributed state feedback control or a distributed output feedback control solves the robust output regulation problem of the auxiliary system, then the same control law solves the cooperative robust output regulation problem of the original multi‐agent systems.     

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.     

A semi-global low-and-high gain design technique for linear systems with input saturation—stabilization and disturbance rejection

In this paper we propose a linear low-and-high gain design technique to solve the semi-global stabilization problem for a class of linear systems subject to input saturation. The central idea behind this new technique is to increase the utilization of the available control capability of the system. The power of this new semi-global design technique is shown by solving the problem of semi-global stabilization with input-additive disturbance rejection which is formulated as a semi-global practical stabilization problem.     

Semi-global robust output regulation for a class of singular nonlinear systems via nonlinear internal model

Most of existing results on robust output regulation problem of singular nonlinear systems are limited to local solutions. In this paper, the semi-global robust output regulation problem for a class of singular nonlinear systems is investigated by using a nonlinear internal model. Attaching a nonlinear internal model to the singular nonlinear system yields an augmented singular nonlinear system whose semi-global robust stabilisation solution leads to the solution of the semi-global robust output regulation problem of the original singular nonlinear system. The solvability conditions of the semi-global output regulation problem are established by addressing the solvability of the robust stabilisation problem of augmented singular nonlinear system. Finally, a numerical simulation example is used to illustrate the design of the semi-global regulator for the singular nonlinear systems.     

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.     

Semi‐Global Robust Output Regulation for A Class of Singular Nonlinear Systems with Unknown Algebraic Equations

This paper considers semi‐global robust output regulation problem for a class of singular nonlinear systems whose algebraic equations are not precisely known. Since the algebraic equations are not known, the output regulation problem of singular nonlinear systems cannot be solved by directly reducing the singular nonlinear system into a normal nonlinear system. Based on internal model principle, we convert the robust output regulation problem of singular nonlinear systems into a robust stabilization problem of an augmented singular nonlinear system. The augmented singular nonlinear system is also with unknown algebraic equations. However, without transforming the singular nonlinear system into a normal nonlinear system, it is shown that the augmented singular nonlinear system can be semi‐globally stabilized by a high gain output feedback control law under some reasonable assumptions. Moreover, the semi‐global stabilization control law of the augmented singular nonlinear systems also solves the semi‐global robust output regulation problem of the original singular nonlinear system.     

Output feedback stabilization of spacecraft autonomous rendezvous subject to actuator saturation

This paper studies the output feedback dynamic gain scheduled control for stabilizing a spacecraft rendezvous system subject to actuator saturation. By using the parametric Lyapunov equation and the gain scheduling technique, a new observer-based output feedback controller is proposed to solve the semi-global stabilization problem for spacecraft rendezvous system with actuator saturation. By scheduling the design parameter online, the convergence rates of the closed-loop system are improved. Numerical simulations show the effectiveness of the proposed approaches.     

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.     

On semi-global stabilization of minimum phase nonlinear systems without vector relative degrees

Recently, we developed a structural decomposition for multiple input multiple output nonlinear systems that are affine in control but otherwise general. This structural decomposition simplifies the conventional backstepping design and allows a new backstepping design procedure that is able to stabilize some systems on which the conventional backstepping is not applicable. In this paper we further exploit the properties of such a decomposition for the purpose of solving the semi-global stabilization problem for minimum phase nonlinear systems without vector relative degrees. By taking advantage of special structure of the decomposed system, we first apply the low gain design to the part of system that possesses a linear dynamics. The low gain design results in an augmented zero dynamics that is locally stable at the origin with a domain of attraction that can be made arbitrarily large by lowering the gain. With this augmented zero dynamics, backstepping design is then applied to achieve semi-global stabilization of the overall system.     

Global robust practical output regulation for nonlinear systems in output feedback form by output‐based event‐triggered control

In this paper, we study the event‐triggered global robust practical output regulation problem for a class of nonlinear systems in output feedback form with any relative degree. Our approach consists of the following three steps. First, we design an internal model and an observer to form the so‐called extended augmented system. Second, we convert the original problem into the event‐triggered global robust practical stabilization problem of the extended augmented system. Third, we design an output‐based event‐triggered control law and a Zeno‐free output‐based event‐triggered mechanism to solve the stabilization problem, which, in turn, leads to the solvability of the original problem. Finally, we apply our result to the controlled hyperchaotic Lorenz systems.     

Robust practical output regulation for a class of uncertain linear minimum‐phase systems by output‐based event‐triggered control

In this paper, we consider the robust practical output regulation problem for a class of SISO uncertain linear minimum‐phase systems subject to external disturbances by an output‐based event‐triggered control law, where the reference inputs and the external disturbances are both generated by a so‐called exosystem with known dynamics. Our approach consists of two steps. First, on the basis of the internal model principle, we convert the problem into the robust practical stabilization problem of a well‐defined augmented system. Second, we design an output‐based event‐triggered mechanism and an output‐based event‐triggered control law to solve the stabilization problem, which in turn leads to the solvability of the original problem. What is more, we show that the event‐triggered mechanism prevents the Zeno behavior from happening. A numerical example is given to illustrate the design. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

基于自适应分布式滤波观测器的多智能体系统编队控制

本文考虑了全局指令系统输出信息受到信道扰动情况下线性多智能体系统的编队控制问题.首先,基于协作式输出调节理论框架对线性多智能体系统的编队控制问题进行数学建模.其次,针对受到信道扰动的全局指令系统输出信息,提出了一类基于受扰输出的自适应分布式滤波观测器,在降低网络信息交换量的同时消除扰动的影响.最后,设计了输出反馈确定等价控制律,解决了线性多智能体系统的分布式编队控制问题.给出了数值仿真结果检验控制性能.     

Global robust output regulation for a class of multivariable systems

In this paper, we study the global robust output regulation problem for a class of multivariable nonlinear systems. The problem is first converted into a stabilization problem of an augmented system composed of the original plant and an internal model. The augmented system is a multi‐input system containing both dynamic uncertainty and time‐varying static uncertainty. By decomposing the multi‐input control problem into several single‐input control problems, we will solve the problem by solving several single‐input control problems via a recursive approach utilizing the changing supply function technique. The theoretical result is applied to the speed tracking control and load torque disturbance rejection problem of a surface‐mounted permanent magnet synchronous motor. Copyright © 2011 John Wiley & Sons, Ltd.     

An output-based distributed observer and its application to the cooperative linear output regulation problem

In this paper, we first extend an existing stability result for a class of linear switched systems. This extended result will relax the existence conditions of the output-based distributed observer for a leader system subject to jointly connected switching communication networks in the literature. As an application of this output-based distributed observer, we solve the cooperative output regulation problem of a linear multi-agent system subject to jointly connected switching communication networks by composing a purely decentralized control law and the output-based distributed observer based on the certainty equivalence principle.     

Speed tracking control of surface‐mounted permanent‐magnet synchronous motor with unknown exosystem

The surface‐mounted permanent‐magnet synchronous motor is a two‐input, two‐output nonlinear system. The multi‐input, multi‐output nature of the system has posed some specific challenges to various control methods. Recently, the robust output regulation problem of the system subject to a known neutrally stable exosystem was studied. The problem came down to a global robust stabilization problem of an augmented system composed of the original plant and an internal model. In this paper, we will further study the robust output regulation problem of the system subject to an unknown neutrally stable exosystem. Like in the case where the exosystem is known, the current problem can be solved by globally stabilizing an augmented system. But unlike in the case where the exosystem is known, the augmented system takes a much more complicated form because of uncertainty in the exosystem than the case where the exosystem is known. In particular, the dynamic uncertainty in the current augmented system contains linearly parameterized uncertainty, and hence is not input‐to‐state stable. By utilizing some dynamic coordinate transformation technique, and combining some robust control and adaptive control techniques, we will solve the problem via a recursive approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Global robust output regulation of lower triangular systems with unknown control direction

This paper presents the solvability conditions for the global robust output regulation problem for lower triangular nonlinear systems assuming the control direction is unknown. The approach used is an integration of the robust stabilization technique and Nussbaum gain technique.     

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.      

Global control of nonlinear systems with uncertain output function using homogeneous domination approach

This paper addresses the problem of using output feedback to globally control a class of nonlinear systems whose output functions are not precisely known. First, for the nominal linear system, we design a homogeneous state compensator without requiring precise information of the output function, and construct a nonlinear stabilizer with adjustable coefficients by using the generalized adding a power integrator technique. Then based on the homogeneous domination approach, a scaling gain is introduced into the proposed output feedback controller, which can be used by tuning the scaling gain to solve: (i) the problem of global output feedback stabilization for a class of upper‐triangular systems; and (ii) the problem of global practical output tracking for a class of lower‐triangular systems. Copyright © 2011 John Wiley & Sons, Ltd.