Robust control of nonlinear semi‐strict feedback systems using finite‐time disturbance observers

The output tracking controller design problem is dealt with for a class of nonlinear semi‐strict feedback systems in the presence of mismatched nonlinear uncertainties, external disturbances, and uncertain nonlinear virtual control coefficients of the subsystems. The controller is designed in a backstepping manner, and to avoid the shortcoming of ‘explosion of terms’, the dynamic surface control technique that employs a group of first‐order low‐pass filters is adopted. At each step of the virtual controller design, a robust feedback controller employing some effective nonlinear damping terms is designed to guarantee input‐to‐state practical stable property of the corresponding subsystem, so that the system states remain in the feasible domain. The virtual controller is enhanced by a finite‐time disturbance observer that estimates the disturbance term in a finite‐time. The properties of the composite control system are analyzed theoretically. Furthermore, by exploiting the cascaded structure of the control system, a simplified robust controller is proposed where only the first subsystem employs a disturbance observer. The performance of the proposed methods is confirmed by numerical examples. Copyright © 2017 John Wiley & Sons, Ltd.     

一类非匹配不确定非线性系统的鲁棒跟踪控制制

针对一类半严格反馈型不确定非线性系统,提出一种鲁棒反演滑模变结构控制方法.采用反演控制方法设计了使前n-1阶子系统稳定的虚拟控制律,抑制非匹配不确定性的影响;在第n步设计了一种连续可导的滑模变结构控制律,消除控制抖振,实现了对存在未知不确定性及扰动系统的鲁棒输出跟踪.通过Lyapunov定理证明了闭环系统所有信号最终有界.仿真结果验证了该方法的有效性.     

Two‐stage stability control for strict‐feedback systems with input delays and input nonlinear uncertainties

In this paper, a two‐stage control procedure is proposed for stabilization of a class of strict‐feedback systems with unknown constant time delays and nonlinear uncertainties in the input. A nominal controller is first designed to compensate input time delays without considering input nonlinear uncertainties. Extended from backstepping algorithm, input delay compensation is realized by means of predicted states that are computed through integration of cascaded system dynamics, making the nominal closed‐loop system asymptotically stable. Based on the nominal controller presented for the input delay system, a multi‐timescale system is subsequently developed to estimate the unknown input nonlinearity and make the estimate approach the nominal control input as fast as possible. It is proved that the proposed control scheme can make states of the strict‐feedback systems converge to zero and all the signals of the closed‐loop systems are guaranteed to be bounded in the presence of input time delays and nonlinear uncertainties. Simulation verification is carried out to illuminate the effectiveness of the proposed control approach.     

Multi‐parametric extremum seeking‐based iterative feedback gains tuning for nonlinear control

We study in this paper the problem of iterative feedback gains auto‐tuning for a class of nonlinear systems. For the class of input–output linearizable nonlinear systems with bounded additive uncertainties, we first design a nominal input–output linearization‐based robust controller that ensures global uniform boundedness of the output tracking error dynamics. Then, we complement the robust controller with a model‐free multi‐parametric extremum seeking control to iteratively auto‐tune the feedback gains. We analyze the stability of the whole controller, that is, the robust nonlinear controller combined with the multi‐parametric extremum seeking model‐free learning algorithm. We use numerical tests to demonstrate the performance of this method on a mechatronics example. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive Robust Output Tracking Control of Uncertain Nonlinear Cascade Systems with Disturbance and Multiple Unknown Time‐Varying Delays

In this paper, an adaptive robust controller is designed for a class of uncertain nonlinear cascade systems with multiple time‐varying delays under external disturbance. It is assumed that multiple time‐varying delays are not exactly known and, therefore, the delayed terms must not appear in the adaptation and control laws. Accordingly, by using a Lyapunov‐Krasovskii function, delays are deleted from the adaptation and control laws. A controller based on an adaptive backstepping approach is designed to assure the global asymptotic tracking of the desired output and boundedness of the other states. The proposed controller is proved to be robust against unknown time‐varying delays and external disturbances applying to the system. Simulation results are provided to show the effectiveness of the proposed approach.     

Robust backstepping output tracking control for SISO uncertain nonlinear systems with unknown virtual control coefficients

The output tracking controller design problem is dealt with for a class of nonlinear strict-feedback form systems in the presence of nonlinear uncertainties, external disturbance, unmodelled dynamics and unknown time-varying virtual control coefficients. A new method based on signal compensation is proposed to design a linear time-invariant robust controller, which consists of a nominal controller and a robust compensator. It is shown that the closed-loop control system with a controller designed by the proposed method has robust asymptotical practical tracking property for any bounded initial conditions and robust tracking transient property if all initial states are zero.     

Robust Control System Design for an Uncertain Nonlinear System Using Minimax LQG Design Method

A systematic approach to design a nonlinear controller using minimax linear quadratic Gaussian regulator (LQG) control is proposed for a class of multi‐input multi‐output nonlinear uncertain systems. In this approach, a robust feedback linearization method and a notion of uncertain diffeomorphism are used to obtain an uncertain linearized model for the corresponding uncertain nonlinear system. A robust minimax LQG controller is then proposed for reference command tracking and stabilization of the nonlinear system in the presence of uncertain parameters. The uncertainties are assumed to satisfy a certain integral quadratic constraint condition. In this method, conventional feedback linearization is used to cancel nominal nonlinear terms and the uncertain nonlinear terms are linearized in a robust way. To demonstrate the effectiveness of the proposed approach, a minimax LQG‐based robust controller is designed for a nonlinear uncertain model of an air‐breathing hypersonic flight vehicle (AHFV) with flexibility and input coupling. Here, the problem of constructing a guaranteed cost controller which minimizes a guaranteed cost bound has been considered and the tracking of velocity and altitude is achieved under inertial and aerodynamic uncertainties.     

Robust approximation‐based adaptive control of multiple state delayed nonlinear systems with unmodeled dynamics

This paper addresses the problem of tracking control for a class of uncertain nonstrict‐feedback nonlinear systems subject to multiple state time‐varying delays and unmodeled dynamics. To overcome the design difficulty in system dynamical uncertainties, radial basis function neural networks are employed to approximate the black‐box functions. Novel continuous functions that deal with whole states uncertainties are introduced in each step of the adaptive backstepping to make the controller design feasible. The robust problem caused by unmodeled dynamics when constructing a stable controller is solved by employing an auxiliary signal to regulate its boundedness. A novel Lyapunov‐Krasovskii functional is developed to compensate for the delayed nonlinearity without requiring the priori knowledge of its upper bound functions. On the basis of the proposed robust adaptive neural controller, all the closed‐loop signals are semiglobal uniformly ultimately bounded with good tracking performance.     

非匹配不确定系统的显式反步变结构控制

研究非线性多输入多输出不确定系统在非匹配条件下的鲁棒输出跟踪问题.基于相对阶的假设,给出了多输入多输出不确定系统的标准型;进而结合反步设计方法和变结构控制方法,提出一种非匹配条件下非线性不确定系统鲁棒输出跟踪问题的显式反步变结构控制器设计方法.所给跟踪算法不仅只由不确定性的变化范围直接确定,而且有效地克服了现有反步设计算法因隐式递推关系和复杂偏导数计算给实时控制带来的困难.     

基于非线性干扰观测器的高超声速飞行器滑模反演控制

针对高超声速飞行器非线性、强耦合和参数不确定弹性体模型,提出了一种基于非线性干扰观测器的滑模反演控制方法.将飞行器曲线拟合模型分解为速度子系统和高度相关子系统并表示为严格反馈形式,分别采用滑模和反演方法设计实际控制量与虚拟控制量.采用1阶低通滤波器获取虚拟控制量的导数,解决了传统反演控制方法"微分项膨胀"问题.基于改进滑模微分器设计了一种新型非线性干扰观测器,以此对模型不确定项进行估计和补偿.仿真结果表明,该控制器对模型不确定性和气动弹性影响具有鲁棒性,且实现了对速度和高度参考输入的稳定跟踪.     

Robust nonlinear control of a three-tank system using finite-time disturbance observers

A finite-time disturbance observer-based robust control method is proposed for output tracking of the Inteco threetank system in the presence of mismatched uncertainties. The controller is designed in a backstepping manner. At each step of the virtual controller design, a robust feedback controller with some effective nonlinear damping terms is designed so that the system states remain in the feasible domain. The nonlinear uncertainty is compensated by a finite-time disturbance observer. And to avoid the shortcoming of “explosion of terms”, the dynamic surface control technique which employs a low-pass filter is adopted at each step of the virtual controller design. Attention is paid to reducing the measurement noise effects and to initialization technique of the system states and reference output trajectory. Theoretical analysis is performed to clarify the control performance. And the theoretical results are verified based on the experimental studies on the real Inteco three-tank system.     

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.     

一种非线性多环递归自适应跟踪控制

针对控制输入有界的变参数广义高阶非线性系统跟踪控制问题,给出一种多环递归跟踪的鲁棒控制方法.通过分层引入虚拟跟踪器,将高阶系统分解为多个独立子系统;内环虚拟跟踪器使内环输出指数收敛于外环虚拟输入,最内环设计自适应控制器补偿参数摄动和外部干扰,并保证输出指数收敛于外环虚拟输入;多环递归跟踪实现系统输出精确跟踪期望输入,理论证明闭环系统的全局渐近收敛性.数值仿真验证了多环跟踪控制器的可行性和合理性.     

高超声速飞行器非线性鲁棒控制律设计

高超声速飞行器具有模型非线性程度高、耦合程度强、参数不确定性大、抗干扰能力弱等特点,其自主控制具有较大的挑战.论文提出了一种基于鲁棒补偿技术和反馈线性化方法的非线性鲁棒控制方法.文中首先采用反馈线性化的方法对纵向模型进行输入输出线性化,实现速度和高度通道的解耦和非线性模型的线性化.针对得到的线性模型,设计包括标称控制器和鲁棒补偿器的线性控制器.基于极点配置原理,设计标称控制器使标称线性系统具有期望的输入输出特性,利用鲁棒补偿器来抑制参数不确定性和外界扰动对于闭环控制系统的影响.基于小增益定理,证明了闭环控制系统的鲁棒稳定性和鲁棒跟踪性能.相比于非线性回路成形控制方法,仿真结果表明了所设计非线性鲁棒控制算法的有效性和优越性.     

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

This paper addresses the output feedback tracking control of a class of multiple‐input and multiple‐output nonlinear systems subject to time‐varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory‐based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time‐varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady‐state tracking accuracy in spite of the presence of time‐varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a Lyapunov‐Krasovskii functional. A specific study on a 2‐link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme.     

Robust Output Feedback Consensus of High-order Multi-agent Systems with Nonlinear Uncertainties

In this paper, the output feedback consensus problem of high-order multi-agent systems with nonlinear uncertainties is researched by the robust control method. By the dimensional extension of the observation matrix, the consensus control problem is transformed into a stability problem. Then the robust controller is designed by combining the nominal controller and the robust compensator. The nominal controller can obtain desired nominal performance based on the output informations. The robust compensator, which relys on robust signal compensation technology, is order to suppress the nonlinear uncertainties. According to the proposed method, output consensus error can be guaranteed as small as desired. Finally, simulation results are given to illustrate the effectiveness of this control method.     

四旋翼无人机鲁棒自适应姿态控制

 四旋翼无人机的姿态控制是自主飞行控制的核心,针对四旋翼姿态易受外界环境干扰和内部参数摄动等不确定性影响的问题,设计了一种鲁棒自适应反步控制器,以提高四旋翼的鲁棒性。建立了四旋翼完整的姿态运动模型,并将其转化为含有广义不确定性的多输入多输出非线性系统。根据该系统满足严格反馈的结构特点,设计了反步控制器; 针对系统中存在的外部干扰和内部参数摄动等不确定性,引入了一类鲁棒自适应函数来抵消该不确定性对系统的影响; 采用非线性跟踪微分器估计虚拟控制量的微分信号,减小了反步控制器设计中普遍存在的“计算膨胀”问题; 通过构造Lyapunov 函数证明闭环系统是稳定且指数收敛的。仿真结果表明,所设计控制器具有良好的控制效果和鲁棒性。     

Robust Tracking Control For A Wheeled Mobile Manipulator With Dual Arms Using Hybrid Sliding‐Mode Neural Network

In this paper, a robust tracking controller is proposed for the trajectory tracking problem of a dual‐arm wheeled mobile manipulator subject to some modeling uncertainties and external disturbances. Based on backstepping techniques, the design procedure is divided into two levels. In the kinematic level, the auxiliary velocity commands for each subsystem are first presented. A sliding‐mode equivalent controller, composed of neural network control, robust scheme and proportional control, is constructed in the dynamic level to deal with the dynamic effect. To deal with inadequate modeling and parameter uncertainties, the neural network controller is used to mimic the sliding‐mode equivalent control law; the robust controller is designed to compensate for the approximation error and to incorporate the system dynamics into the sliding manifold. The proportional controller is added to improve the system's transient performance, which may be degraded by the neural network's random initialization. All the parameter adjustment rules for the proposed controller are derived from the Lyapunov stability theory and e‐modification such that uniform ultimate boundedness (UUB) can be assured. A comparative simulation study with different controllers is included to illustrate the effectiveness of the proposed method.     

Robust Finite‐Time Stability Control of a Class of High‐Order Uncertain Nonlinear Systems

In this study, a novel robust finite‐time stability controller is proposed for a class of high‐order uncertain nonlinear systems. It uses the dynamic surface control (DSC) approach to simplify the traditional backstepping design for high‐order nonlinear systems, thus avoiding the “explosion of terms”. The finite‐time stability of the closed‐loop system is guaranteed to have high performance, such as fast transient and strong robustness to dynamic uncertainties, and the tracking error is made arbitrarily small. Simulation results of two examples indicate that the proposed controller is effective.     

Adaptive Fuzzy Control for Nonlinear Time‐Delay Systems with Dynamical Uncertainties

In this paper, an adaptive fuzzy backstepping robust control approach is proposed for a class of SISO nonlinear strict‐feedback systems. The nonlinear systems addressed in this paper are assumed to possess three uncertainties: (i) the unstructured uncertainties; (ii) the time delays; and (iii) the dynamics uncertainties. In adaptive backstepping recursive design, fuzzy logic systems are used to approximate the unstructured uncertainties. A nonlinear damping technique and Lyapunov–Krasovskii functions are introduced to cancel the effects of the dynamics uncertainties and deal with the time delays, respectively. Combining the backstepping technique and a small gain approach, a stable adaptive fuzzy robust control approach is developed. It is proved that all the signals of the closed‐loop system are semi‐golablly uniformaly ultimately bounded (SUUB). The effectiveness of the proposed approach is illustrated by a simulation example.