基于区间二型T-S模糊模型的网络控制系统的输出反馈预测控制

针对干扰作用下的非线性网络控制系统,给出了带一个自由控制作用的输出反馈预测控制方法.首先,利用区间二型T-S模糊模型描述具有参数不确定性的非线性对象,采用马尔科夫链描述系统中的随机丢包过程,由此建立了丢包网络环境下的非线性网络控制系统的数学模型.然后,通过引入二次有界技术得到了干扰作用下网络控制系统的稳定性描述方法,并在此基础上给出了状态观测器的线性矩阵不等式条件.最后,基于估计状态,通过将无穷时域控制作用参数化为一个自由控制作用加一个线性反馈律得到了输出反馈预测控制方法.论文的特色在于构建了在线更新误差椭圆集合的基本方法,满足了约束条件下输出反馈预测控制保证稳定性的要求.仿真例子验证了所提方法的有效性.     

Robust adaptive control of uncertain non-linear systems using neural networks

This paper presents a robust adaptive output feedback control design method for uncertain non-affine non-linear systems, which does not rely on state estimation. The approach is applicable to systems with unknown but bounded dimensions and with known relative degree. A neural network is employed to approximate the unknown modelling error. In fact, a neural network is considered to approximate and adaptively make ineffective unknown plant non-linearities. An adaptive law for the weights in the hidden layer and the output layer of the neural network are also established so that the entire closed-loop system is stable in the sense of Lyapunov. Moreover, the robustness of the system against the approximation error of neural network is achieved with the aid of an additional adaptive robustifying control term. In addition, the tracking error is guaranteed to be uniformly and asymptotically stable, rather than uniformly ultimately bounded, by using this additional control term. The proposed control algorithm is relatively straightforward and no restrictive conditions on the design parameters for achieving the systems stability are required. The effectiveness of the proposed scheme is shown through simulations of a non-affine non-linear system with unmodelled dynamics, and is compared with a second-sliding mode controller.     

Robust output tracking for non-linear systems

The problem of output tracking for a single-input single-output non-linear system in the presence of uncertainties is studied. The notions relative degree and minimum-phase for non-linear systems are reviewed. Given a bounded desired tracking signal with bounded derivatives, a control law is designed for minimum-phase non-linear systems which results in tracking of this signal by the output. This control law is modified in the presence of uncertainties associated with the model vector fields to reduce the effects of these uncertainties on the tracking errors. Two types of uncertainties are considered: those satisfying a generalized matching condition but otherwise unstructured, and linear parametric uncertainties. It is shown that for systems with the first type of uncertainty, high-gain control laws can result in small tracking errors of O(?), where e is a small design parameter. An alternative scheme based on variable structure control strategy is shown to yield zero tracking errors. Adaptive control techniques are used for systems with linear parametric uncertainties. For systems with relative degree larger than one, a new adaptive control scheme is presented which is considerably simpler than the augmented error scheme suggested previously by Narendra et al. (1978) for linear systems and by Sastry and Isidori (1987) for non-linear systems. Contrary to the augmented error scheme, however, this scheme results in small rather than zero tracking errors.     

A Lyapunov-based adaptive control framework for discrete-time non-linear systems with exogenous disturbances

A direct adaptive non-linear control framework for discrete-time multivariable non-linear uncertain systems with exogenous bounded disturbances is developed. The adaptive non-linear controller addresses adaptive stabilization, disturbance rejection and adaptive tracking. The proposed framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop system; that is, asymptotic stability with respect to part of the closed-loop system states associated with the plant. In the case of bounded energy ? ₂ disturbances the proposed approach guarantees a non-expansivity constraint on the closed-loop input–output map. Finally, three illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.     

Robust output tracking control for the systems with uncertainties

A new robust tracking control is proposed for the minimum phase dynamical systems with parameter uncertainties and unmatched disturbance, where only the input-output measurement of the system is employed. The system parameters may vary slightly around their corresponding nominal values. The disturbance is assumed to be bounded. However, the upper and lower bounds are unknown. First, the frame of the control law is presented. Then, a special bounded signal is generated by the disturbance and the model uncertainties are estimated by a new non-linear method, where the upper and lower bounds of the special signal are adaptively updated online. Finally, the robust tracking control is synthesized by using the estimate of the special signal. The output tracking error can be made as small as necessary by choosing the design parameters. The attraction of the proposed method lies in its robustness to uncertainties and its ease of implementation. Example and simulation results are presented to show the effectiveness of the proposed algorithm.     

Adaptive stabilization of the Kuramoto-Sivashinsky equation

The paper is concerned with adaptive stabilization of a reaction-diffusion system governed by the Kuramoto-Sivashinsky equation (a non-linear partial differential equation). Under the existence of bounded deterministic disturbances, the adaptive stabilizer is constructed by the concept of high-gain non-linear output feedback and the estimation mechanism of the unknown parameters. In the control system, the global asymptotic stability and convergence of the system state to zero will be guaranteed. The problem of set point regulation is also considered.     

The bounded energy optimal control for a class of distributed parameter systems†

The bounded energy optimal control for one-dimensional linear stationary distributed parameter system is solved here. The criterion function is a quadratic functional of the output.

Obtaining the optimal control involves the computation of the solution of a certain non-linear integral equation. The method of solving this integral equation is approximating the kernel of the integral operator by a sequence of degenerate kernels. It is shown that the sequence of approximate solutions of the approximate integral equations converges to the optimal solution; and that the sequence of approximate values of the criterion, converges to the optimal value of the criterion.     

Adaptive feedforward and feedback control of non-linear time-varying uncertain systems

An adaptive regulation scheme is proposed for a class of non-linear time-varying systems with parametric uncertainties. The proposed approach is based upon a combination of the adaptive backstepping design method and a feedforward control scheme to design a non-linear adaptive feedforward and feedback controller, such that robust output tracking can be achieved even in the presence of structured uncertainties, as well as time-varying, measurable disturbances. Although the systematic design procedure does not a priori satisfy the feedback linearizable system with triangular structures, however, the constructed condition must be satisfied to ensure that the control scheme has a stable inversion. Under the feasibility condition, the states of the resulting closed-loop system would be guaranteed boundedness and converge to a bounded set. Finally, the proposed methodology is illustrated by a chemical reactor example.     

Robust tracking and disturbance rejection of bounded rate signals for uncertain/non-linear systems

We consider the problem of designing controllers for non-linear/uncertain systems to achieve tracking of a reference output signal in the presence of a disturbance input signal. When the exogenous signal (combined reference and disturbance) is constant, we require that the tracking error eventually go to zero. When the exogenous signal has a bounded rate, we require that the tracking error be eventually bounded with a bound which only depends on the bound on the magnitude of the rate of the exogenous signal. We also require that the state and control input are bounded when the exogenous signal is bounded. We propose controllers which have a classical PI (proportional integral) structure using state feedback. For linear systems and specific classes of non-linear/uncertain systems we present conditions whose satisfaction guarantees the existence of controllers which achieve the desired behaviour. Satisfaction of these conditions also yields the controller gain matrices.     

Stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function

A more general class of stochastic non-linear systems with unmodelled dynamics and uncertain non-linear functions are considered in this paper. With the concept of ISpS being extended to stochastic case, by combining changing supply function technique with backstepping design technique, an adaptive output-feedback controller is proposed. It is shown that all the solutions of the closed-loop system are uniformly bounded in probability, and the output can be regulated to an arbitrarily small neighbourhood of the origin in probability. A simulation example demonstrates the control scheme.     

Non-linear output feedback stabilization on a bounded region of attraction

In this paper it is shown that, for multi-input single-output non-affine non-linear systems, when a state feedback control stabilizes an equilibrium point of a plant with a certain bounded region of attraction, it is also stabilized by an output feedback controller with arbitrarily small loss of the region. Moreover, the proposed output feedback controller has the dynamic order n which is the same as the order of the plant. From any given state feedback, an explicit form of the overall controller is provided. A sufficient condition presented for the result is shown to be necessary and sufficient for regional uniform observability when the system is input affine. Thus, the result can be regarded as a regional separation principle for affine non-linear systems.     

An output feedback tracking controller for systems diffeomorphic to the non-linear observer form

An output feedback tracking controller is proposed for single-input, single-output non-linear systems that are diffeomorphic to the non-linear observer form. Difficulty in obtaining the output injection terms of the non-linear observer form is solved by a numerical technique and the interpolation method using the radial basis function (RBF) network. The trained RBF networks approximate output injection terms in a compact interval and are utilized for building a non-linear observer. In constructing the output tracking controller the backstepping control method is adopted based on the state estimates.     

Robust near-optimal output feedback control of non-linear systems

This work proposes a robust near-optimal non-linear output feedback controller design for a broad class of non-linear systems with time-varying bounded uncertain variables. Both vanishing and non-vanishing uncertainties are considered. Under the assumptions of input-to-state stable (ISS) inverse dynamics and vanishing uncertainty, a robust dynamic output feedback controller is constructed through combination of a high-gain observer with a robust optimal state feedback controller synthesized via Lyapunov's direct method and the inverse optimal approach. The controller enforces exponential stability and robust asymptotic output tracking with arbitrary degree of attenuation of the effect of the uncertain variables on the output of the closed-loop system, for initial conditions and uncertainty in arbitrarily large compact sets, provided that the observer gain is sufficiently large. Utilizing the inverse optimal control approach and singular perturbation techniques, the controller is shown to be near-optimal in the sense that its performance can be made arbitrarily close to the optimal performance of the robust optimal state feedback controller on the infinite time-interval by selecting the observer gain to be sufficiently large. For systems with non-vanishing uncertainties, the same controller is shown to ensure boundedness of the states, uncertainty attenuation and near-optimality on a finite time-interval. The developed controller is successfully applied to a chemical reactor example.     

Robust output feedback stabilization of a class of time-varying non-linear systems

This paper deals with the problem of robust output feedback stabilization of a class of time-varying non-linear systems. This class of systems involves two kinds of time-varying uncertainties: those norm-bounded and those bounded by a smooth non-linear function of the output. Under the assumption that the zero dynamics of the system are uniformly asymptotically stable and some additional mild conditions, we show via a Lyapunov function approach that the uncertain system can be robustly stabilized by a time-varying non-linear output feedback controller. The order of this controller turns out to be one less than the relative degree of the uncertain system. A systematic design procedure is given for constructing the controller. Illustrative examples are given. Note that the results generalize several previous results on robust output feedback stabilization.     

Adaptive hierarchical tuning of fuzzy controllers

Fuzzy controller design includes both linear and non-linear dynamic analysis. The knowledge base parameters associated within the fuzzy rule base influence the non-linear control dynamics while the linear parameters associated within the fuzzy output signal influence the overall control dynamics. For distinct identification of tuning levels, an equivalent linear controller output and a normalized non-linear controller output are defined. A linear proportional-integral-derivative (PID) controller analogy is used for determining the linear tuning parameters. Non-linear tuning is derived from the locally defined control properties in the non-linear fuzzy output. The non-linearity in the fuzzy output is then represented in a graphical form for achieving the necessary non-linear tuning. Three different tuning strategies are evaluated. The first strategy uses a genetic algorithm to simultaneously tune both linear and non-linear parameters. In the second strategy the non-linear parameters are initially selected on the basis of some desired non-linear control characteristics and the linear tuning is then performed using a trial and error approach. In the third method the linear tuning is initially performed off-line using an existing linear PID law and an adaptive non-linear tuning is then performed online in a hierarchical fashion. The control performance of each design is compared against its corresponding linear PID system. The controllers based on the first two design methods show superior performance when they are implemented on the estimated process system. However, in the presence of process uncertainties and external disturbances these controllers fail to perform any better than linear controllers. In the hierarchical control architecture, the non-linear fuzzy control method adapts to process uncertainties and disturbances to produce superior performance.     

含有界扰动系统的多模型自适应控制

对含有有界扰动和参数不确定性的离散时间被控对象建立多个辨识模型, 覆盖被控对象的参数不确定性. 给定指标切换函数, 构成多模型自适应控制器. 引入“局部化”技术, 在保持计算精度的同时, 提高了计算速度. 同时证明, 多模型自适应控制可以保证闭环系统输入输出稳定, 且保证对给定有界参考输入、被控对象输出可在一给定界范围内跟踪参考输入.     

Exponential tracking of feedback linearizable non-linear control systems with uncertainties

This paper studies the robust output tracking problem of feedback linearizable non-linear control systems with uncertainties. Utilizing the input-output feedback linearization technique and the Lyapunov method for non-linear state feedback synthesis, a robust globally exponential output tracking controller design methodology for a broad class of non-linear control systems with uncertainties is developed. The underlying theoretical approaches are the differential geometry approach and the composite Lyapunov approach. One utilizes the parametrized coordinate transformation to transform the original non-linear system with uncertainties into a singularly perturbed model with uncertainties and the composite Lyapunov approach is then applied for output tracking. To demonstrate the practical applicability, the paper has investigated a pendulum control system.     

The Popov criterion for strongly stable distributed parameter systems

In this article we generalize the Popov criterion to the class of strongly stable infinite-dimensional linear systems; the semigroup is strongly stable and the input to state, state to output and input to output maps are all bounded on the infinite-time interval. One application is to show that integral control can be used to track constant reference signals for positive-real strongly stable systems in the presence of sectorial non-linearities. A second application is to show the robustness of asymptotic stability of positive-real strongly stable systems to a large class of non-linear perturbations. Systems satisfying the assumptions in this paper include dissipative systems with collocated actuators and sensors.     

基于RBF神经网络观测器飞控系统故障诊断

为了解决非线性系统采用解析方法进行故障诊断困难的问题,利用神经网络可逼近任意连续有界非线性函数的能力,提出了一种基于RBF神经网络观测器的故障检测与诊断方法,并详细论述了该故障诊断方法的构造原理。以含有非线性项的飞行控制系统的作动器模型为例,仅作动器的输入输出可测量,通过构造RBF神经网络观测器来拟合作动器系统模型,逼近其在正常情况下的输出。最后在飞控系统的闭环控制环境下,对作动器的三种典型故障进行了计算机仿真诊断,结果表明故障诊断方法是有效的。