Robust adaptive neural control for a class of uncertain MIMO nonlinear systems

In this paper, a novel robust adaptive neural control scheme is proposed for a class of uncertain multi-input multi-output nonlinear systems. The proposed scheme has the following main features: (1) a kind of Hurwitz condition is introduced to handle the state-dependent control gain matrix and some assumptions in existing schemes are relaxed; (2) by introducing a novel matrix normalisation technique, it is shown that all bound restrictions imposed on the control gain matrix in existing schemes can be removed; (3) the singularity problem is avoided without any extra effort, which makes the control law quite simple. Besides, with the aid of the minimal learning parameter technique, only one parameter needs to be updated online regardless of the system input–output dimension and the number of neural network nodes. Simulation results are presented to illustrate the effectiveness of the proposed scheme.     

Robust analysis and control for a class of uncertain nonlinear discrete-time systems

This paper deals with the problem of robust analysis and control of a class of nonlinear discrete-time systems with (constant) uncertain parameters. For the analysis problem we use a polynomial Lyapunov function and we generalize, for nonlinear systems, the “extended stability” notion proposed by Oliveira et al. (1999) in the context of linear discrete-time uncertain systems. As a result, we propose an LMI optimization problem to maximize an estimate of the domain of attraction, and also extend this approach to the synthesis problem by considering parameter-dependent Lyapunov functions and nonlinear multipliers. Numerical examples illustrate the approach and show its potential for solving analysis and control problems of nonlinear discrete-time systems.     

一类不确定非线性离散系统的模糊自适应控制器设计

针对一类不确定非线性离散系统,提出一种带有自动可调伸缩因子的模糊自适应控制方法.该控制器设计方法的优点是模糊逻辑系统的逼近精度不再依赖于模糊逻辑系统的结构和规则数目,参数自适应律调节与被逼近函数的特征和逼近精度有关,因此能有效减少在线估计的参数数目,且设计方法能够保证闭环系统的所有状态半全局一致终极有界.最后,通过数值仿真算例表明所提出方法的有效性.     

一类不确定非线性系统的鲁棒自适应控制

针对一类MIMO不确定非线性系统的输出跟踪问题, 基于自适应反步法和滑模控制为其设计了鲁棒自适应控制器. 模型包含3种不确定性: 1) 参数不确定性; 2) 输入增益的不确定性; 3) 代表系统未建模动态和干扰的不确定函数, 该函数有界. 以非完整移动机械臂的输出跟踪控制为目标, 对其进行仿真实验, 实验结果表明所提出的控制算法是正确有效的.     

Robust adaptive control of a class of nonlinear uncertain systems

A smooth robust dynamic feedback controller is constructed, and the problem of robust H∞ almost disturbance attenuation with internal stability is solved for high-order nonlinear systems with parameter uncertainties. Finally, illustrative example and simulation results demonstrate the effectiveness of the proposed method.     

Direct adaptive robust NN control for a class of discrete-time nonlinear strict-feedback SISO systems

In this paper, a direct adaptive neural network control algorithm based on the backstepping technique is proposed for a class of uncertain nonlinear discrete-time systems in the strict-feedback form. The neural networks are utilized to approximate unknown functions, and a stable adaptive neural network controller is synthesized. The fact that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded is proven and the tracking error can converge to a small neighborhood of zero by choosing the design parameters appropriately. Compared with the previous research for discrete-time systems, the proposed algorithm improves the robustness of the systems. A simulation example is employed to illustrate the effectiveness of the proposed algorithm.     

Adaptive control of a class of discrete-time MIMO nonlinear systems with uncertain couplings

In this article, adaptive control is investigated for a class of discrete-time multi-input-multi-output nonlinear systems in block-triangular form with uncertain couplings of delayed states among subsystems. Future states prediction is carried out to facilitate adaptive control design and auxiliary outputs are introduced to develop a novel compensation mechanism for the uncertain nonlinear couplings. By using Lyapunov method and ordering signals growth rate, it is rigorously proved that all the signals in the whole closed-loop systems are globally bounded and the output tracking errors asymptotically converge to zeros. The effectiveness of the proposed control is demonstrated in the simulation study.     

一类不确定非线性系统的鲁棒自适应ε2输出跟踪控制

针对一类不确定非线性系统，讨论了鲁棒自适应ε-输出跟踪问题．利用Backstepping方法设计了一种自适应光滑状态反馈控制器，使系统输出跟踪给定的C^1参考输出信号．在参考信号及其导数均有界的条件下，得到了全局ε-输出跟踪，且闭环系统所有信号均全局一致有界．仿真结果表明了该设计方法的有效性．     

一类不确定互联系统的鲁棒分散自适应控制

利用反演法的系统性和结构特点,研究了一类含有非线性参数的不确定非线性互联系统的鲁棒分散自适应控制问题.首先,在较直观、较一般的假定下,根据系统的结构特点利用反演法设计出其控制器和自适应律,并且每个子系统控制器和自适应律的构成只利用了本身系统的状态信息,即所谓的分散控制;其次,利用Lyapunov理论证明了所设计的控制器和自适应律使得被控系统的状态及参数估计误差一致终极有界.最后,算例仿真验证了所设计的控制算法的有效性.     

一类不确定非线性系统的鲁棒自适应轨迹线性化控制

针对一类不确定非线性系统,研究了一种新的鲁棒自适应轨迹线性化控制方案.利用径向基神经网络的在线逼近能力以及被控对象分析模型的有用信息设计一种径向基神经网络干扰观测器来估计系统中存在的不确定性.观测器输出用于设计补偿控制律抵消不确定性对系统性能的影响,鲁棒自适应控制律用于克服逼近误差.采用Lyapunov方法严格证明了在自适应调节律作用下闭环系统所有误差信号最终有界.最后利用倒立摆系统验证了新方法的有效性.     

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 of uncertain discrete-time state-delay systems

This paper focuses on the controller resilience and performance deterioration issues due to inaccuracies in controller implementation. It addresses the problem of resilient adaptive control problem for a class of discrete-time state-delay systems and norm-bounded uncertainties against controller gain variations. Adaptive control schemes are constructed for the case of known gain perturbation bounds and then extended to accommodate unknown norm-bounded perturbations. Necessary and sufficient conditions for delay-independent asymptotic stability are established. An expanded state-space system called the “Compact Form” is established to derive delay-dependent criteria for stability and adaptive stabilization schemes. All the developed results are conveniently expressed in linear matrix inequalities format. A detailed simulation result is presented to demonstrate the developed theory.     

Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems

In this paper, both full state and output feedback adaptive neural network (NN) controllers are presented for a class of strict-feedback discrete-time nonlinear systems. Firstly, Lyapunov-based full-state adaptive NN control is presented via backstepping, which avoids the possible controller singularity problem in adaptive nonlinear control and solves the noncausal problem in the discrete-time backstepping design procedure. After the strict-feedback form is transformed into a cascade form, another relatively simple Lyapunov-based direct output feedback control is developed. The closed-loop systems for both control schemes are proven to be semi-globally uniformly ultimately bounded.     

Intelligent adaptive control for MIMO uncertain nonlinear systems

This paper investigates an intelligent adaptive control system for multiple-input–multiple-output (MIMO) uncertain nonlinear systems. This control system is comprised of a recurrent-cerebellar-model-articulation-controller (RCMAC) and an auxiliary compensation controller. RCMAC is utilized to approximate a perfect controller, and the parameters of RCMAC are on-line tuned by the derived adaptive laws based on a Lyapunov function. The auxiliary compensation controller is designed to suppress the influence of residual approximation error between the perfect controller and RCMAC. Finally, two MIMO uncertain nonlinear systems, a mass–spring–damper mechanical system and a Chua’s chaotic circuit, are performed to verify the effectiveness of the proposed control scheme. The simulation results confirm that the proposed intelligent adaptive control system can achieve favorable tracking performance with desired robustness.     

一类MIMO非线性时滞系统的鲁棒自适应控制

针对一类具有非线性输入的MIMO时变时滞系统,基于变结构控制原理,提出了一种稳定自适应控制器设计的新方案.该方案通过使用Lyapunov-Krasovskii(L-K)泛函抵消了因未知时变时滞带来的系统不确定性;进一步,利用Young's不等式和参数自适应估计取消了非线性死区输入模犁和不确定项假设中各种参数均为已知的要求.通过理论分析,证明了闭环控制系统半全局一致终结有界,跟踪误差收敛到零的一个邻域内.     

一类未知MIMO非线性离散系统的改进自适应准滑模解耦控制

针对一类带有外部扰动的未知MIMO非线性离散系统,提出一种新型自适应准滑模控制算法.该算法基于非参数动态线性化技术,运用高阶滑模控制的思想实现带有扰动系统的二阶准滑模控制.同时,利用扰动解耦技术,在控制器的设计中引入离散扩张状态观测器(DESO)对系统各回路间的耦合以及数据模型的未建模动态进行补偿,以进一步实现多变量系统的解耦,提升控制品质.理论分析和仿真结果说明了所提出方法的有效性和可行性.     

Robust adaptive control for a class of MIMO nonlinear systems with guaranteed error bounds

The design of stabilizing controllers for multiple-input-multiple-output (MIMO) nonlinear plants with unknown nonlinearities is a challenging problem. The high dimensionality coupled with the inability to identify the nonlinearities online or offline accurately motivates the design of stabilizing controllers based on approximations or on approximate estimates of the plant nonlinearities that are simple enough to be generated in real time. The price paid in such case, could be lack of theoretical guarantees for global stability, and nonzero tracking or regulation error at steady state. In this paper, a nonlinear robust adaptive control algorithm is designed and analyzed for a class of MIMO nonlinear systems with unknown nonlinearities. The proposed control scheme provides a general approach to bypass the stabilizability problem where the estimated plant becomes uncontrollable without any restrictive assumptions. The controller is continuous and guarantees closed-loop semi-global stability and convergence of the tracking error to a small residual set. The size of the tracking error at steady state can be specified a priori and guaranteed by choosing certain design parameters. A procedure for choosing these parameters is presented. The properties of the proposed control algorithm are demonstrated using simulations.     

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.     

Robust adaptive control for a class of uncertain strict‐feedback nonlinear systems

In this paper, robust adaptive control is presented for a class of perturbed strict‐feedback nonlinear systems with both completely unknown control coefficients and parametric uncertainties. The proposed design method does not require the a priori knowledge of the signs of the unknown control coefficients. For the first time, the key technical Lemma is proven when the Nussbaum function is chosen by N(ζ)=ζ²cos(ζ), based on which the proposed robust adaptive scheme can guarantee the global uniform ultimate boundedness of the closed‐loop system signals. Simulation results show the validity of the proposed scheme. Copyright © 2008 John Wiley & Sons, Ltd.     

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。