Robust adaptive control of robot manipulators using Bernstein polynomials as universal approximator

This article presents a robust adaptive controller for electrically driven robots using Bernstein polynomials as universal approximator. The lumped uncertainties including unmodeled dynamics, external disturbances, and nonimplemented control signals (they assumed as a function of time, instead a function of several variables) are represented with this powerful mathematical tool. The polynomial coefficients are then tuned based on the adaptation law obtained in the stability analysis. A comprehensive approach is adopted to include the saturated and unsaturated areas and also the transition between these areas in the stability analysis. As a result, the stability and the performance of the proposed controller have been improved considerably in dealing with actuator saturation. Also, in comparison with a recent paper based on uncertainty estimation using Taylor series, the proposed controller is less computational due to reducing the size of the matrix of convergence rate. A performance evaluation has been carried out to verify satisfactory performance of transient response of the controller. Simulation results on a Puma560 manipulator actuated by geared permanent magnet dc motors have been presented to guarantee its satisfactory performance.     

Robust impedance control of robot manipulators using differential equations as universal approximator

This paper presents a robust impedance controller for robot manipulators using function approximation techniques (FATs). Recently, some FAT-based robust impedance control approaches have been presented using Fourier series expansion or Legendre polynomials for uncertainty estimation. However, the dimensions of regressor matrices in these approaches are relatively large. This problem becomes hypersensitive especially for higher degree of freedom robot manipulators. In this paper, a simpler and less computational FAT-based robust controller is presented without considering discontinuous nonlinearities. It is assumed that the lumped uncertainty can be modelled by a linear differential equation with unknown coefficients. Then, using the Stone–Weierstrass theorem, it is verified that these differential equations are universal approximators. The advantage of the proposed controller in comparison with previous related works is reducing the dimensions of regressor matrices. Simulation results on a Puma560 robot manipulator indicate the efficiency of the proposed method.     

Robust adaptive control of discrete-time systems using persistent excitation

An important result in the robust adaptive control of continuous-time systems, using the persistent excitation of the reference input, was recently given by Narendra and Annaswamy (1986, IEEE Trans. Aut. Control, AC-31, 306–315). According to this result, the global boundedness of all the signals in the adaptive system can be assured if the degree of persistent excitation of the reference input is larger than an appropriate bound on the external disturbance. The main theorem in Narendra and Annaswamy (1986) is proved for a class of plants characterized by the property that the reference model used in the adaptive controller could be chosen to be strictly positive real, a condition which involves constraints on the relative degree of the plant. This paper presents a generalization of the above result to plants of arbitrary relative degree. Together with the work reported in the earlier paper, it demonstrates that the boundedness of all the signals in an adaptive system in the presence of bounded disturbances and arbitrary initial conditions can be assured by increasing the degree of persistent excitation of the reference input.     

Robust adaptive control for nonlinear uncertain systems

A direct robust adaptive control framework for nonlinear uncertain systems with constant linearly parameterized uncertainty and nonlinear state-dependent uncertainty is developed. The proposed framework is Lyapunov-based and guarantees partial asymptotic robust stability of the closed-loop system; that is, asymptotic robust stability with respect to part of the closed-loop system states associated with the plant. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach.     

Robust adaptive control for interval time-delay systems

1 Introduction The problem of time-delay is commonly encountered in various engineering systems, such as electric, pneumatic and hydraulic networks, long transmission lines, etc., and it is also a great source of systems instability and poor perfor- mance. During the last decades, we have seen an increasing interest for the control of this class of systems and many results have reported in the literature [1～5]. On the other hand, it has been recognized that nonlinear uncertainties are unavoid…     

Robust adaptive boundary control of semilinear PDE systems using a dyadic controller

In this paper, we describe a dyadic adaptive control framework for output tracking in a class of semilinear systems of partial differential equations with boundary actuation and unknown distributed nonlinearities. The dyadic adaptive control framework uses the linear terms in the system to split the plant into 2 virtual subsystems, one of which contains the nonlinearities, whereas the other contains the control input. Full‐plant‐state feedback is used to estimate the unmeasured individual states of the 2 subsystems as well as the nonlinearities. The control signal is designed to ensure that the controlled subsystem tracks a suitably modified reference signal. We prove the well posedness of the closed‐loop system rigorously and derive conditions for closed‐loop stability and robustness using finite‐gain stability theory.     

一类不确定系统的鲁棒自适应控制算法

对具有有界扰动和未建模动态的多变量系统,设计鲁棒稳定的自适应控制律,并进行了稳定性分析。在设计中,采用死区与正规化信号相结合的方法,控制器采用极点配置的形式。正规化信号的引入,使得建模误差和扰动产生的影响对正规化信号有界。对极点配置控制律中出现的奇异性用投影算法加以消除。与其他一些文献上的算法相比,该算法较为简单,易于执行。     

Robust and adaptive backstepping control for nonlinear systems using RBF neural networks

In this paper, two different backstepping neural network (NN) control approaches are presented for a class of affine nonlinear systems in the strict-feedback form with unknown nonlinearities. By a special design scheme, the controller singularity problem is avoided perfectly in both approaches. Furthermore, the closed loop signals are guaranteed to be semiglobally uniformly ultimately bounded and the outputs of the system are proved to converge to a small neighborhood of the desired trajectory. The control performances of the closed-loop systems can be shaped as desired by suitably choosing the design parameters. Simulation results obtained demonstrate the effectiveness of the approaches proposed. The differences observed between the inputs of the two controllers are analyzed briefly.     

Robust design of adaptive control systems using conic sector theory

This paper presents a design approach for discrete adaptive control systems which provides a quantitative measure of the effect of design alternatives such as (i) adaptive gain, (ii) model order, and (iii) sampling rate, on stability in the presence of unmodeled plant dynamics. The proposed method, based on the conic conditions developed by Ortega et al. (1985, IEEE Trans. Aut. Control, AC-30, 1179–1187), is illustrated using a benchmark example. The results demonstrate that the sector conditions permit design tradeoffs to be made such that stability is maintained despite the model-plant mismatch.     

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.     

非线性模糊时滞系统鲁棒自适应控制

研究一类基于模糊T-S模型的非线性时滞系统鲁棒镇定问题．基于记忆型状态反馈策略，首先给出由T-S模糊模型描述的非线性时滞系统在时滞精确已知情况下的鲁棒镇定准则；然后给出非线性时滞系统在时滞未知情况下的鲁棒自适应控制策略．所设计的控制器可确保闭环系统渐近稳定，且具有良好的可操作性．最后通过仿真实例证明了该方法的正确性和有效性．     

Robust adaptive control of proper systems

To date, all the adaptive control algorithms have been proposed only for strictly proper systems. In this paper, a scheme is proposed to design an adaptive controller for proper systems. To study the robustness of the adaptive controller, both additive and multiplicative types of unmodeled dynamics are considered and can also be allowed to be proper, or even improper. Global bounded input bounded output stability is established. The achievement of a small in the mean tracking error and perfect tracking/rejection of deterministic trajectories/disturbances in the absence of system unmodeled dynamics are discussed. The results are also verified by simulation studies     

Robust adaptive control for a class of uncertain non-affine nonlinear systems using affine-type neural networks

A robust adaptive control is proposed for a class of single-input single-output non-affine nonlinear systems. In order to approximate the unknown nonlinear function, a novel affine-type neural network is used, and then to compensate the approximation error and external disturbance a robust control term is employed. By Lyapunov stability analysis for the closed-loop system, it is proved that tracking errors asymptotically converge to zero. Moreover, an observer is designed to estimate the system states because all the states may not be available for measurements. Furthermore, the adaptation laws of neural networks and the robust controller are given out based on the Lyapunov stability theory. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed control method.     

基于ELM的一类MIMO仿射非线性系统的鲁棒自适应控制

针对一类多输入多输出(MIMO) 仿射非线性动态系统, 提出一种基于极限学习机(ELM) 的鲁棒自适应神经控制方法. ELM随机确定单隐层前馈网络(SLFNs) 的隐含层参数, 仅需调整网络的输出权值, 能以极快的学习速度获得良好的推广性. 在所提出的控制方法中, 利用ELM逼近系统的未知非线性项, 针对ELM网络的权值、逼近误差及外界扰动的未知上界值分别设计参数自适应律, 通过Lyapunov 稳定性分析可以保证闭环系统所有信号半全局最终一致有界. 仿真结果表明了该控制方法的有效性.

     

一类非线性时滞系统的鲁棒间接自适应控制

针对一类不确定非线性时滞系统,基于变结构控制原理,利用多层神经网络逼近的能力,提出具有投影算法的间接自适应控制方案。该方案通过监督控制器保证闭环系统所有信号有界,并引入综合误差的自适应补偿项来消除建模误差的影响。理论分析证明跟踪误差收敛到零,仿真结果表明该方法有的效性。     

基于Kp=LDU分解的多变量离散时间系统鲁棒模型参考自适应控制

针对具有未建模动态且相对阶大于1的一类多变量离散时间系统,利用其高频增益矩阵分解建立新的参数模型,在较弱假设下,进一步研究了直接型鲁棒模型参考自适应控制问题.由离散时间系统的交换引理,建立了闭环系统的所有信号与规范化信号的联系.以一种系统化的方法,严格地分析了闭环系统的稳定性与鲁棒性.     

一类不确定延迟系统的鲁棒自适应控制

针对一类不确定的延迟系统，提出一种鲁棒的模型参考自适应控制设计方案．它不同于以往将所有延迟部分转化为系统的未建模动态的方案，该方案只是把延迟偏离标称值的扰动转化为系统的未建模动态，而将能够获得的延迟标称值信息加入系统的建模部分，从而使系统的建模更为精确．同时，研究了这种其建模部分含有延迟的系统的稳定性和鲁棒性．仿真结果验证了该方案的有效性．     

Robust discrete-time set-based adaptive predictive control for nonlinear systems

The problem of robust adaptive predictive control for a class of discrete-time nonlinear systems is considered. First, a parameter estimation technique, based on an uncertainty set estimation, is formulated. This technique is able to provide robust performance for nonlinear systems subject to exogenous variables. Second, an adaptive MPC is developed to use the uncertainty estimation in a framework of min–max robust control. A Lipschitz-based approach, which provides a conservative approximation for the min–max problem, is used to solve the control problem, retaining the computational complexity of nominal MPC formulations and the robustness of the min–max approach. Finally, the set-based estimation algorithm and the robust predictive controller are successfully applied in two case studies. The first one is the control of anonisothermal CSTR governed by the van de Vusse reaction. Concentration and temperature regulation is considered with the simultaneous estimation of the frequency (or pre-exponential) factors of the Arrhenius equation. In the second example, a biomedical model for chemotherapy control is simulated using control actions provided by the proposed algorithm. The methods for estimation and control were tested using different disturbances scenarios.     

不确定非线性系统的鲁棒自适应输出反馈控制

基于自适应非线性阻尼,提出一种鲁棒自适应输出反馈控制方法。该方法适用于带有未建模动态、未知非线性、有界扰动、未知非线性参数和不确定控制系数的多输入多输出非线性系统。理论证明,在一定的假设条件下,该方法能保证闭环系统所有动态信号有界;不论有多少不确定非线性参数、多高阶的非线性系统,只需要一个自适应控制参数和观察参数;而且通过选择适当的控制器和观测器参数,能使控制误差和估计误差达到任意小。仿真结果表明了所提出方法的有效性。     

Robust adaptive fuzzy VSS control for a class of uncertain nonlinear systems using small gain design

In this paper, a novel robust adaptive fuzzy variable structure control (RAFVSC) scheme is proposed for a class of uncertain nonlinear systems. The uncertain nonlinear system and gain functions originating from modeling errors and external disturbances are all unstructured (or non-repeatable), state-dependent and completely unknown. The Takagi–Sugeno type fuzzy logic systems are used to approximate uncertain functions in the systems and the RAFVSC is designed by use of the input-to-state stability (ISS) approach and small gain theorem. In the algorithm, there are three advantages which are that the asymptotic stability of adaptive control in the presence of unstructured uncertainties can be guaranteed, the possible controller singularity problem in some of existing adaptive control schemes using feedback linearization techniques can be removed and the adaptive mechanism with minimal learning parameterizations can be achieved. The performance and effectiveness of the proposed methods are discussed and illustrated with two simulation examples.