基于反步法非线性纯反馈系统的控制器设计

针对由于非线性纯反馈系统存在非仿射性结构使得用以往的坐标变换难以设计出控制器的问题,提出了一种新的坐标变换,并引入了一阶控制输入的辅助系统来处理非线性纯反馈系统。首先,结合新提出的坐标变换,计算出新状态方程;然后,基于反步法在每一步中设计出正定的Lyapunov函数;最后,通过设计虚拟控制器和实际的辅助控制器使得Lyapunov的导数负定,这样从理论上解决了非线性纯反馈系统的跟踪问题。仿真实验表明所设计的辅助控制器能使得纯反馈闭环系统所有状态信号有界,控制输出能跟踪到给定信号,跟踪误差渐近地趋于稳定,从而达到要求。     

MIMO纯反馈受限系统无模型非线性比例反演控制

针对模型未知的MIMO纯反馈系统,提出一种新的控制设计方案.该方案基于预设性能控制思想设计非线性比例控制器,并将其引入反演设计的每一步,以构建非线性比例反演控制器,并融合考虑了模型未知、状态受限、输入受限以及预设性能的需求,且无需引入任何逼近理论和自适应控制等技术即可保证系统具有良好的抗扰性和鲁棒自适应性,控制器结构极为简单.最后,基于Lyapunov稳定性定理证明了闭环系统所有信号一致有界,仿真结果验证了所提出设计方案的可行性和有效性.     

非仿射纯反馈系统自适应神经网络快速预设性能控制

鉴于在纯反馈系统控制器设计过程中广泛采用的反推法需要逐级设计虚拟控制律, 设计过程复杂, 本文通过变量替换将一类未知非仿射纯反馈系统变换为等效的积分链式系统. 利用有限时间收敛的微分器对转换系统的状态进行估计, 并构造时变的误差面. 通过对误差面的瞬态与稳态值进行性能约束并设计自适应预设性能控制器, 实现了对跟踪误差的预设性能控制. 最后, 基于Lyapunov理论进行了稳定性分析, 证明了闭环系统所有信号半全局最终一致有界. 仿真算例表明了控制方法的有效性.     

基于ISS的非线性纯反馈系统的自适应动态面控制

研究一类具有未知死区的非线性纯反馈系统的自适应控制问题．基于输入状态稳定理论和小增益定理,提出一种自适应动态面控制方案．该方案有效地减少了可调参数的数目,避免了传统后推设计中由于需要对虚拟控制反复求导而导致的计算复杂性．理论分析证明了闭环系统是半全局一致终结有界的．     

一类不确定非线性系统的预定性能自适应控制

本文研究了一类不确定严格反馈非线性系统的预定性能控制问题.为保证系统预定性能,引入了一个简单的障碍型Lyapunov函数.结合反推设计法,给出了一种新的自适应控制算法.理论与实验结果表明,所得控制器不仅保证了系统预定性能,且使得闭环系统所有信号有界.     

一类纯反馈非线性系统的简化自适应神经网络动态面控制

针对一类完全非仿射纯反馈非线性系统,提出一种简化的自适应神经网络动态面控制方法.基于隐函数定理和中值定理将未知非仿射输入函数进行分解,使其含有显式的控制输入;利用简化的神经网络逼近未知非线性函数,对于阶SISO纯反馈系统,仅一个参数需要更新;动态面控制可消除反推设计中由于对虚拟控制反复求导而导致的复杂性问题.通过Lyapunov稳定性定理证明了闭环系统的半全局稳定性,数值仿真验证了方法的有效性.     

基于ADP的导引控制一体化全状态受限反演控制

针对导引控制一体化设计中状态受限及非线性最优问题，提出了一种结合反演控制与自适应动态规划（ADP）技术，考虑全状态受限的新型导引控制一体化设计方法.首先，将状态受限的严格反馈系统通过坐标变换转化为非状态受限系统.然后，采用前馈反演控制与反馈最优控制相结合的设计思路，利用ADP技术在线求解非线性HJB方程得到最优解.最后通过李亚普诺夫理论证明了系统的闭环稳定性与所有信号的一致有界性.与传统方法的对比仿真验证了该设计方法的可行性与优越性.     

非仿射纯反馈系统的间接自适应神经网络控制

针对非仿射纯反馈系统,提出了一种新的设计方案.与现有文献中方法不同,该方案不是直接利用逼近技巧构建理想的反馈控制器.首先通过自抗扰思想将非仿射纯反馈系统转化成含有未知控制系数以及未知非线性的仿射系统,并且证明了可行性.然后结合微分器和全调节径向基函数神经网络,利用自适应反演技巧设计了自抗扰控制器,微分器的引入避免了传统反演的计算复杂性.最后,从理论上证明了所设计的控制器能够保证闭环系统所有信号半全局一致有界,并且证明了系统状态渐进收敛到零点的残集内.仿真例子验证了算法的有效性.     

一种非线性PD控制器设计

为了提高PD控制器的性能,提出了一种非线性设计方法。利用电容极间电场和PD控制器的控制作用之间存在的一些相似性,构造了一种非线性函数,并以此形成一种非线性PD控制器,这种控制器能为系统的运行状态提供灵活的增益策略;利用系统的运行状态信息,在相平面中实时旋转该电容结构,可以减少这种非线性PD控制器的设计参数。通过对一个机械手系统进行仿真,结果表明,这种控制方式能够获得较好的系统动态响应速度和参数鲁棒性能。     

基于ISS的非线性纯反馈系统的自适应动态面控制

研究一类具有未知死区的非线性纯反馈系统的自适应控制问题．基于输入状态稳定理论和小增益定理,提出一种自适应动态面控制方案．该方案有效地减少了可调参数的数目,避免了传统后推设计中由于需要对虚拟控制反复求导而导致的计算复杂性．理论分析证明了闭环系统是半全局一致终结有界的．

     

Robust adaptive prescribed performance control for a class of nonlinear pure‐feedback systems

An adaptive prescribed performance control design procedure for a class of nonlinear pure‐feedback systems with both unknown vector parameters and unmodeled dynamics is presented. The unmodeled dynamics lie within some bounded functions, which are assumed to be partially known. A state transformation and an auxiliary system are proposed to avoid using the cumbersome formula to handle the nonaffine structure. Simultaneously, a parameter‐type Lyapunov function and L function are designed to ensure the prescribed performance of the pure‐feedback system. As illustrated by examples, the proposed adaptive prescribed performance control scheme is shown to guarantee global uniform ultimate boundedness. At the same time, this method not only guarantees the prescribed performance of the system but also makes the tracking error asymptotically close to a certain value or stable.     

A low-complexity global approximation-free control scheme with prescribed performance for unknown pure feedback systems

A universal, approximation-free state feedback control scheme is designed for unknown pure feedback systems, capable of guaranteeing, for any initial system condition, output tracking with prescribed performance and bounded closed loop signals. By prescribed performance, it is meant that the output error converges to a predefined arbitrarily small residual set, with convergence rate no less than a certain prespecified value, having maximum overshoot less than a preassigned level. The proposed state feedback controller isolates the aforementioned output performance characteristics from control gains selection and exhibits strong robustness against model uncertainties, while completely avoiding the explosion of complexity issue raised by backstepping-like approaches that are typically employed to the control of pure feedback systems. In this respect, a low complexity design is achieved. Moreover, the controllability assumptions reported in the relevant literature are further relaxed, thus enlarging the class of pure feedback systems that can be considered. Finally, simulation studies clarify and verify the approach.     

Passivity-based robust feedback control for non-linear systems with input dynamical uncertainty

This paper addresses the robust feedback control problem for a class of non-linear systems with uncertain input dynamics. The main objective is to develop a passivity-based systematic design approach for this kind of uncertain system. First, a passivity condition is presented for a non-linear system in feedback interconnection form, and then it is shown that with the help of this condition, a state feedback control law can be designed to render the uncertain system passive. Moreover, the extensions of the passivation controller are investigated in two cases where the uncertainty allows unknown control direction and there exists the external disturbance, respectively. It will be shown that an adaptive controller with a Nussbaum-type function can be incorporated into the passivation controller to deal with the unknown control direction and the L ₂-gain performance can be achieved by gain re-assignment of the passivation controller. Finally, a numerical example is given to demonstrate the proposed approach.     

Time-domain performance based non-linear state feedback control of constrained linear systems

This article describes a method to design a non-linear state feedback controller that meets a set of time-domain specifications not attainable by linear state feedback. Using a constrained polynomial interpolation technique, an input signal is computed that satisfies the desired time-domain constraints on the input and state-trajectories. The computed input is constructed by non-linear combinations of the states, such that a non-linear state feedback law is obtained. Stability of the resulting closed-loop polynomial system is analysed using sum-of-squares techniques. An illustrative example is presented, showing that the proposed non-linear controller outperforms the best linear static state feedback. To validate the proposed method, experiments on a fourth-order motion system have been carried out.     

State-feedback control of non-linear systems†

A design method for state-feedback controllers for single-input non-linear systems is proposed. The method makes use of the transformations of the non-linear system into ‘controllable-like’ canonical forms. The resulting non-linear state feedback is designed in such a way that the eigenvalues of the linearized closed-loop model are invariant with respect to any constant operating point. The method constitutes an alternative approach to the design methodology recently proposed by Baumann and Rugh. Also a review of different transformation methods for non-linear systems is presented. An example and simulation results of different control strategies are provided to illustrate the design technique.     

Fault-tolerant control for a class of non-linear systems with dead-zone

In this paper, a fault-tolerant control scheme is proposed for a class of single-input and single-output non-linear systems with the unknown time-varying system fault and the dead-zone. The non-linear state observer is designed for the non-linear system using differential mean value theorem, and the non-linear fault estimator that estimates the unknown time-varying system fault is developed. On the basis of the designed fault estimator, the observer-based fault-tolerant tracking control is then developed using the backstepping technique for non-linear systems with the dead-zone. The stability of the whole closed-loop system is rigorously proved via Lyapunov analysis and the satisfactory tracking control performance is guaranteed in the presence of the unknown time-varying system fault and the dead-zone. Numerical simulation results are presented to illustrate the effectiveness of the proposed backstepping fault-tolerant control scheme for non-linear systems.     

An ISS-modular approach for adaptive neural control of pure-feedback systems

Controlling non-affine non-linear systems is a challenging problem in control theory. In this paper, we consider adaptive neural control of a completely non-affine pure-feedback system using radial basis function (RBF) neural networks (NN). An ISS-modular approach is presented by combining adaptive neural design with the backstepping method, input-to-state stability (ISS) analysis and the small-gain theorem. The difficulty in controlling the non-affine pure-feedback system is overcome by achieving the so-called “ISS-modularity” of the controller-estimator. Specifically, a neural controller is designed to achieve ISS for the state error subsystem with respect to the neural weight estimation errors, and a neural weight estimator is designed to achieve ISS for the weight estimation subsystem with respect to the system state errors. The stability of the entire closed-loop system is guaranteed by the small-gain theorem. The ISS-modular approach provides an effective way for controlling non-affine non-linear systems. Simulation studies are included to demonstrate the effectiveness of the proposed approach.     

Adaptive finite‐time neural backstepping control for multi‐input and multi‐output state‐constrained nonlinear systems using tangent‐type nonlinear mapping

This article focuses on the problem of adaptive finite‐time neural backstepping control for multi‐input and multi‐output nonlinear systems with time‐varying full‐state constraints and uncertainties. A tan‐type nonlinear mapping function is first proposed to convert the strict‐feedback system into a new pure‐feedback one without constraints. Neural networks are utilized to cope with unknown functions. To improve learning performance, a composite adaptive law is designed using tracking error and approximate error. A finite‐time convergent differentiator is adopted to avoid the problem of “explosion of complexity.” By theoretical analysis, all the signals of system are proved to be bounded, the outputs can track the desired signals in a finite time, and full‐state constraints are not transgressed. Finally, comparative simulations are offered to confirm the validity of the proposed control scheme.     

A linear differential operator approach to flatness based tracking for linear and non-linear systems

This contribution presents a flatness based solution to the tracking for linear systems in differential operator representation. Since the differential operator representation is a flat system representation, tracking controllers can easily be designed using dynamic output feedback. Then, the differential operator approach for flatness based tracking of linear systems is extended to non-linear systems. The design of the resulting linear time varying dynamic output feedback controller is based on a linearization about the trajectory, which directly yields the differential operator representation. Different from the non-linear flatness based controller design the new approach uses linear methods, both in stabilizing the tracking and in computing the output feedback controller. The proposed design procedure assures exact tracking in the steady state when no disturbances are present. A simple example demonstrates the design of a dynamic output feedback controller for the tracking of a non-linear system.