Output regulation problem for a class of regular hyperbolic systems

This paper investigates the output regulation problem for a class of regular first-order hyperbolic partial differential equation (PDE) systems. A state feedback and an error feedback regulator are considered to force the output of the hyperbolic PDE plant to track a periodic reference trajectory generated by a neutrally stable exosystem. A new explanation is given to extend the results in the literature to solve the regulation problem associated with the first-order hyperbolic PDE systems. Moreover, in order to provide the closed-loop stability condition for the solvability of the regulator problems, the design of stabilising feedback gain and its dual problem design of stabilising output injection gain are considered in this paper. This paper develops an easy method to obtain an adjustable stabilising feedback gain and stabilising output injection gain with the aid of the operator Riccati equation.     

Adaptive Learning Control of Nonlinear Systems by Output Error Feedback

This paper addresses the problem of designing an output error feedback control for single-input, single-output nonlinear systems with uncertain, smooth, output-dependent nonlinearities whose local Lipschitz constants are known. The considered systems are required to be observable, minimum phase with known relative degree and known high frequency gain sign: linear systems are included. The reference output signal is assumed to be smooth and periodic with known period. By developing in Fourier series expansion a suitable periodic input reference signal, an output error feedback adaptive learning control is designed which ldquolearnsrdquo the input reference signal by identifying its Fourier coefficients: bounded closed loop signals and exponential tracking of both input and output reference signals are obtained when the Fourier series expansion is finite, while arbitrary small tracking errors are exponentially achieved otherwise. The resulting control is not model based, is independent of the system order and depends only on the relative degree, the reference signal period and the high frequency gain sign.     

Practical Output Regulation of Uncertain Strict‐Feedback Form Systems

In this paper, an output feedback control is proposed to solve the practical output regulation problem of a class of nonlinear systems. In the first step of the design procedure, two sets of coordinate transformations are used to convert the output regulation problem of the system in the strict‐feedback form into the regulation problem of the transformed system in the uncertain normal form. Then, for the resulting system, a state feedback in the cast of nested sliding mode control is designed. Finally, by using the nonlinear separation principle, the output feedback controller is achieved by substituting the estimated states, resulting from the high‐gain observer, instead of real states. It can be shown that the states of the closed‐loop system are ultimately bounded. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Output feedback decoupling of multivariable systems

Necessary and sufficient conditions for output feedback decoupilng of linear time-invariant multivariable systems into single input-multioutput subsystems are derived in frequency domain. The conditions imply a new constructive method for determining a constant gain output feedback matrix and some of its elements can be freely chosen to reassign the closed-loop poles.     

Global Robust Output Regulation by State Feedback for Strict Feedforward Systems

This note studies the global robust output regulation problem by state feedback for strict feedforward systems. By utilizing the general framework for tackling the output regulation problem , the output regulation problem is converted into a global robust stabilization problem for a class of feedforward systems that is subject to both time-varying static and dynamic uncertainties. Then the stabilization problem is solved by using a small gain based bottom-up recursive design procedure.     

混合频小增益动态输出反馈控制综合

本文主要研究线性连续时间系统经动态输出反馈的混合频小增益控制综合问题. 提出了一种使相应闭环系统渐近稳定并满足有限频范围和全频范围小增益条件要求的动态输出反馈控制器的新设计方法. 设计条件以一系列线性矩阵不等式的解的形式给出. 最后, 给出一个数值例子来说明设计程序以及这种方法对比于现有方法的优势.     

Output feedback control for MIMO non-linear systems with unknown sign of the high frequency gain matrix

The paper presents a new output feedback adaptive control scheme for multi-input and multi-output (MIMO) non-linear systems whose non-linear terms depend only on the output variable based on the backstepping approach with vector form. The assumption on the prior knowledge of the high frequency gain matrix in existing results is reduced and the new required condition for the high frequency gain matrix can be easily checked for certain plants so that the proposed method is widely applicable. This control scheme guarantees the global stability of the closed-loop systems and makes the tracking error be arbitrary small. A simulation example is included to demonstrate the proposed algorithm.     

Uniform Practical Nonlinear Output Regulation

In this paper, we present a solution to the problem of asymptotic and practical semiglobal regulation by output feedback for nonlinear systems. A key feature of the proposed approach is that practical regulation is achieved uniformly with respect to the dimension of the internal model and to the gain of the stabilizer near the zero error manifold. This property renders the approach interesting for a number of real cases by bridging the gap between output regulation theory and advanced engineering applications. Simulation results regarding meaningful control problems are also presented.      

Output Regulation Of A Class Of Singular Nonlinear Systems With The Normal Output Feedback Controller

Existing results for output regulation of singular nonlinear systems via normal output feedback control require the normalizability assumption. In this paper, we will show that, for a large class of singular nonlinear systems, it is possible to construct a normal output feedback control to solve the regulation problem without the normalizability assumption. The major result is illustrated by an example.     

经输出动态反馈的非线性奇异系统输出调节问题

讨论非线性奇异系统的输出调节问题,在没有可正常化的假设条件下,给出了降阶的 正常状态空间的输出动态反馈控制器的设计,并导出了这种控制器存在的充分必要条件.     

Output feedback regulation of a class of high‐order feedforward nonlinear systems with unknown time‐varying delay in the input under measurement sensitivity

An output feedback regulation problem is considered for a class of high‐order feedforward nonlinear systems with delay in the input under measurement sensitivity. The key features are that the considered systems have uncertain high‐order feedforward nonlinearity and unknown time‐varying delay in the input. Then, the controller is supposed to be engaged where the output feedback information is distorted by measurement sensitivity. Our proposed controller has two gains—fixed and adaptive gains. The fixed gain is first designed to compensate for measurement sensitivity, and the adaptive gain is next utilized to dominate both unknown input delay and uncertain high‐order feedforward nonlinearity. Simulation examples are given to highlight the advantage of our control scheme.     

Semi‐Global Robust Output Regulation for A Class of Singular Nonlinear Systems with Unknown Algebraic Equations

This paper considers semi‐global robust output regulation problem for a class of singular nonlinear systems whose algebraic equations are not precisely known. Since the algebraic equations are not known, the output regulation problem of singular nonlinear systems cannot be solved by directly reducing the singular nonlinear system into a normal nonlinear system. Based on internal model principle, we convert the robust output regulation problem of singular nonlinear systems into a robust stabilization problem of an augmented singular nonlinear system. The augmented singular nonlinear system is also with unknown algebraic equations. However, without transforming the singular nonlinear system into a normal nonlinear system, it is shown that the augmented singular nonlinear system can be semi‐globally stabilized by a high gain output feedback control law under some reasonable assumptions. Moreover, the semi‐global stabilization control law of the augmented singular nonlinear systems also solves the semi‐global robust output regulation problem of the original singular nonlinear system.     

具有时滞的Lurie型组合系统的分散输出反馈镇定

通过构造一比较系统,将Lurie型组合系统的稳定性问题转化为讨论维数较低的比较系统的稳定性问题,并利用M矩阵特性导出比较系统稳定的一个充分条件;为求取输出反馈增益,建立等价的稳定条件的QLMI表示形式.这一方法的特点是使大系统的稳定控制器设计的复杂度保持在子系统一级的水平上,给出的实例说明算法在实际工程应用中是有效的.     

Linear output feedback with dynamic high gain for nonlinear systems

We propose a linear output feedback with dynamic high gain for global regulation of a class of nonlinear systems. The uncertain nonlinearities are assumed to be bounded by a polynomial function of the output multiplied by unmeasured states. The crucial point made in this paper is that a linear observer-based output feedback can globally regulate an equilibrium of strongly nonlinear systems, provided that a single high gain is appropriately tuned.     

Output regulation of uncertain nonlinear systems with nonlinear exosystems

An adaptive control algorithm is proposed for output regulation of uncertain nonlinear systems in output feedback form under disturbances generated from nonlinear exosystems. A new nonlinear internal model is proposed to generate the desired input term for suppression of the disturbances. The proposed internal model design is based on boundedness of the disturbance, high gain design and saturation. It is capable to tackle disturbances in any specified initial conditions. Some uncertainties in the systems are allowed, provided that they do not affect the desired feedforward control term, and they are tackled by using nonlinear dominant functions and an adaptive control coefficient. The proposed control algorithm ensures the global convergence of the state variables to the invariant manifold, which implies that the measurement or the tracking error approaches to zero asymptotically.     

一类非线性系统的间接自适应输出反馈模糊控制

针对一类未知非线性系统,提出一种输出反馈控制方法。首先在假设系统状态已知的情况下设计状态反馈控制器,实现跟踪性能。然后在系统状态不完全可测的情况下,通过设计高增益观测器对系统的状态进行估计,实现输出反馈控制器设计。最后证明所设计的输出反馈控制器可获得状态反馈控制器所取得的最大最小问题的跟踪性能。     

数据驱动的保证收敛速率最优输出调节

针对具有外部系统扰动的线性离散时间系统的输出调节问题,提出了可保证收敛速率的数据驱动最优输出调节方法,包括状态可在线测量系统的基于状态反馈的算法,与状态不可在线测量系统的基于输出反馈的算法.首先,该问题被分解为输出调节方程求解问题与反馈控制律设计问题,基于输出调节方程的解,通过引入收敛速率参数,建立了可保证收敛速率的最...     

非线性系统的模糊自适应输出反馈控制

针对一类未知非线性系统,考虑系统状态不完全可测的情况,利用Lyapunov综合方法设计了一种基于高增益观测器的模糊鲁棒自适应输出反馈控制器,并证明在一定条件下,所设计的输出反馈控制器能获得状态反馈控制器的性能。     

Output regulation of time-varying systems

In this paper the output regulation problem for linear time-varying systems is considered. Replacing the regulator equation by a regulator differential equation we give a necessary and sufficient condition for the problem to be solvable. As in the time-invariant case we first solve the output regulation problem by state feedback and obtain the required condition. Then with the aid of observers we show that the same condition solves the general problem with measurement feedback. We then consider the classes of almost periodic and periodic systems and refine the main results. A simple example of an almost periodic system and simulation results are given to illustrate the theory.     

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.