A necessary and sufficient condition for input-to-state stability of quantised feedback systems

For zooming-out/in method used in the design of quantised feedback systems, the property of the duration of zoom-out mode (this duration is defined as capture time) is essential to input-to-state stability (ISS) of systems. This paper shows that a necessary and sufficient condition of achieving ISS with respect to external disturbances for quantised feedback systems is that capture time under the proposed coding scheme is uniformly bounded. It further shows that the coding scheme under which capture time is only bounded and not uniformly bounded cannot guarantee ISS of systems. A coding scheme is designed for uniformly bounded capture time and therefore achieves ISS of systems.     

Decentralised robust stabilisation of uncertain large-scale interconnected time-delay systems with unknown upper bounds of uncertainties

The problem of decentralised robust stabilisation is considered for a class of uncertain large-scale time-delay interconnected dynamical systems. In the paper, the upper bounds of delayed state perturbations, uncertainties, interconnection terms, and external disturbances are assumed to be completely unknown, and the delays are assumed to be any non-negative constants. For such a class of uncertain large-scale time-delay interconnected systems, a new method is presented whereby a class of adaptation-free decentralised local robust state feedback controllers can be constructed. In addition, it is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed to be uniformly ultimately bounded. Finally, as an application to the practical mechanical systems, some simulations of a numerical example are provided to demonstrate the validity of the theoretical results.     

Decentralised adaptive robust control of uncertain large-scale interconnected systems with multiple time-varying delays

The problem of decentralised adaptive robust stabilisation is considered for a class of uncertain large-scale time-delay interconnected dynamical systems. It is assumed that the upper bounds of the uncertainties, interconnection terms and external disturbances are unknown, and that the time-varying delays are any nonnegative continuous and bounded functions, and do not require that their derivatives have to be less than one. For such a class of uncertain large-scale time-delay interconnected systems, a new method is presented whereby a class of continuous memoryless decentralised local adaptive robust state feedback controllers is proposed. It is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. In addition, since the proposed decentralised local adaptive robust state feedback controllers are completely independent of time delays, the results obtained in this article may also be applicable to a class of large-scale interconnected dynamical systems with uncertain time delays. Finally, a numerical example is given to demonstrate the validity of the results.     

Adaptive output feedback tracking control for a class of uncertain nonlinear systems using neural networks.

This correspondence addresses the problem of designing robust tracking control for a class of uncertain nonlinear MIMO second-order systems. An adaptive neural-network-based output feedback tracking controller is constructed such that all the states and signals involved are uniformly bounded and the tracking error is uniformly ultimately bounded. Only the output measurement is required for feedback. The implementation of the neural network basis functions depends only on the desired reference trajectory. Therefore, the intelligent adaptive output feedback controller developed here possesses the properties of computational simplicity and easy implementation. A simulation example of controlling mass-spring-damper mechanical systems is made to confirm the effectiveness and performance of the developed control scheme.     

An internal model principle is necessary and sufficient for linear output synchronization

Output synchronization of a network of heterogeneous linear state–space models under time-varying and directed interconnection structures is investigated. It is shown that, assuming stabilizability and detectability of the individual systems and imposing very mild connectedness assumptions on the interconnection structure, an internal model requirement is necessary and sufficient for synchronizability of the network to polynomially bounded trajectories. The resulting dynamic feedback couplings can be interpreted as a generalization of existing methods for identical linear systems.     

Contraction-based stabilisation of nonlinear singularly perturbed systems and application to high gain feedback

Recent development of contraction theory-based analysis has opened the door for inspecting differential behaviour of singularly perturbed systems. In this paper, a contraction theory-based framework is proposed for stabilisation of singularly perturbed systems. The primary objective is to design a feedback controller to achieve bounded tracking error for both standard and non-standard singularly perturbed systems. This framework provides relaxation over traditional quadratic Lyapunov-based method as there is no need to satisfy interconnection conditions during controller design algorithm. Moreover, the stability bound does not depend on smallness of singularly perturbed parameter and robust to additive bounded uncertainties. Combined with high gain scaling, the proposed technique is shown to assure contraction of approximate feedback linearisable systems. These findings extend the class of nonlinear systems which can be made contracting.     

String stability of interconnected systems

Introduces the notion of string stability of a countably infinite interconnection of a class of nonlinear systems. Intuitively, string stability implies uniform boundedness of all the states of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded. It is well known that the input output gain of all the subsystems less than unity guarantees that the interconnected system is input-output stable. The authors derive sufficient (“weak coupling”) conditions which guarantee the asymptotic string stability of a class of interconnected systems. Under the same “weak coupling” conditions, string-stable interconnected systems remain string stable in the presence of small structural/singular perturbations. In the presence of parameter mismatch, these “weak coupling” conditions ensure that the states of all the subsystems are all uniformly bounded when a gradient-based parameter adaptation law is used and that the states of all the systems go to zero asymptotically     

Control of large scale interconnected systems with input and state delays using decentralized adaptive state observers

This paper investigates the problem of decentralized model reference adaptive control (MRAC) for a class of large scale interconnected systems with both state and input delays. The upper bounds of the interconnection terms are considered to be unknown. Time varying delays in the nonlinear interconnection terms are bounded and nonnegative continuous functions and their derivatives are not necessarily less than one. For exact prediction, a decentralized adaptive state observer is designed and a nested predictor based approach is established to predict the future states of the input delay compensation. It is shown that the solutions of uncertain large‐scale time‐delay interconnected systems converge uniformly exponentially to a desired small ball. The effectiveness of the proposed approaches is illustrated by two examples.     

基于双增益方法的不确定非线性系统的输出反馈调节问题

研究一类具有多种不确定性的非线性系统的全局输出反馈调节问题.所研究系统的一个显著特点是非线性项被未知增长率和多项式形式的输出函数的乘积界定,难点是在输出受不确定参数摄动的情况下如何抑制非线性项.提出一种改进的双增益方法来设计输出反馈控制器,可以确保闭环系统所有信号全局一致有界并且原系统状态收敛到零.最后,采用质量弹簧机械系统的输出反馈镇定问题来说明控制策略的有效性.     

A general boundedness result for interconnected nonlinear systems

A general boundedness result is given for the feedback interconnection of two nonlinear stable systems. Using the same input-output approach as in the standard small-gain theorem, the sufficient condition given here relaxes the finite-gain stability assumption and does not require a boundedness result for all possible bounded exogenous inputs. This condition has a simple graphical interpretation that utilizes graphs of bounding functions     

Decentralized robust H<Subscript>∞</Subscript> output feedback control for value bounded uncertain large-scale interconnected systems

In this paper, decentralized robust H_∞ output feedback control problem for large-scale interconnected system with value bounded uncertainties in the state, control input and interconnection matrices is investigated. A new bounded real lemma for the large-scale interconnected systems is derived by Lyapunov stability theory and linear matrix inequality method. Based on the new bounded real lemma, a sufficient condition expressed as matrix inequalities for the existence of a decentralized robust H_∞ output feedback controller is obtained. The controller which enables the closed-loop large-scale system robust stable and satisfies the given H_∞ performance is designed through a homotopy iterative method. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Observer-based adaptive neural dynamic surface control for a class of non-strict-feedback stochastic nonlinear systems

The problem of adaptive output feedback stabilisation is addressed for a more general class of non-strict-feedback stochastic nonlinear systems in this paper. The neural network (NN) approximation and the variable separation technique are utilised to deal with the unknown subsystem functions with the whole states. Based on the design of a simple input-driven observer, an adaptive NN output feedback controller which contains only one parameter to be updated is developed for such systems by using the dynamic surface control method. The proposed control scheme ensures that all signals in the closed-loop systems are bounded in probability and the error signals remain semi-globally uniformly ultimately bounded in fourth moment (or mean square). Two simulation examples are given to illustrate the effectiveness of the proposed control design.     

Design of robust controllers for time-delay systems

The problem of stabilizing linear dynamical time-delay systems subject to bounded uncertainties is investigated. Two memoryless feedback controllers are considered. It is established that when the matching conditions are met and certain bounding relations are satisfied, then the linear controller renders the zero-response of the system asymptotically stable. Saturation-type controllers are shown to guarantee that all system responses are uniformly ultimately bounded     

Event‐triggered control for discrete‐time linear systems subject to bounded disturbance

This paper considers event‐triggering controller design for directly observable discrete‐time linear systems subject to bounded disturbances. The main control objective is diminishing the influence aroused by the disturbances despite a reduction of the communication. Criteria are given to design feedback controllers in order to guarantee that systems are uniformly ultimately bounded in an ellipsoidal‐positive invariant set, which is used as an estimate of control performance for disturbance rejection. An optimization for minimizing the ellipsoidal‐positive invariant set is achieved by synthesizing the feedback control gain and the given event‐triggering conditions in LMIs. The effectiveness and applicability of the controller are illustrated by simulations and experimental implementations. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive output feedback control of uncertain nonlinear systems based on dynamic surface control technique

An adaptive output feedback control approach is studied for a class of uncertain nonlinear systems in the parametric output feedback form. Unlike the previous works on the adaptive output feedback control, the problem of ‘explosion of complexity’ of the controller in the conventional backstepping design is overcome in this paper by introducing the dynamic surface control (DSC) technique. In the previous schemes for the DSC technique, the time derivative for the virtual controllers is assumed to be bounded. In this paper, this assumption is removed. It can be proven that the resulting closed‐loop system is stable in the sense that all the signals are semi‐global uniformly ultimately bounded and the system output tracks the reference signal to a bounded compact set. A simulation example is given to verify the effectiveness of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.     

A feedforward–feedback controller for infinite‐dimensional systems and regulation of bounded uniformly continuous signals

We design a controller for infinite‐dimensional linear systems (with bounded control, observation and feedthrough operators) which, under certain assumptions, achieves asymptotic tracking of arbitrary bounded uniformly continuous reference signals in the presence of disturbances. The proposed controller is of feedforward–feedback type: The dynamic feedback part is used to stabilize the closed‐loop system consisting of the plant and the controller, whereas the feedforward part is tuned using the regulator equations to achieve the regulation of desired signals. We also completely solve the regulator equations for SISO systems, and we discuss robustness properties of the proposed controller. A useful feature in our design is that the feedforward part of the controller can be designed independently of the feedback part. This automatically leads to a degree of robustness in the stabilizing part of the controller, which is not present in the existing state feedback controllers solving the same output regulation problem. Copyright © 2006 John Wiley & Sons, Ltd.     

Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems

In this paper, both full state and output feedback adaptive neural network (NN) controllers are presented for a class of strict-feedback discrete-time nonlinear systems. Firstly, Lyapunov-based full-state adaptive NN control is presented via backstepping, which avoids the possible controller singularity problem in adaptive nonlinear control and solves the noncausal problem in the discrete-time backstepping design procedure. After the strict-feedback form is transformed into a cascade form, another relatively simple Lyapunov-based direct output feedback control is developed. The closed-loop systems for both control schemes are proven to be semi-globally uniformly ultimately bounded.     

采用还原方法的不确定关联时滞系统的鲁棒分散镇定

针对一类具有多输入时滞项及互联时滞项的不确定关联系统，提出了系统可鲁棒分散镇定的充分条件，即一组线性矩阵不等式(LMI)有解．系统的不确定性是未知时变且范数有界的，基于还原方法及LMI技术给出系统设计状态反馈分散控制器的方法．该控制器保证闭环系统全局渐近稳定，且设计简单，计算量小，易于工程实现．最后通过仿真例子说明了该方法的有效性．     

Asymptotic stability of controlling uncertain dynamical systems

Asymptotic stabilization of general uncertain dynamical systems is investigated. A new class of continuous feedback controls is proposed to guarantee asymptotic stability for any uncertain systems whose nominal system is uniformly asymptotically stable. The analysis is based on a new theoretical result on asymptotical stability. The required information about uncertain dynamics in the system is merely that the uncertainties are bounded in euclidean norm by a known function of the system state.