Design of output feedback consensus controllers for nonlinear sampled-data multi-agent systems of strict-feedback form

Design of reduced-order observer-based output feedback consensus controllers for nonlinear sampled-data multi-agent systems of strict-feedback form is considered based on nonlinear sampled-data control and consensus control theories. As a practical application of the proposed design method, output feedback consensus control for sampled-data fully actuated ships is also discussed.     

Continuous output feedback stabilization for nonlinear systems based on sampled and delayed output measurements

This paper addresses the problem of output feedback stabilization for nonlinear systems with sampled and delayed output measurements. Firstly, sufficient conditions are proposed to ensure that a class of hybrid systems are globally exponentially stable. Then, based on the sufficient conditions and a dedicated construction continuous observer, an output feedback control law is presented to globally exponentially stabilize the nonlinear systems. The output feedback stabilizer is continuous and hybrid, and can be derived without discretization. The maximum allowable sampling period and the maximum delay are also given. At last, a numerical example is provided to illustrate the design methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Quantised and sampled output feedback for nonlinear systems

In this paper we consider the analysis and design of an output feedback controller for a perturbed nonlinear system in which the output is sampled and quantised. Using the attractive ellipsoid method, which is based on Lyapunov analysis techniques, together with the relaxation of a nonlinear optimisation problem, sufficient conditions for the design of a robust control law are obtained. Since the original conditions result in nonlinear matrix inequalities, a numerical algorithm to obtain the solution is presented. The obtained control ensures that the trajectories of the closed-loop system will converge to a minimal (in a sense to be made specific) ellipsoidal region. Finally, numerical examples are presented in order to illustrate the applicability of the proposed design method.     

A partial parameterization of nonlinear output feedback controllers for saturated linear systems

This paper addresses the stabilization problem of linear systems subject to input saturation. The major purpose is to introduce nonlinearity into control laws so as to expand the design freedom for performance enhancement. To this end, a new approach is developed which involves a partial differential matrix inequality (PDMI). A class of stabilizing feedback laws is explicitly obtained by solving this PDMI analytically and the feedback laws are parameterized by a nonlinear function. Further, it is revealed that any linear observer can be used to realize the output feedback stabilization. Numerical examples, including the seek control of a hard disk drive, show that the introduced nonlinearity does contribute to the improvement of system performance. The application to integral control is also discussed.     

Robust tracking control for a class of MIMO nonlinear systems with measurable output feedback

This paper proposes a robust output feedback controller for a class of nonlinear systems to track a desired trajectory. Our main goal is to ensure the global input-to-state stability (ISS) property of the tracking error nonlinear dynamics with respect to the unknown structural system uncertainties and external disturbances. Our approach consists of constructing a nonlinear observer to reconstruct the unavailable states, and then designing a discontinuous controller using a back-stepping like design procedure to ensure the ISS property. The observer design is realized through state transformation and there is only one parameter to be determined. Through solving a Hamilton–Jacoby inequality, the nonlinear control law for the first subsystem specifies a nonlinear switching surface. By virtue of nonlinear control for the first subsystem, the resulting sliding manifold in the sliding phase possesses the desired ISS property and to certain extent the optimality. Associated with the new switching surface, the sliding mode control is applied to the second subsystem to accomplish the tracking task. As a result, the tracking error is bounded and the ISS property of the whole system can be ensured while the internal stability is also achieved. Finally, an example is presented to show the effectiveness of the proposed scheme. Copyright © 2007 John Wiley & Sons, Ltd.     

Design of reduced-order observers for nonlinear sampled-data strict-feedback systems with actuator dynamics and disturbances

We design reduced-order observers for nonlinear sampled-data strict-feedback systems with actuator dynamics and disturbances. First, we use the property of the Euler model of sampled-data systems and the structure of discrete-time observers to design reduced-order observers of the Euler model. Then, we show that the designed observers are semiglobal and practical in T for the exact model. We also give both numerical and practical examples to illustrate the proposed design of reduced-order observers.     

Observers for discrete-time nonlinear systems

The problem of observers for discrete-time nonlinear systems has been considered and a simple, easy-to-implement algorithm is given whose convergence properties are guaranteed for autonomous and forced systems. Some numerical examples show the effectiveness of the proposed observer.     

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.     

On the state observation and output feedback problems for nonlinear uncertain dynamic systems

In this paper, we examine the problems of state observation and state trajectory control by output feedback for the class of non-linear systems in [3,11]. We begin by modifying a known discontinuous variable structure type observer into a continuous type observer that guarantees the observation error is Globally Exponentially Stable (GES). We then modify a known discontinuous variable structure type output feedback controller into continuous type output feedback controller that forces the state to the origin in the GES sense. Specific time-varying bounds on the observation error and the state trajectory are also developed; revealing how the corresponding observer or control parameters can be adjusted to improve the system performance.     

Finite-time output feedback stabilization of high-order uncertain nonlinear systems

This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.     

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.     

不确定非线性系统的鲁棒自适应输出反馈控制

基于自适应非线性阻尼,提出一种鲁棒自适应输出反馈控制方法。该方法适用于带有未建模动态、未知非线性、有界扰动、未知非线性参数和不确定控制系数的多输入多输出非线性系统。理论证明,在一定的假设条件下,该方法能保证闭环系统所有动态信号有界;不论有多少不确定非线性参数、多高阶的非线性系统,只需要一个自适应控制参数和观察参数;而且通过选择适当的控制器和观测器参数,能使控制误差和估计误差达到任意小。仿真结果表明了所提出方法的有效性。     

Flocking with connectivity preservation for disturbed nonlinear multi-agent systems by output feedback

This paper considers the problem of flocking with connectivity preservation for a class of disturbed nonlinear multi-agent systems. In order to deal with the nonlinearities in the dynamic of all agents, some auxiliary variables are introduced into the state observer for stability analysis. By proposing a bounded potential function and using adaptive theory, a novel output feedback consensus algorithm is developed to guarantee that the states of all agents achieve flocking with connectivity preservation.     

Global finite-time output feedback stabilisation for a class of uncertain nontriangular nonlinear systems

This article addresses the problem of global finite-time output feedback stabilisation for a class of nonlinear systems in nontriangular form with an unknown output function. Since the output function is not precisely known, traditional observers based on the output is not implementable. We first design a state observer and use the observer states to construct a controller to globally stabilise the nominal system without the perturbing nonlinearities. Then, we apply the homogeneous domination approach to design a scaled homogeneous observer and controller with an appropriate choice of gain to render the nonlinear system globally finite-time stable.     

带传输滞后的离散系统的观测器及输出动态反馈

针对带输出传输滞后的线性离散系统,讨论了其状态观测器设计问题.利用滞后输出信息,给出了状态观测器的设计方法,并得到状态观测器存在的充要条件,进而设计出基于观测器的输出动态反馈控制器,证明了闭环系统满足极点分离原理.数值仿真验证了所提出方法的有效性.     

Global output feedback control for a class of nonlinear systems with unknown homogenous growth condition

This paper investigates the problem of global control for a class of nonlinear systems via output feedback. The system nonlinearities satisfy the homogenous growth condition with unknown growth rate. First, a homogenous observer is constructed for estimating the system state. Then, two novel dynamic gains are presented to deal with the unknown growth rate. Subsequently, by adding a power integrator technique, a dynamic output feedback controller is designed to guarantee that all the signals of the closed‐loop system are bounded and the system states globally converge to origin. Finally, an example is provided to illustrate the validity of the proposed control scheme.     

Leader-follower consensus control of Lipschitz nonlinear systems by output feedback

This paper deals with the leader-follower consensus problem of Lipschitz nonlinear systems under fixed directed communication networks. Both state and output feedback control are proposed based on state and output measurements of neighbouring agents, respectively. Laplacian matrix features are explored for the stability analysis, and the sufficient conditions are derived to solve the consensus problem. Finally, simulation results are included to demonstrate the effectiveness of the output-based consensus controller.     

Semi‐global stabilization via linear sampled‐data output feedback for a class of uncertain nonlinear systems

This paper develops a systematic design scheme to construct a linear sampled‐data output feedback controller that semi‐globally asymptotically stabilizes a class of uncertain systems with both higher‐order and linear growth nonlinearities. To deal with the uncertain coefficients in the systems, a robust state feedback stabilizer and a reduced‐order sampled‐data observer, both in the linear form, are constructed and then integrated together. The semi‐global attractivity and local stability are delicately proved by carefully selecting a scaling gain using the output feedback domination approach and a sampling period sufficiently small to restrain the state growth under a zero‐order‐holder input. Copyright © 2014 John Wiley & Sons, Ltd.