Output feedback stabilisation for a cascaded wave PDE-ODE system subject to boundary control matched disturbance

In this paper, we consider output feedback stabilisation for a wave PDE-ODE system with Dirichlet boundary interconnection and external disturbance flowing the control end. We first design a variable structure unknown input type state observer which is shown to be exponentially convergent. Then, we estimate the disturbance in terms of the estimated state, an idea from active disturbance rejection control. These enable us to design an observer-based output feedback stabilising control to this uncertain PDE-ODE system.     

Observer-based H-infinity output feedback control with feedback gain and observer gain variations for Delta operator system

Considering that the controller feedback gain and the observer gain are of additive norm-bounded variations, a design method of observer-based H-infinity output feedback controller for uncertain Delta operator systems is proposed in this paper. A sufficient condition of such controllers is presented in linear matrix inequality （LMI） forms. A numerical example is then given to illustrate the effectiveness of this method, that is, the obtained controller guarantees the closed-loop system asymptotically stable and the expected H-infinity performance even if the controller feedback gain and the observer gain are varied.     

A note to output feedback adaptive control for uncertain system with static nonlinearity

The problem of control design for a system represented as linear stationary and static nonlinear parts is considered. It is assumed that the linear part is unknown and strictly minimum phase. The nonlinear part is known inaccurately, it is irreducible to an input of the linear block, and generally does not satisfy sector restrictions. An adaptive regulator ensuring asymptotic stability is synthesized. The output of a control system, but not its derivatives, is used as a measured variable.     

Discrete-time neural network output feedback control of nonlinear discrete-time systems in non-strict form

An adaptive neural network (NN)-based output feedback controller is proposed to deliver a desired tracking performance for a class of discrete-time nonlinear systems, which are represented in non-strict feedback form. The NN backstepping approach is utilized to design the adaptive output feedback controller consisting of: (1) an NN observer to estimate the system states and (2) two NNs to generate the virtual and actual control inputs, respectively. The non-causal problem encountered during the control design is overcome by using a dynamic NN which is constructed through a feedforward NN with a novel weight tuning law. The separation principle is relaxed, persistency of excitation condition (PE) is not needed and certainty equivalence principle is not used. The uniformly ultimate boundedness (UUB) of the closed-loop tracking error, the state estimation errors and the NN weight estimates is demonstrated. Though the proposed work is applicable for second order nonlinear discrete-time systems expressed in non-strict feedback form, the proposed controller design can be easily extendable to an nth order nonlinear discrete-time system.     

State feedback and estimation of well-posed systems

The class of well-posed systems includes many systems modeled by partial differential equations with boundary control and point sensing as well as many other systems with possibly unbounded control and observation. The closed-loop system created by applying state-feedback to any well-posed system is well-posed. A state-space realization of the closed loop is derived. A similar result holds for state estimation of a well-posed system. Also, the classical state-feedback/estimator structure extends to well-posed systems. In the final section state-space realizations for a doubly coprime factorization for well-posed systems are derived.This research was partially supported by the Fields Institute, which is funded by grants from the Ontario Ministry of Colleges and Universities and the Natural Sciences and Engineering Research Council of Canada, and by a grant from the Natural Sciences and Engineering Research Council of Canada.     

Economic model predictive control with triggered evaluations: State and output feedback

In this work, we focus on the computation load reduction in the optimization of economic model predictive control (EMPC) for nonlinear systems. Specifically, event-based triggering approach is adopted to significantly reduce the number of evaluations of the EMPC. First, we consider the case that state feedback is available and design a triggering condition based on the difference between the actual system state and its predicted value. At a sampling time, if the triggering condition is satisfied, the EMPC is re-evaluated. Subsequently, we consider the case that only output feedback is available. In this case, a robust moving horizon estimator is used to reconstruct the state information from output measurements and the corresponding triggering condition is based on the difference between the measured and predicted output as well as its time derivatives. For both cases, the EMPC is redesigned to account for potential open-loop operations. Sufficient conditions that ensure the closed-loop stability are provided for both cases. A chemical process is used to illustrate the effectiveness of the proposed designs.     

Robust nonlinear output feedback control for brake by wire control systems

This work proposes a nonlinear output feedback control law for active braking control systems. The control law guarantees bounded control action and can cope also with input constraints. Moreover, the closed-loop system properties are such that the control algorithm allows to detect—without the need of a friction estimator—if the closed-loop system is operating in the unstable region of the friction curve, thereby allowing to enhance both braking performance and safety. The design is performed via Lyapunov-based methods and its effectiveness is assessed via simulations on a multibody vehicle simulator.     

Quantized output feedback control for networked control systems

This paper addresses the problem of output feedback control for networked control systems (NCSs) with limited communication capacity. Firstly, we propose a new model to describe the non-ideal network conditions and the input/output state quantization of the NCSs in a unified framework. Secondly, based on our newly proposed model and an improved separation lemma, the observer-based controller is developed for the asymptotical stabilization of the NCSs, which are shown in terms of nonlinear matrices inequalities. The nonlinear problems can be computed through solving a convex optimization problems, and the observed and controller gains could be derived by solving a set of linear matrix inequalities. Thirdly, two simulation examples are given to demonstrate the effectiveness of the proposed method.     

Global sampled-data output feedback control for a class of feedforward nonlinear systems

This paper investigates the problem of global output feedback stabilization for a class of feedforward nonlinear systems via linear sampled-data control. To solve the problem, we first construct a linear sampled-data observer and controller. Then, a scaling gain is introduced into the proposed observer and controller. Finally, we use the sampled-data output feedback domination approach to find the explicit formula for choosing the scaling gain and the sampling period which renders the closed-loop system globally asymptotically stable. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.     

Adaptive output feedback control for nonlinear time-delay systems using neural network

This paper extends the adaptive neural network （NN） control approaches to a class of unknown output feedback nonlinear time-delay systems. An adaptive output feedback NN tracking controller is designed by backstepping technique. NNs are used to approximate unknown functions dependent on time delay, Delay-dependent filters are introduced for state estimation. The domination method is used to deal with the smooth time-delay basis functions. The adaptive bounding technique is employed to estimate the upper bound of the NN approximation errors. Based on Lyapunov- Krasovskii functional, the semi-global uniform ultimate boundedness of all the signals in the closed-loop system is proved, The feasibility is investigated by two illustrative simulation examples.     

非线性不确定系统的直接自适应输出反馈模糊控制

针对一类单输入单输出非线性不确定系统，基于状态观测器并结合自适应模糊系统和滑模控制，提出一种稳定的直接自适应模糊输出反馈控制算法。该算法不需要系统状态可测的条件，并能保证闭环系统稳定。仿真结果表明了该方法的有效性。     

Adaptive output feedback control methodology applicable to non-minimum phase nonlinear systems

An adaptive output feedback control methodology is developed for a class of uncertain multi-input multi-output nonlinear systems using linearly parameterized neural networks. The methodology can be applied to non-minimum phase systems if the non-minimum phase zeros are modeled to a sufficient accuracy. The control architecture is comprised of a linear controller and a neural network. The neural network operates over a tapped delay line of memory units, comprised of the system's input/output signals. The adaptive laws for the neural-network weights employ a linear observer of the nominal system's error dynamics. Ultimate boundedness of the error signals is shown through Lyapunov's direct method. Simulations of an inverted pendulum on a cart illustrate the theoretical results.     

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.     

Adaptive learning control of linear systems by output error feedback

This paper addresses the problem of designing an output error feedback tracking control for single-input, single-output uncertain linear systems when the reference output signal is smooth and periodic with known period T. The considered systems are required to be observable, minimum phase, with known relative degree and known high frequency gain sign. By developing in Fourier series expansion a suitable unknown periodic input reference signal, an output error feedback adaptive learning control is designed which ‘learns’ the input reference signal by identifying its Fourier coefficients: bounded closed-loop signals and global exponential tracking of both the input and the output reference signals are obtained when the Fourier series expansion is finite, while global exponential convergence of the input and output tracking errors into arbitrarily small residual sets is achieved otherwise. The structure of the proposed controller depends only on the relative degree, the reference signal period, the high frequency gain sign and the number of estimated Fourier coefficients.     

A gradient flow approach to on-line robust pole assignment for synthesizing output feedback control systems

Pole assignment is a basic design method for synthesis of feedback control systems. In this paper, a gradient flow approach is presented for robust pole assignment in synthesizing output feedback control systems. The proposed approach is shown to be capable of synthesizing linear output feedback control systems via on-line robust pole assignment. Convergence of the gradient flow can be guaranteed. Moreover, with appropriate design parameters the gradient flow converges exponentially to an optimal solution to the robust pole assignment problem and the closed-loop control system based on the gradient flow is globally exponentially stable. These desired properties make it possible to apply the proposed approach to slowly time-varying linear control systems. Simulation results are shown to demonstrate the effectiveness and advantages of the proposed approach.     

A gradient flow approach to decentralised output feedback optimal control

This paper visits the quadratic optimal control problem of decentralised control systems via static output feedback. A gradient flow approach is introduced as a tool to compute the optimal output feedback gain. Several nice properties are revealed concerning the convergence of the gain matrix along the trajectory of an ordinary differential equation obtained from the gradient of objective cost, i.e. the objective cost is decreasing along this trajectory. If the equilibrium points are isolated, the convergence can be guaranteed. A simulation example is given to illustrate the effectiveness of this approach.     

Semi‐global output feedback tracking control for fully actuated ships

An output feedback trajectory tracking controller for a kind of 3 degrees of freedom (DOF) ship motion nonlinear model is designed. The closed‐loop control system is proven to be uniformly semi‐globally exponential stable with a separate stability result for the observer by applying nonlinear cascaded system theory. Simulation results on a model ship, Cybership II, are presented to validate the proposed control scheme. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society