基于Backstepping 的非仿射非线性系统鲁棒控制

针对一类不确定非仿射非线性系统的跟踪控制问题, 提出一种鲁棒Backstepping 控制策略. 首先, 为利用仿 射非线性方法设计控制器, 给出一种适用于全局的非仿射非线性近似方法; 然后, 设计快速收敛非线性微分器以估计复合干扰和获取虚拟信号的微分, 进而给出不确定非仿射非线性系统的复合控制器, 其中鲁棒项和阻尼项分别用于减少逼近误差和近似方法中动态误差对系统跟踪的影响; 最后, 通过仿真实验验证了所提出方法的有效性.     

Robust model predictive control for constrained continuous-time nonlinear systems

In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.     

Robust control for nonlinear systems with unknown perturbations using simplified robust right coprime factorisation

This article is concerned with operator-based robust control for nonlinear feedback system with unknown perturbations with simplified robust right coprime factorisation method. By the designed simplified robust controllers, the Bezout identity for the nominal nonlinear system and the perturbed nonlinear system are guaranteed to be simply satisfied, which means that not only the nonlinear system with nominal plant but also that with perturbed plant can be stabilised. Moreover, the plant output can be guaranteed to asymptotically track the reference output. The effectiveness of the proposed design scheme is verified by the simulation results.     

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 output regulation of minimum phase nonlinear systems using conditional servocompensators

We consider the design of a robust continuous sliding mode controller for the output regulation of a class of minimum‐phase nonlinear systems. Previous work has shown how to do this by incorporating a linear servocompensator in the sliding mode design, but the transient performance is degraded when compared to ideal sliding mode control. Extending previous ideas from the design of ‘conditional integrators’ for the case of asymptotically constant references and disturbances, we design the servocompensator as a conditional one that provides servocompensation only inside the boundary layer; achieving asymptotic output regulation, but with improved transient performance. We give both regional as well as semi‐global results for error convergence, and show that the controller can be tuned to recover the performance of an ideal sliding mode control. Copyright © 2005 John Wiley & Sons, Ltd.     

Robust control approach for input–output linearizable nonlinear systems using high‐gain disturbance observer

This paper addresses a robust control approach for a class of input–output linearizable nonlinear systems with uncertainties and modeling errors considered as unknown inputs. As known, the exact feedback linearization method can be applied to control input–output linearizable nonlinear systems, if all the states are available and modeling errors are negligible. The mentioned two prerequisites denote important problems in the field of classical nonlinear control. The solution approach developed in this contribution is using disturbance rejection by applying feedback of the uncertainties and modeling errors estimated by a specific high‐gain disturbance observer as unknown inputs. At the same time, the nonmeasured states can be calculated from the estimation of the transformed system states. The feasibility and conditions for the application of the approach on mechanical systems are discussed. A nonlinear multi‐input multi‐output mechanical system is taken as a simulation example to illustrate the application. The results show the robustness of the control design and plausible estimations of full‐rank disturbances.Copyright © 2012 John Wiley & Sons, Ltd.     

Regulation of nonlinear systems using conditional integrators

This paper studies the regulation of nonlinear systems using conditional integrators. Previous work introduced the tool of conditional integrators that provide integral action inside a boundary layer while acting as stable systems outside, leading to improvement in transient response while achieving asymptotic regulation in the presence of unknown constant disturbances or parameter uncertainties. The approach, however, is restricted to a sliding mode control framework. This paper extends this tool to a fairly general class of state feedback control laws, with the stipulation that we know a Lyapunov function for the closed‐loop system. Asymptotic regulation with improvement in transient response is done by using the Lyapunov redesign technique to implement the state feedback control as a saturated high‐gain feedback and introducing a conditional integrator to provide integral action inside a boundary layer. Improvement in the transient response using conditional integrators is demonstrated with an experimental application to the pendubot. Copyright © 2005 John Wiley & Sons, Ltd.     

Robust consensus tracking for a class of heterogeneous second‐order nonlinear multi‐agent systems

This paper deals with the robust consensus tracking problem for a class of heterogeneous second‐order nonlinear multi‐agent systems with bounded external disturbances. First, a distributed adaptive control law is proposed based on the relative position and velocity information. It is shown that for any connected undirected communication graph, the proposed control law solves the robust consensus tracking problem. Then, by introducing a novel distributed observer and employing backstepping design techniques, a distributed adaptive control law is constructed based only on the relative position information. Compared with the existing results, the proposed adaptive consensus protocols are in a distributed fashion, and the nonlinear functions are not required to satisfy any globally Lipschitz or Lipschitz‐like condition. Numerical examples are given to verify our proposed protocols. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Robust adaptive neural control of uncertain pure-feedback nonlinear systems

In this paper, a robust adaptive neural control design approach is presented for a class of uncertain pure-feedback nonlinear systems. To reduce the complexity of the both controller structure and computation, only one neural network is used to approximate the lumped unknown function of the system at the last step of the recursive design process. By this approach, the complexity growing problem existing in conventional methods can be eliminated completely. Stability analysis shows that all the closed-loop system signals are uniformly ultimately bounded, and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters. Simulation results demonstrate the effectiveness and merits of the proposed approach.     

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.     

Nonlinear robust state feedback control system design for nonlinear uncertain systems

This paper presents a systematic approach to the design of a nonlinear robust dynamic state feedback controller for nonlinear uncertain systems using copies of the plant nonlinearities. The technique is based on the use of integral quadratic constraints and minimax linear quadratic regulator control, and uses a structured uncertainty representation. The approach combines a linear state feedback guaranteed cost controller and copies of the plant nonlinearities to form a robust nonlinear controller with a novel control architecture. A nonlinear state feedback controller is designed for a synchronous machine using the proposed method. The design provides improved stability and transient response in the presence of uncertainty and nonlinearity in the system and also provides a guaranteed bound on the cost function. An automatic voltage regulator to track reference terminal voltage is also provided by a state feedback equivalent robust nonlinear proportional integral controller. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust decentralized adaptive fuzzy control for a class of large‐scale MIMO nonlinear systems

In this paper, a novel decentralized robust adaptive fuzzy control scheme is proposed for a class of large‐scale multiple‐input multiple‐output uncertain nonlinear systems. By virtue of fuzzy logic systems and the regularized inverse matrix, the decentralized robust indirect adaptive fuzzy controller is developed such that the controller singularity problem is addressed under a united design framework; no a priori knowledge of the bounds on lumped uncertainties are being required. The closed‐loop large‐scale system is proved to be asymptotically stable. Simulation results confirmed the validity of the approach presented. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust adaptive tracking of uncertain nonlinear systems by output feedback

We investigate the problem of robust adaptive tracking by output feedback for a class of uncertain nonlinear systems. Based on the high‐gain scaling technique and a new adaptive law, a linear‐like output feedback controller is constructed. Only one dynamic gain is designed, which makes the controller easier to implement. Furthermore, by modifying the update law, the adaptive controller is robust to bounded external disturbance and is able to guarantee the convergence of the output tracking error to an arbitrarily small residual set. A numerical example is used to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

一类非线性参数系统的鲁棒自适应控制

针对一类具有非线性参数和未知非线性的非线性系统, 提出了一种鲁棒自适应控制设计方法, 该方法能保证所有信号全局一致有界, 并且使所研究的非线性系统的范围大大扩大.     

Output transient trajectory shaping control for a class of nonlinear systems

This paper presents a transient trajectory shaping (TTS) control method for the SISO strict feedback nonlinear systems. The TTS control refers to explicitly constraining the system output tracking error transient trajectories within predesigned time‐varying boundaries while they are converging to equilibrium. By this method, the boundaries of system output transient trajectories can be designed a priori according to the system transient control performance requirements in both symmetric and asymmetric ways. With a class of time‐varying boundary functions, control laws can be devised by utilizing the enhanced differential unbounded function techniques. Such control laws can ascertain that the system output tracking errors travel within their respectively predesigned time‐varying boundaries while converging to origin. To handle the control input exaggeration issue in TTS, input constraint control techniques are proposed to effectively reduce the required control input magnitude for second‐order systems. A numerical example is utilized to show the effectiveness of the proposed TTS control methods. Copyright © 2013 John Wiley & Sons, Ltd.     

基于干扰观测器的一类不确定非线性系统鲁棒H∞控制

为了降低控制器对干扰的要求,基于干扰观测器提出一类多输入多输出不确定非线性系统的鲁棒H∞控制方法．将系统的内部不确定性和外部干扰组成复合干扰,设计基于小波神经网络的复合干扰观测器,并提出干扰观测器的参数调节方案使观测器能以高精度逼近复合干扰．同时在控制器中引入鲁棒控制项用来抑制观测器误差给系统带来的影响,所设计的控制器能使系统的跟踪误差小于一个给定的性能指标．最后给出一个仿真算例验证了本控制方案的有效性．     

Robust nonlinear feedback design via quantifier elimination theory

In this note symbolic-computation methods are used to design simple, fixed-structure, robust controllers for nonlinear systems. Design specifications are reduced to logically quantified polynomial inequalities. The quantifier-elimination (QE) software package QEPCAD is used to eliminate quantifiers on state and plant parameters, to obtain regions of admissible controllers parameters, that guarantee robust stability and performance. Copyright © 1999 John Wiley & Sons, Ltd.     

参数不确定时滞系统的鲁棒P ID 控制

提出一种简单而有效的参数不确定时滞系统鲁棒PID控制器设计方法．通过在kp-ki平面上绘制稳定边界线,确定稳定的PID控制器参数区域;推导了一阶不稳定时滞系统PI控制器和PID控制器的存在性条件;基于推广到时滞系统的棱边定理,确定所有鲁棒PID控制器参数集．仿真实例表明了该方法的优越性．     

Robust control for uncertain nonlinear systems with state‐dependent control direction

The control direction is the multiplier of the control term. In this study, the control direction is considered as an unknown function of state and allowed to cross zero and change its sign smoothly. Based on the analysis of system dynamics at the points where the control direction is zero, a robust controller is proposed by integrating with a bounding function and a Nussbaum‐type gain. Under the proposed controller, the system approaches zero if zero is accessible, or to the accessible point closest to zero if zero is not accessible by any control. The control performance is illustrated by simulated examples. Copyright © 2010 John Wiley & Sons, Ltd.