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 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.     

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.     

Robust cooperative output regulation under exosystem detectability constraint

ABSTRACT

This paper revisits the robust cooperative output regulation problem for a class of linear uncertain multi-agent systems. In particular, it is assumed here that the agents in the system can only access incomplete measurements of the exosystem, and the local regulated error signals are not available to the agents to be used in control. Under these assumptions, the agents in the system cannot independently reconstruct the exosystem dynamics, or rely on their own local measurements to achieve the objectives of the output regulation problem. The solution to the regulation problem proposed in this paper is a distributed dynamic control law that reconstructs the exosystem states, given a mild collective detectability assumption. Furthermore, the proposed distributed control law incorporates an internal model of the exosystem to allow for uncertain dynamics of the multi-agent system. A numerical example is offered to illustrate the effectiveness of the proposed control solution.     

An adaptive regulation problem and its application

This paper studies an adaptive regulation problem for the modified FitzHugh-Nagumo neuron model under external electrical stimulation. We first present the solution of the global robust output regulation problem for output feedback system with an uncertain exosystem which models the external electrical stimulation with unknown frequency and amplitude. Then, we show that the robust control problem for the modified FitzHugh-Nagumo neuron model can be formulated as the global robust output regulation problem and the solvability conditions for the output regulation problem for the modified FitzHugh-Nagumo neuron model are all satisfied. Then, we apply the obtained output regulation result to constructing an output feedback control law for the modified FitzHugh-Nagumo neuron model to achieve global stability of the closed-loop system in the presence of uncertain parameters and external stimulus. An example is given to show that the proposed algorithm can completely reject the external electrical stimulation.     

一类非线性输出反馈系统的自适应输出调节问题

本文讨论一类非线性系统的全局鲁棒输出调节问题.假定被控非线性系统的系统输入方向未知,且产生参考或扰动信号的外部系统含未知参数,这为控制律的设计带来了挑战.文章使用自适应控制方法和内模原理,解决了一类相对阶为1的非线性输出反馈系统的输出调节问题,并将结果应用于处理Lorenz系统的渐近跟踪问题.     

Robust controller design for infinite‐dimensional exosystems

In this paper, we consider robust output regulation of distributed parameter systems with infinite‐dimensional exosystems capable of generating polynomially growing signals. We design an observer‐based error feedback controller solving the control problem. The controller is chosen in such a way that it incorporates an internal model of the infinite‐dimensional exosystem. The remaining parameters of the controller are chosen to stabilize the closed‐loop system strongly. We also analyze the classes of signals generated by the exosystem. In particular, we explore the connection between the smoothness properties of the reference and disturbance signals and the strictness of the conditions required for the existence of a controller solving the robust output regulation problem. Copyright © 2012 John Wiley & Sons, Ltd.     

A general framework for tackling the output regulation problem

Output regulation aims to achieve, in addition to closed-loop stability, asymptotic tracking and disturbance rejection for a class of reference inputs and disturbances. Thus, it poses a more challenging problem than stabilization. For over a decade, the nonlinear output regulation problem has been one of the focuses in nonlinear control research, and active research on this problem has generated many fruitful results. Nevertheless, there are two hurdles that impede the further progress of the research on the output regulation problem. The first one is the assumption that the solution or the partial solution of the regulator equations is polynomial. The second one is the lack of a systematic mechanism to handle the global robust output regulation problem. We establish a general framework that systematically converts the robust output regulation problem for a general nonlinear system into a robust stabilization problem for an appropriately augmented system. This general framework, on one hand, relaxes the polynomial assumption, and on the other hand, offers a greater flexibility to incorporate recent new stabilization techniques, thus setting a stage for systematically tackling the robust output regulation with global stability.     

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.      

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.     

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.     

Robust output regulation and the preservation of polynomial closed‐loop stability

In this paper, we study the robust output regulation problem for distributed parameter systems with infinite‐dimensional exosystems. The main purpose of this paper is to demonstrate the several advantages of using a controller that achieves polynomial closed‐loop stability, instead of a one stabilizing the closed‐loop system strongly. In particular, the most serious unresolved issue related to strongly stabilizing controllers is that they do not possess any known robustness properties. In this paper, we apply recent results on the robustness of polynomial stability of semigroups to show that, on the other hand, many controllers achieving polynomial closed‐loop stability are robust with respect to large and easily identifiable classes of perturbations to the parameters of the plant. We construct an observer based feedback controller that stabilizes the closed‐loop system polynomially and solves the robust output regulation problem. Subsequently, we derive concrete conditions for finite rank perturbations of the plant's parameters to preserve the closed‐loop stability and the output regulation property. The theoretical results are illustrated with an example where we consider the problem of robust output tracking for a one‐dimensional heat equation.Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Global robust output regulation of multivariable systems with nonlinear exosystem

It is well known that multi‐input, multi‐output nature of nonlinear system and generalized exosystem have posed some challenges to output regulation theory. Recently, the global robust output regulation problem for a class of multivariable nonlinear system subject to a linear neutrally stable exosystem has been studied. It has been shown that a linear internal model‐based state feedback control law can lead to the solution of previous problem. In this paper, we will further study the global robust output regulation problem of the system subject to a nonlinear exosystem. By utilizing nonlinear internal model design and decomposing the multi‐input control problem into several single‐input control problems, we will solve the problem by recursive control law design. The theoretical result is applied to the non‐harmonic load torque disturbance rejection problem of a surface‐mounted permanent magnet synchronous motor. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed output regulation for multi-agent systems with norm-bounded uncertainties

In this paper, we consider the distributed robust output regulation problem for multi-agent systems (MASs). It is involved with a group of heterogeneous high-order linear uncertain systems and an linear exosystem. The regulated output is a combination of the output of MAS and the exosystem, which is defined based on controlling demands. Distributed controllers are designed to ensure that the regulated output converges to the origin and meanwhile the closed-loop MAS is stable. The sufficient conditions for the solvability of distributed output regulation problem are given in terms of linear matrix inequalities. And algorithms are proposed to design distributed dynamic controllers with state feedback and output feedback, via the help of internal models. It is shown that, for any time-invariant norm-bounded uncertainties, the given controllers can realise the objective of output regulation.     

Global Robust Output Regulation for a Class of Switched Nonlinear Systems with Nonlinear Exosystems

The problem of global robust output regulation for a class of switched nonlinear systems with nonlinear exosystems is investigated in this paper where not all subsystems are stabilizable. First, as an extension of the concept of non‐switched internal model, this paper defines a switched internal model, which together with the plant is called the switched augmented system. Also, we show that the problem of output regulation for the switched nonlinear system can be converted into a global robust regulation problem of the switched augmented system. Second, based on the average dwell time method, the global robust regulation problem under a class of switching signals with average dwell time is solved, which leads to the solution of the problem of global robust output regulation. Finally, an example is provided to demonstrate the effectiveness of the proposed design approach.     

Robust output regulation for discrete‐time nonlinear systems

In this paper, we will establish a framework that can convert the robust output regulation problem for discrete‐time nonlinear systems into a robust stabilization problem for an appropriately augmented system consisting of the given plant and a specific dynamic system called internal model. We then apply this framework to solve the local robust output regulation problem for a general class of discrete‐time nonlinear systems. The results of this paper gives a discrete‐time counterpart of the recent results on the continuous‐time robust output regulation problem. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

具有自适应内模的一类非线性系统输出调节问题

研究一类包含未知非线性项的非线性系统的鲁棒输出调节问题.此类非线性系统由一包含未知参数的线性中性稳定的外系统驱动.首先运用调节器方程组解和标准内模将输出调节问题转化为镇定问题;然后给出控制律镇定闭环系统,同时利用镇定输入项和外系统信息设计出自适应内模方程.控制律使得闭环系统的信号全局最终有界,且误差被调节至预先设定的任意小的精度值.仿真结果验证了所提出设计方法的有效性.     

A general formulation and solvability of the global robust output regulation problem

While the output regulation problem for linear systems accommodates both bounded and unbounded exogenous signals, the existing formulation of the output regulation problem for nonlinear systems only allows bounded exogenous signals produced by an exosystem with a neutrally stable equilibrium. In particular, when it comes to the robust output regulation problem, the only admissible exogenous signal is a finite combination of step and sinusoidal functions. In this paper, we give a general formulation of the robust output regulation problem that admits unbounded exogenous signals, and contains the previous formulations as special cases when the system is linear or when the exogenous signals are bounded. Then, we give conditions under which the problem can be solved by solving a robust stabilization problem of an augmented system. Finally, we apply our general result to obtain the solvability conditions of the general robust output regulation problem for the class of lower triangular nonlinear systems.