Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.     

Design of disturbance observer based on adaptive-neural control for large-scale time-delay systems in the presence of actuator fault and unknown dead zone

This article presents an adaptive neural compensation scheme for a class of large-scale time delay nonlinear systems in the presence of unknown dead zone, external disturbances, and actuator faults. In this article, the quadratic Lyapunov–Krasovskii functionals are introduced to tackle the system delays. The unknown functions of the system are estimated by using radial basis function neural networks. Furthermore, a disturbance observer is developed to approximate the external disturbances. The proposed adaptive neural compensation control method is constructed by utilizing a backstepping technique. The boundedness of all the closed-loop signals is guaranteed via Lyapunov analysis and the tracking errors are proved to converge to a small neighborhood of the origin. Simulation results are provided to illustrate the effectiveness of the proposed control approach.     

Delay compensated control of the Stefan problem and robustness to delay mismatch

This paper presents a control design for the one‐phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid‐solid phase change phenomenon which describes the time evolution of a material's temperature profile and the interface position. The actuator delay is modeled by a first‐order hyperbolic partial differential equation (PDE), resulting in a cascaded transport‐diffusion PDE system defined on a time‐varying spatial domain described by an ordinary differential equation (ODE). Two nonlinear backstepping transformations are utilized for the control design. The setpoint restriction is given to guarantee a physical constraint on the proposed controller for the melting process. This constraint ensures the exponential convergence of the moving interface to a setpoint and the exponential stability of the temperature equilibrium profile and the delayed controller in the norm. Furthermore, robustness analysis with respect to the delay mismatch between the plant and the controller is studied, which provides analogous results to the exact compensation by restricting the control gain.     

Multilevel adaptive control of nonlinear interconnected systems

This paper presents an adaptive backstepping-based multilevel approach for the first time to control nonlinear interconnected systems with unknown parameters. The system consists of a nonlinear controller at the first level to neutralize the interaction terms, and some adaptive controllers at the second level, in which the gains are optimally tuned using genetic algorithm. The presented scheme can be used in systems with strong couplings where completely ignoring the interactions leads to problems in performance or stability. In order to test the suitability of the method, two case studies are provided: the uncertain double and triple coupled inverted pendulums connected by springs with unknown parameters. The simulation results show that the method is capable of controlling the system effectively, in both regulation and tracking tasks.     

基于反步自适应神经网络的船舶航迹控制

针对欠驱动船舶在稳定航速条件下轨迹跟踪问题,提出了一种基于自适应神经网络与反步法相结合的控制算法.该算法将实际的欠驱动船舶视为模型完全未知的非线性系统,利用神经网络的函数逼近特性实现控制器中非线性部分的在线估计,采用同时调整输入层-隐层、隐层-输出层间的权值阵的方法进行神经网络权值调整.通过选取积分型Lyapunov函数证明了闭环系统的稳定性.仿真实验表明该控制策略具有良好的跟踪特性,可以实现对期望航迹的精确跟踪.     

On the backstepping design procedure for multiple input nonlinear systems

In a recent paper, we developed a structural decomposition for multiple input multiple output nonlinear systems that are affine in control but otherwise general. In this paper, we exploit the structural properties of such a decomposition in the application of the backstepping design technique on multiple input nonlinear systems. In particular, this decomposition simplifies the conventional backstepping design and motivates new backstepping design procedures that are able to stabilize systems on which the conventional backstepping procedure is not applicable. Copyright © 2011 John Wiley & Sons, Ltd.     

Integrated relative position and attitude control of spacecraft in proximity operation missions

This paper addresses an integrated relative position and attitude control strategy for a pursuer spacecraft flying to a space target in proximity operation missions. Relative translation and rotation dynamics are both presented, and further integratedly considered due to mutual couplings, which results in a six degrees-of-freedom (6-DOF) control system. In order to simultaneously achieve relative position and attitude requirements, an adaptive backstepping control law is designed, where a command filter is introduced to overcome "explosion of terms". Within the Lyapunov framework, the proposed controller is proved to ensure the ultimate boundedness of relative position and attitude signals, in the presence of external disturbances and unknown system parameters. Numerical simulation demonstrates the effect of the designed control law.     

Design of a two‐level controller for an active suspension system

The paper focuses on a control design for a vehicle suspension system in which a balance between different performance demands is achieved. The starting point of the control design is a full–car model which contains nonlinear components, i.e. the dynamics of the dampers and springs and nonlinear actuator dynamics. In order to handle the high complexity of the problem this paper proposes the design of a two‐level controller of an active suspension system. The required control force is computed by applying a high‐level controller, which is designed using a linear parameter varying (LPV) method. For the control design the model is augmented with weighting functions specified by the performance demands and the uncertainty assumptions. The actuator generating the necessary control force is modelled as a nonlinear system for which a low‐level force‐tracking controller is designed. To obtain the low‐level controller a backstepping method is proposed. As an alternative solution a feedback linearization method is also presented. The operation of the controller is illustrated through simulation examples. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Modeling and global trajectory tracking control for an over-actuated MAV

This paper deals with an original micro aerial vehicle (MAV) design, the Omnicopter MAV. It has two central coaxial rotors with fixed-pitch propellers and three perimeter mounted ducted fans with servo motors performing thrust vectoring. Compared with traditional rotary wing MAVs that have inherent underactuation, the Omnicopter possesses some advantages in mobility, for example, lateral translation with zero attitude and hover with nonzero attitude. The trajectory tracking control design, global stability analysis, and control allocation are demonstrated through numerical simulation. The advantage of zero attitude translation is illustrated through experimental results.     

结合误差变换的Bouc-Wen迟滞非线性系统反步控制器设计

针对智能材料执行器中非平滑、多映射的迟滞非线性,采用Bouc-Wen模型描述迟滞,并提出了一种基于误差变换的反步控制器设计方案.首先利用Bouc-Wen模型中的变量特性,通过预设性能函数,将误差约束在预设范围内.然后通过误差变换,将一个对输出误差存在约束的跟踪问题转化为一个无约束的镇定问题.最后利用反步控制法设计迟滞系统的控制器,该控制方法保证期望的跟踪精度,并能将误差限定在设定范围内且满足预设性能,提高了系统的暂态和稳态性能.仿真结果表明设计方法的有效性.