Adaptive Output Feedback Control for a Class of Uncertain Stochastic Nonlinear Systems With Unknown Time‐Delays

This paper investigates the problem of output feedback control for a class of stochastic nonlinear systems with time‐delays. Using dynamic gain scaling technique, an adaptive update law is introduced to the observer and controller to deal with the unknown parameters. Based on the Lyapunov‐Krasovskii functional and stochastic Barbalat's lemma, it is proved that the proposed universal‐type adaptive output feedback controller can regulate all the states of the closed‐loop system almost surely. A simulation example is presented to illustrate the effectiveness of the proposed design procedure.     

基于参数辨识的自适应解耦控制算法的研究

多变量模型的复杂结构、强耦合性、被控对象参数的未知、慢时变等问题要求控制器必须具有良好的自适应性,针对以上问题提出了一种基于改进的广义最小方差闭环自适应解耦控制器实现更好的自适应,其由参数可调的控制器和自适应控制律组成,此控制器通过将闭环系统方程的传递函数矩阵等于期望的对角矩阵来实现解耦,同时改进的辨识算法可进行在线辨识控制器的参数实现同步自适应解耦。通过以CARMA为多变量控制模型,采用该方法进行仿真有效的解决了多变量之间的耦合性。结果表明该方法能够适应相应的变化,跟踪性能较好,且具备良好的解耦能力,进而保证了闭环系统的稳定性,从而验证了此方法能够效提高控制系统的稳定性和鲁棒性。     

不确定机器人的自适应神经网络控制与学习

针对具有未知动态的电驱动机器人,研究其自适应神经网络控制与学习问题.首先,设计了稳定的自适应神经网络控制器,径向基函数(RBF)神经网络被用来逼近电驱动机器人的未知闭环系统动态,并根据李雅普诺夫稳定性理论推导了神经网络权值更新律.在对回归轨迹实现跟踪控制的过程中,闭环系统内部信号的部分持续激励(PE)条件得到满足.随着PE条件的满足,设计的自适应神经网络控制器被证明在稳定的跟踪控制过程中实现了电驱动机器人未知闭环系统动态的准确逼近.接着,使用学过的知识设计了新颖的学习控制器,实现了闭环系统稳定、改进了控制性能.最后,通过数字仿真验证了所提控制方法的正确性和有效性.     

Design of strictly positive real systems using constant outputfeedback

The authors present a linear matrix inequality (LMI) approach to the strictly positive real (SPR) synthesis problem: find an output feedback K such that the closed loop system T(s) is SPR. The authors establish that if no such constant output feedback K exists, then no dynamic output feedback with a proper transfer matrix exists to make the closed-loop system SPR. The existence of K to guarantee the SPR property of the closed-loop system is used to develop an adaptive control scheme that can stabilize any system of arbitrary unknown order and unknown parameters     

Linear adaptive control of a class of SISO nonaffine nonlinear systems

This paper addresses the problem of linear adaptive control for a class of uncertain continuous-time single-input single-output (SISO) nonaffine nonlinear dynamic systems. Using the implicit function theory, the existence of an ideal controller which can achieve control objectives is firstly demonstrated. However, this ideal controller cannot be known and computed even if the system model is well known. The aim of our work is to construct this unknown ideal controller using a simple linear controller with the free parameters updated online by a stable adaptation mechanism designed to minimise the error between the unknown ideal controller and the used linear controller. Since the mathematical model of the system is assumed unknown in this work, the proposed control scheme can be regarded as a simple model free controller for the studied class of nonaffine systems. We prove that the closed-loop system is stable and all the signals are bounded. An application of the proposed linear adaptive controller for a nonaffine system is illustrated through the simulation results to demonstrate the effectiveness of the proposed control scheme.     

Adaptive Stabilization for a Class of Stochastic Nonlinearly Parameterized Nonholonomic Systems with Unknown Control Coefficients

This paper investigates the problem of adaptive state feedback stabilization for a class of stochastic nonlinearly parameterized nonholonomic systems in chained form with unknown control coefficients. By defining two new unknown parameters whose dynamic updating laws are properly chosen and also by skilfully using the parameter separation, input‐state‐scaling, and integrator backstepping techniques, an adaptive state feedback controller is successfully designed, which guarantees that the closed‐loop system is asymptotically stabilized in probability. A simulation example is provided to illustrate the effectiveness of the proposed approach.     

Decentralised adaptive control for a class of stochastic switched interconnected nonlinear systems

In this paper, we focus on the problem of adaptive stabilisation for a class of interconnected uncertain switched stochastic nonlinear systems. Classical adaptive and backstepping technique are employed for control synthesis. Instead of estimating the switching parameters directly, we design the adaptive controller based on the estimations of bounds on switching time-varying parameters. A smooth function is introduced to deal with the difficulties caused by unknown interactions and tuning function approach is used to circumvent the overparameter problem. It is shown that under the action of the proposed controller all the signals of the overall closed-loop systems are globally uniformly bounded in probability under arbitrary switching. Simulation results are presented to illustrate the effectiveness of the proposed approach.     

RCMAC-based adaptive control design for brushless DC motors

This paper proposes a recurrent cerebellar model articulation controller (RCMAC)-based adaptive control for brushless DC motors. This control system is composed of a RCMAC and a compensation controller. RCMAC is used to mimic an ideal controller, and the compensation controller is designed to compensate for the approximation error between the ideal controller and RCMAC. The Lyapunov stability theory is utilized to derive the parameter tuning algorithm, so that the uniformly ultimately bound stability of the closed-loop system can be achieved. For comparison, a fuzzy control, an adaptive fuzzy control and the developed RCMAC-based adaptive control are implemented on a field programmable gate array chip for controlling a brushless DC motor. Experimental results reveal that the proposed RCMAC-based adaptive control system can achieve the best tracking performance. Moreover, since the developed RCMAC-based adaptive control scheme uses a hyperbolic tangent function to compensate for the approximation error, there is no chattering phenomenon in the control effort. Thus, the proposed control method is more suitable for real-time practical control applications.     

Nonlinear adaptive control for power integrator triangular systems by switching linear controllers

In this paper, a nonlinear adaptive stabilizer is designed for a class of power integrator triangular systems with the following four features: (i) the chained integrators have the powers of positive odd numbers, which makes the linearization of the studied system uncontrollable; (ii) the nonlinear function contains the virtual control variables; (iii) the bound of the nonlinear parameters entering the function nonlinearity is not required to be known a priori; and (iv) there exists an unknown control coefficient with the unknown bound in the control channel. Our proposed adaptive controller is a switching type controller, in which the designed adaptive stabilizer takes a two‐step procedure: a linear stabilizing controller containing the tuning gains is first designed by the adding a power integrator technique. Switching logic is then proposed to tune online the gains in a switching manner. The proposed adaptive controller globally asymptotically stabilizes the considered system in the sense that, for any initial conditions, the state converges to the origin while all the signals of the closed‐loop system are bounded. Simulation studies clarify and verify the approach. Copyright © 2014 John Wiley & Sons, Ltd.     

冷轧机的轧辊偏心鲁棒重复控制

设计了用于冷轧机的轧辊偏心补偿的鲁棒重复控制器.首先根据对象的期望闭环特性及扰动信号频率,确定低通滤波器的截止频率,然后通过引入状态反馈来保证闭环系统的鲁棒稳定性,把重复控制器的设计问题转化为H∞状态反馈控制器的设计问题,给出了控制器参数整定算法,最后通过在控制系统中引入一个前向系数来进一步改善和提高系统的动态性能与稳态控制精度,给出了前向系数的整定方法.仿真结果表明,当系统对象参数存在摄动时,这种控制器仍然能够实现对轧辊偏心的高精度补偿.     

Adaptive Regulation Against Unknown Narrow Band Disturbances Applied to the Flying Height Control in Data Storage Systems

This paper presents an adaptive regulation approach in linear systems against exogenous narrow band inputs such as disturbances or reference signals consisting of a linear combination of biased sinusoids with unknown amplitudes, frequencies, and phases. The design of the regulator is based on considering a Q‐parameterized set of stabilizing controllers for the linear system, where an adaptive FIR filter with fixed IIR filtering is adopted as the Q parameter. The goal of the adaptation is to search within the set of stabilizing controllers for a controller, or equivalently a Q parameter, that yields regulation in the closed loop system. The proposed adaptive regulation algorithm is applied to an active suspension beam system, which is motivated by the flying height control problem in data storage systems. The experimental result of the closed loop system shows the effectiveness of the proposed adaptive regulator in achieving the desired tracking performance under unknown exogenous disturbances.     

An approach to adaptive control using real time identification

An adaptive controller consisting of a real time identifier and a minimum variance regulator is discussed. The identification is done by augmenting the state with the unknown parameters of the process. This usually leads to a non-linear filtering problem. By choosing a model of special structure the problem can, however, be reduced to a linear problem. The control law is derived using stochastic optimal control theory. By choosing a special criterion, the stochastic control problem can be solved analytically. The behaviour of the adaptive controller is illustrated in two examples.     

具有输入和输出约束的高阶随机系统神经网络控制

针对高阶非线性系统,开展自适应神经网络跟踪控制器设计,系统受到随机扰动的影响.首次把输入和输出约束问题引入到高阶系统的跟踪控制中,并假定系统动态是未知.首先借用高斯误差函数表达连续可微的非对称饱和模型以实现输入约束,和障碍Lyapunov函数保证系统输出受限;其次,针对高阶非线性系统,径向基函数(RBF)神经网络用来克服未知系统动态和随机扰动.在每一步的backstepping计算中,仅用到单一的自适应更新参数,从而克服了过参数问题;最后,基于Lyapunov稳定性理论提出自适应神经网络控制策略,并减少了学习参数.最终结果表明设计的控制器能保证所有闭环信号半全局最终一致有界,并能使跟踪误差收敛到零值小的邻域内.仿真研究进一步验证了提出方法的有效性.     

具有输入量化和全状态约束的非严格反馈随机非线性系统的有限时间动态面控制

研究具有输入量化和全状态约束的非严格反馈随机非线性系统的有限时间自适应跟踪控制.首先,利用双曲正切函数进行非线性映射,消除全状态约束的限制,将系统变换为无约束系统;其次,引入滞回量化器克服量化信号中的抖动和量化误差.为实现有限时间控制,提出概率意义下半全局有限时间稳定控制方法,加快系统的收敛速度,并在此基础上采用径向基函数神经网络逼近未知非线性函数;接着,基于动态面控制技术和高斯函数的性质,对变换后的非严格反馈随机系统进行自适应控制设计,所设计的控制器能够保证闭环系统中的所有信号在概率意义下有限时间稳定;最后通过仿真实验表明所设计控制方案的有效性.     

Integral sliding mode compensator for load pressure control of die-cushion cylinder drive

This paper discusses problems of the load pressure control of electro-hydraulic drives in a presence of unknown disturbances and parametrical uncertainties. In many applications, the standard, linear control methods do not assure a satisfactory dynamical behavior and are likely to fail if a working point or the system properties change drastically. In order to guarantee a desired robustness and precision of the closed-loop system, a combination of the input–output linearization technique with the integral sliding mode is proposed. The structure of the presented controller is very simple, and can be easily implemented in standard industrial PLC's. The commissioning and tuning of the controller are uncomplicated and the adjustment procedure is partially automated. Conducted tests confirm a very good and robust performance of the closed loop control. The results are compared with those obtained with conventional linear controllers (P and PI).     

Direct adaptive NN control of a class of nonlinear systems

In this paper, direct adaptive neural-network (NN) control is presented for a class of affine nonlinear systems in the strict-feedback form with unknown nonlinearities. By utilizing a special property of the affine term, the developed scheme,avoids the controller singularity problem completely. All the signals in the closed loop are guaranteed to be semiglobally uniformly ultimately bounded and the output of the system is proven to converge to a small neighborhood of the desired trajectory. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. Simulation results are presented to show the effectiveness of the approach.     

Immersion and invariance based fault tolerant adaptive spacecraft attitude control

In this paper, an immersion and invariance (I&I) adaptive fault tolerant satellite attitude tracking control scheme is proposed. The proposed controller is capable of track the desired trajectory in the presence of unknown actuator multiplicative faults and unknown inertial matrix. Also based on Lyapunov direct method, all closed loop signals are proven to be globally asymptotically stable. The main advantage of this controller is improving closed loop performance while maintaining stability in the presence of unknown actuator faults. This method does not rely on certainty equivalence principle so it can be used to control the transient response of overall closed loop system by means of controlling the parameter estimation behavior which is not possible in traditional adaptive control. Numerical simulations are performed to demonstrate the effectiveness of proposed control scheme.     

一类具有未知控制方向非线性系统的输出反馈自适应控制

研究了一类控制方向未知非线性系统的输出反馈自适应镇定问题. 首先, 通过一线性状态变换, 将未知控制系数集中起来, 从而将原系统变换为适于控制设计的新系统. 然后, 分别引入状态观测器和参数估计器, 并应用积分反推和调节函数方法, 给出了输出反馈稳定控制律的构造性设计过程. 可以证明，所设计的控制器确保原系统状态渐近收敛到原点, 而其它闭环系统状态有界. 仿真结论验证了所提出方法的有效性.     

含未知信息的轮式移动机器人编队确定学习控制

本文研究含未知信息的轮式移动机器人(wheeled mobile robots,WMR)的编队控制问题.首先,基于领航–跟随法和虚拟结构法,将WMR编队控制问题转化为跟随机器人对参考虚拟机器人的跟踪控制问题.然后,利用径向基函数神经网络(radial basis function neural networks,RBF NN)对WMR的未知系统动态进行学习,以及根据李雅普诺夫稳定性理论设计了稳定的自适应RBF NN控制器和RBF NN权值估计的学习率.依据确定学习理论,闭环系统内部信号在对回归轨迹实现跟踪控制的过程中满足部分持续激励(persistent excitation,PE)条件.随着PE条件的满足,RBF NN权值估计收敛到其理想权值,实现了对未知闭环系统动态的准确学习.最后,利用学习结果设计了RBF NN学习控制器,保证了控制系统的稳定与收敛,实现了闭环稳定性和改进了控制性能,并通过仿真验证了所提控制方法的正确性和有效性.