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 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.     

Output regulation of linear plants subject to constraints

Output regulation problems for continuous-time linear systems with state and/or input constraints are studied. The problems are formulated in global and semi-global setting by using state or full information feedback. The goal of this paper is to develop solvability conditions for the posed problems. Moreover, appropriate regulators are constructed under the solvability conditions. To state the solvability conditions clearly, a taxonomy of constraints is introduced which delineates the constraints into several categories. Such a taxonomy of constraints provides a classification of linear plants with constraints and identifies what types of output regulation problems are solvable. Results developed here include as a special case the results obtained in the literature for systems with only input constraints. The constraint taxonomy also identifies some intrinsically hard constraints (non-right invertible constraints) for which the solvability conditions of global/semi-global output regulation problems are not clear yet. As a special case of output regulation, we also consider tracking problems with constraints. It is shown that if there exists a state feedback controller with a stabilizing domain of attraction, then one can find a regulator with a tracking domain of attraction arbitrarily close to the stabilizing domain.     

Output‐feedback stabilization for planar output‐constrained switched nonlinear systems

In this paper, globally asymptotical stabilization problem for a class of planar switched nonlinear systems with an output constraint via smooth output feedback is investigated. To prevent output constraint violation, a common tangent‐type barrier Lyapunov function (tan‐BLF) is developed. Adding a power integrator approach (APIA) is revamped to systematically design state‐feedback stabilizing control laws incorporating the common tan‐BLF. Then, based on the designed state‐feedback controllers and a constructed common nonlinear observer, smooth output‐feedback controllers, which can make the system output meet the predefined constraint during operation, are proposed to deal with the globally asymptotical stabilization problem of planar switched nonlinear systems under arbitrary switchings. A numerical example is employed to verify the proposed method.     

Linear systems with input nonlinearities: Global stabilization by scheduling a family of H∞-type controllers

A new global stabilization algorithm is presented for linear systems that have (A, B) stabilizable, the eigenvalues of A in the closed left-half plane, but where the controls pass through nonlinearities of a general type. This algorithm is based on a semi-global stabilization solution for the same class of systems. The global solution is constructed by dynamically scheduling the adjustable parameter of the semi-global solution according to the size of the state. The semi-global solution is a family of linear control laws generated by a family of H_∞-type algebraic Riccati equations. We show that the closed-loop state feedback system has the property that additive disturbances which converge exponentially to zero cannot produce unbounded states. This fact is used to show that, under a linear detectability assumption, the state feedback results are recovered when the solution is implemented via a standard linear-based observer.     

Simultaneous External and Internal Stabilization for Continuous and Discrete-Time Critically Unstable Linear Systems with Saturating Actuators

The issues arising in hybrid or simultaneous external as well as internal stabilization of linear systems with saturating actuators are considered. Four different stabilization problems are studied. Roughly, these problems are (1) simultaneous semi-global external as well as semi-global internal stabilization, (2) simultaneous semi-global external as well as global internal stabilization, (3) simultaneous global external as well as semi-global internal stabilization, and (4) simultaneous global external as well as global internal stabilization. As evident from the literature, the requirement of internal stabilization alone either in the global or semi-global sense demands that the linear part of the given system be (a) stabilizable, and (b) has all its poles in the closed left half complex plane for continuous-time systems while it has all its poles inside and/or on the unit circle for discrete-time systems. This implies that the posed simultaneous stabilization problems are solvable at best only under the conditions (a) and (b). Under such conditions, we construct here explicit state as well as measurement feedback controllers for all the four problems in the case of continuous-time systems, and for the problems (1), (2) and (4) in the case of discrete-time systems. The design methodologies used to construct appropriate feedback laws are based on by now familiar low-gain and low-and-high gain design concepts or certain scheduled versions of them.     

Semi-global weighted output average tracking of discrete-time heterogeneousmulti-agent systems subject to input saturation and external disturbances

In this paper, we revisit the semi-global weighted output average tracking problem for a discrete-time multi-agent system subject to input saturation and external disturbances. The multi-agent system consists of multiple heterogeneous linear systems as leader agents and multiple heterogeneous linear systems as follower agents. We design both the state feedback and output feedback control protocols for each follower agent. In particular, a distributed state observer is designed for each follower agent that estimates the state of each leader agent. In the output feedback case, state observer is also designed for each follower agent to estimate its own state. With these estimates, we design low gain-based distributed control protocols, parameterized in a scalar low gain parameter. It is shown that, for any bounded set of the initial conditions, these control protocols cause the follower agents to track the weighted average of the outputs of the leader agents as long as the value of the low gain parameter is tuned sufficiently small. Simulation results illustrate the validity of the theoretical results.     

Semi-global sampled-data output feedback disturbance rejection control for a class of uncertain nonlinear systems

This paper investigates the semi-global output feedback disturbance rejection control problem for a class of uncertain nonlinear systems with additive disturbances using linear sampled-data control. Aiming to reject the adverse effects caused by the uncertainties and unknown nonlinear perturbations which may not satisfy the strict feedback or feedforward structure, a new generalised discrete-time extended state observer is proposed to estimate the disturbance at sampling points. An output feedback disturbance rejection control law is then constructed in a sampled-data form which facilitates digital implementations. By selecting adequate control gains and a sufficiently small sampling period to restrain the state growth under a zero-order-hold input, the semi-global asymptotic stability of the hybrid closed-loop system and the disturbance rejection ability are proved. Both numerical example and an application of a single-link robot arm system demonstrate the feasibility and efficacy of the proposed method.     

非线性微分——代数系统的输出反馈镇定控制

对满足线性增长条件的非线性微分--代数系统, 研究了其输出反馈镇定控制问题. 通过将状态观测器与控制器耦合在一起设计, 构造出一种非初始化的线性高增益状态观测器, 具有良好的鲁棒性. 基于反推设计方法构造出一个线性的动态输出补偿器, 使得整个闭环系统是渐近稳定的. 仿真结果验证了本文所提控制方法的有效性.     

Global sampled‐data output‐feedback stabilization for nonlinear systems with unknown measurement sensitivity

This paper investigates the problem of global output‐feedback stabilization by sampled‐data control for nonlinear systems with unknown measurement sensitivity. By employing the technique of output‐feedback domination, a sampled‐data output‐feedback control law together with a sampled‐data state observer is explicitly constructed. By an exquisite selection of both the domination gain and sampling period, the resultant control law is a globally asymptotic stabilizer even in the presence of unknown measurement sensitivity. The novelty of this paper is the development of a distinct approach which can tackle the problem of output‐feedback stabilization for the nonlinear systems with unknown measurement sensitivity.     

Output regulation of linear systems with bounded continuous feedback

This paper studies the classical problem of output regulation for linear systems subject to control constraint. The asymptotically regulatable region, the set of all initial conditions of the plant and the exosystem for which output regulation is possible, is characterized in terms of the controllable region of the antistable subsystem of the plant. Continuous output regulation laws, of both state feedback type and error feedback type, are constructed from a given stabilizing state feedback law. It is shown that a stabilizing feedback law that achieves a larger domain of attraction leads to a feedback law that achieves output regulation on a larger subset of the asymptotically regulatable region. A feedback law that achieves global stabilization on the asymptotically controllable region leads to a feedback law that achieves output regulation on the entire asymptotically regulatable region.     

Output feedback stabilization of MIMO non-linear systems via dynamic sliding mode

Previous work on asymptotic stabilization of MIMO non-linear systems using dynamic sliding mode control to produce dynamic state feedback has been generalized to dynamic output feedback. All the states in the feedback controller are replaced with estimated states which come from a semi-high-gain observer. The bound on the observer gain is explicitly given, which depends on some previously chosen design parameters. If the given differential input–output (I–O) system is minimum phase and proper, local uniform asymptotic output feedback stabilization can be achieved. In addition, the restriction on the stability of the zero dynamics has been relaxed to weakly minimum phase and semi-global results are obtained under some mild conditions. The stability of the closed-loop system is based on some stability results of triangular systems when continuous or discontinuous controllers are adopted. Two pertinent examples are given to illustrate the design method. Copyright © 1999 John Wiley & Sons, Ltd.     

Semi‐global stabilization of discrete‐time systems subject to non‐right invertible constraints

This paper investigates time‐invariant linear systems subject to input and state constraints. We study discrete‐time systems with full or partial constraints on both input and state. It has been shown earlier that the solvability conditions of stabilization problems are closely related to important concepts such as the right invertibility or non‐right invertibility of the constraints, the location of constraint invariant zeros, and the order of constraint infinite zeros. In this paper, for general time‐invariant linear systems with non‐right invertible constraints, necessary and sufficient conditions are developed under which semi‐global stabilization in the admissible set can be achieved by state feedback. Sufficient conditions are also developed for such a stabilization in the case where measurement feedback is used. Such sufficient conditions are almost necessary. Controllers for both state feedback and measurement feedback are constructed as well. Copyright © 2009 John Wiley & Sons, Ltd.     

Global output‐feedback stabilization for stochastic nonlinear systems: A double‐domination approach

This paper is concerned with global stabilization via output feedback for a class of stochastic nonlinear systems with time‐varying continuous output function. Under linear growth conditions, a new double‐domination method is proposed for the first time to construct an output‐feedback stabilizing controller. Different from the related results, the design of the observer is performed without using the information on the output function and nonlinearities. This paper also provides a viewpoint at the feedback stabilization to eliminate the continuous measurement error originating from inaccurate detection of system state. A simulation example is presented to demonstrate the effectiveness of control strategy.     

一类非线性系统的控制器和观测器设计

研究一类非线性系统的全状态反馈控制问题、观测器设计问题及输出反馈控制设计问题.首先设计出非线性全状态反馈控制器,获得了系统指数镇定的充分条件.然后提出了非线性观测器,并证明了该观测器是指数稳定观测器.进一步,在控制器和观测器问题的充分条件满足的假设下,证明了提出的带估计状态的反馈控制能达到指数镇定.最后,仿真实例验证了所得结果的有效性.     

Quadratic boundedness via dynamic output feedback for constrained nonlinear systems in Takagi–Sugeno’s form

This paper studies output feedback stabilization of Takagi–Sugeno fuzzy systems with input or state constraint and bounded noise. A dynamic output feedback controller is adopted, rather than a controller based on the state observer. The notion of quadratic boundedness specified by a common Lyapunov matrix, which is novel in fuzzy control, is invoked to handle the noise. Under the proposed controller, the state of the closed-loop system is stabilizing to an ellipsoid specified by this common Lyapunov matrix. Two numerical examples are given to show the effectiveness of the controller.     

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.     

非线性微分-代数系统的输出反馈镇定:基于线性采样控制

对满足指数1和线性增长条件的非线性微分-代数系统,本文证明其采样输出反馈镇 定控制问题可解.首先,给出一个线性显式非初始化状态观测器设计;然后,构造出线性的采样输出 反馈控制器,使得整个闭环系统渐近稳定.仿真结果表明了所提控制方法的有效性.     

Global quadratic stabilization of a class of nonlinear systems

The problem of quadratic stabilization for a class of nonlinear systems is examined in this paper. By employing a well-known Riccati approach, we develop a technique for designing a state feedback control law which quadratically stabilizes the system for all admissible uncertainties. This state feedback control law consists of linear and nonlinear feedback control terms. The linear feedback control term is generalized from a well-known H_∞ result, while the nonlinear term can be viewed as a correcting term for the presence of nonlinear bounded uncertainty. This stabilization result is extended to static output feedback and to systems for which the nonlinear uncertainty satisfies generalized matching conditions. Furthermore, we point out that in the presence of nonlinear uncertainty the global quadratic stability may be destroyed by some arbitrary small mismatched uncertainty in the matrix, and proceed to establish the region of semi-global quadratic stability of the controlled system. © 1998 John Wiley & Sons, Ltd.     

一类线性时变系统的输出反馈控制

基于线性时不变系统能控能观标准型变换及非线性系统高增益观测器方法,本文研究了一类线性时变系统 的输出反馈控制问题. 通过引入时变的状态变量坐标变换,分别设计了线性时变系统的状态反馈控制器、状态观测器以及基于 状态观测器的输出反馈控制器. 进一步地,本文分别证明了观测器动态误差是渐近收敛于零的,而状态反馈控制器以及输出反馈控制器可以 保证闭环系统的渐近稳定性.