Incremental passivity and output regulation

In this paper we investigate the use of incremental passivity concepts for the design of nonlinear global regulators. For a specific class of systems and exosystems we show how the problem of designing an internal model-based regulator reduces to the design of an output feedback controller rendering the controlled plant incrementally passive. In this framework we present a result for the design of an output feedback controller achieving incremental passivity for a particular class of nonlinear systems.     

Global sampled-data output feedback stabilisation for a class of nonlinear systems with unknown output function

This paper discusses the problem of global sampled-data output feedback stabilisation for a class of nonlinear systems whose output function is unknown. A systematic design scheme is developed to construct a linear output feedback control law in sampled-data form. An explicit formula for the maximum allowable sampling period is computed to guarantee global stability of the uncertain nonlinear systems under the proposed controller with appropriate gains. Two examples are given to demonstrate the effectiveness of the proposed design procedure.     

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.     

输出多采样反馈控制器及系统稳定性

针对由连续被控对象和数字控制器构成的数字控制系统,将现有的线性系统输出多采样线性反馈数字控制器设计方法推广到非线性系统．并相应地研究了非线性输出多采样反馈控制器及摄动非线性系统．给出了这类非线性输出多采样数字控制系统及其摄动系统的稳定性和鲁棒性条件．     

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.     

Global asymptotic tracking for nonminimum‐phase nonlinear systems in output feedback form

The problem of global asymptotic tracking by output feedback is studied for a class of nonminimum‐phase nonlinear systems in output feedback form. It is proved that the problem is solvable by an n‐dimensional output feedback controller under the two conditions: (a) the nonminimum‐phase nonlinear system can be rendered minimum‐phase by a virtual output; and (b) the internal dynamics of the nonlinear system driven by a desired signal and its derivatives has a bounded solution trajectory. With the help of a new coordinate transformation, a constructive method is presented for the design of a dynamic output tracking controller. An example is given to validate the proposed output feedback tracking control scheme.     

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.     

Distributed adaptive output feedback tracking control for a class of uncertain nonlinear multi-agent systems

This paper addresses the distributed output feedback tracking control problem for multi-agent systems with higher order nonlinear non-strict-feedback dynamics and directed communication graphs. The existing works usually design a distributed consensus controller using all the states of each agent, which are often immeasurable, especially in nonlinear systems. In this paper, based only on the relative output between itself and its neighbours, a distributed adaptive consensus control law is proposed for each agent using the backstepping technique and approximation technique of Fourier series (FS) to solve the output feedback tracking control problem of multi-agent systems. The FS structure is taken not only for tracking the unknown nonlinear dynamics but also the unknown derivatives of virtual controllers in the controller design procedure, which can therefore prevent virtual controllers from containing uncertain terms. The projection algorithm is applied to ensure that the estimated parameters remain in some known bounded sets. Lyapunov stability analysis shows that the proposed control law can guarantee that the output of each agent synchronises to the leader with bounded residual errors and that all the signals in the closed-loop system are uniformly ultimately bounded. Simulation results have verified the performance and feasibility of the proposed distributed adaptive control strategy.     

Decentralised output feedback for a class of nonlinear systems via quantised sampled-data control

We design a decentralised observer-based sampled-data controller with quantised output for a class of interconnected nonlinear systems. Instead of quantising the output directly, we quantise the sampled output to avoid sudden jump. It can be proved that by choosing suitable design parameters, global stability of the system is achieved. An example is given to illustrate the effectiveness of the proposed method.     

Adaptive output feedback control for nonholonomic systems with uncertain chained form

The output feedback adaptive control problem is investigated for nonholonomic systems with strongly nonlinear uncertainties and unknown virtual control directions. A nonlinear output feedback switching controller based on the output measurement of the first subsystem is employed in order to make the state scaling effective and ensure the convergence of the system states. The novel observer/estimator is introduced for state and unknown parameter estimates. The integrator backstepping technique by the use of a constructive recursive is applied to the design of the adaptive controller and to overcome the unknown virtual control directions. The simulation result validates the effectiveness of the proposed scheme.     

Adaptive output feedback regulation for a class of uncertain nonlinear systems

In this paper, the problem of global state regulation by output feedback is investigated for a class of uncertain nonlinear systems satisfying some relaxed upper‐triangular‐type condition. Using a linear dynamic gain observer with two dynamic gains and introducing two appropriate change of coordinates, we give a constructive design procedure for the linear‐like output feedback stabilizing controller. It is proved that the proposed controller globally regulates all the states of the uncertain system and maintains global boundedness of the closed‐loop system. An example is provided to demonstrate the effectiveness of the proposed design scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Global output feedback stabilisation of nonlinear time-delay systems with unknown output function

This paper studies the problem of global output feedback stabilisation for a class of nonlinear time-delay systems with the unknown output function. By constructing the appropriate Lyapunov–Krasovskii functional and observer, skillfully combining generalised adding a power integrator technique, sign function and homogeneous domination approach, an output feedback controller is designed to guarantee globally uniformly asymptotical stability of nonlinear time-delay systems with the unknown output function.     

Iterative learning of model reference adaptive controller for uncertain nonlinear systems with only output measurement

In this paper, a model reference adaptive control strategy is used to design an iterative learning controller for a class of repeatable nonlinear systems with uncertain parameters, high relative degree, initial output resetting error, input disturbance and output noise. The class of nonlinear systems should satisfy some differential geometric conditions such that the plant can be transformed via a state transformation into an output feedback canonical form. A suitable error model is derived based on signals filtered from plant input and output. The learning controller compensates for the unknown parameters, uncertainties and nonlinearity via projection type adaptation laws which update control parameters along the iteration domain. It is shown that the internal signals remain bounded for all iterations. The output tracking error will converge to a profile which can be tuned by design parameters and the learning speed is improved if the learning gain is large.     

On output feedback stabilization of Euler-Lagrange systems with nondissipative forces

This paper provides a solution to the problem of output feedback stabilization of systems described by Euler-Lagrange equations perturbed by nondissipative forces. This class of forces appears in some applications where we must take into account the interaction of the system with its environment. The nonlinear dependence on the unmeasurable part of the state and the loss of the fundamental passivity property render most of the existing results on stabilization of nonlinear systems unapplicable to this problem. The technique we use consists of finding a dynamic output feedback controller and a nonlinear change of coordinates such that the closed loop can be decomposed as a cascade of an asymptotically stable system and an input-to-state stable system. This should be contrasted with the well-known passivity-based technique that aims at a feedback interconnection of passive systems. We believe this design methodology to be of potential applicability to other stabilization problems where passivity arguments are unapplicable.     

Global output feedback stabilisation of nonlinear systems with a unifying linear controller structure

We investigate the problem of global stabilisation by linear output feedback for a class of uncertain nonlinear systems with zero-dynamics. Compared with the previous works, new dilation-based assumptions are introduced that allow the system nonlinearities and its bounding functions to be coupled with all the states. The nonlinear systems of this paper can be considered as an extended form of some low triangular and feedforward systems. Dynamic gain scaling technique is applied to the controller design and stability analysis. It is proved that with a unifying linear controller structure and flexible adaptive laws for the observer gain, global stabilisation of the nonlinear systems can be achieved.     

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.     

Semi‐global output feedback control for nonlinear systems with uncertain time‐delay and output function

This paper considers semi‐global output feedback control for more general nonlinear systems with unknown time‐delay and output function whose derivative is unbounded from above. By introducing a new observer and using the backstepping design method and the Razumikhin stability theorem, an output feedback controller is constructed to achieve a semi‐global stability. Copyright © 2016 John Wiley & Sons, Ltd.     

Global output feedback stabilisation of stochastic high-order feedforward nonlinear systems with time-delay

This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.     

Robust output regulation of minimum phase nonlinear systems using conditional servocompensators

We consider the design of a robust continuous sliding mode controller for the output regulation of a class of minimum‐phase nonlinear systems. Previous work has shown how to do this by incorporating a linear servocompensator in the sliding mode design, but the transient performance is degraded when compared to ideal sliding mode control. Extending previous ideas from the design of ‘conditional integrators’ for the case of asymptotically constant references and disturbances, we design the servocompensator as a conditional one that provides servocompensation only inside the boundary layer; achieving asymptotic output regulation, but with improved transient performance. We give both regional as well as semi‐global results for error convergence, and show that the controller can be tuned to recover the performance of an ideal sliding mode control. Copyright © 2005 John Wiley & Sons, Ltd.     

Global output feedback stabilisation for a class of upper triangular stochastic nonlinear systems

This paper investigates the problem of global output feedback stabilisation for a class of upper triangular stochastic nonlinear systems which are neither necessarily feedback linearisable nor affine in the control input. Based on the adding of a power integrator technique and homogeneous domination approach, an output feedback controller is explicitly constructed to ensure that the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability. A simulation example is provided to demonstrate the effectiveness of the design scheme.