New results on robust output regulation of nonlinear systems with a nonlinear exosystem

The global robust output regulation problem for nonlinear plants subject to nonlinear exosystems has been a challenging problem and has not been well addressed. The main difficulty lies in finding a suitable internal model. The existing internal model for handling the nonlinear exosystem is not zero input globally asymptotically stable, and can only guarantee a local solution for the output regulation problem. In this paper, we first propose a new class of internal models, which is guaranteed to exist under the generalized immersion condition. An advantage of this internal model is that it is zero input globally asymptotically stable. This fact will greatly facilitate the global stabilization of the augmented system associated with the given plant and the internal model. Then we will further utilize this class of internal models to solve the global robust output regulation problem for output feedback systems with a nonlinear exosystem. Copyright © 2011 John Wiley & Sons, Ltd.     

Globally asymptotic stabilization for nonlinear time-delay systems with ISS inverse dynamics

The output feedback stabilization is considered for a class of nonlinear time-delay systems with inverse dynamics in this paper.An appropriate state observer is constructed for the unmeasurable system states in order to realize the control objective.By adopting the backstepping and Lyapunov-Krasovskii functional methods,a systematic design procedure for a memoryless output feedback control law is presented.It is shown that the designed controller can make the closed-loop system globally asymptotically stable while keeping all signals bounded.An illustrative example is discussed to show the effectiveness of the proposed control strategy.     

Semi‐Global Output Feedback Stabilization for a Class of Uncertain Nonlinear Systems

This paper addresses the problem of semi‐global stabilization by output feedback for a class of nonlinear systems whose output gains are unknown. For each subsystem, we first design a state compensator and use the compensator states to construct a control law to stabilize the nominal linear system without the perturbing nonlinearities. Then, combining the output feedback domination approach with block‐backstepping scheme, a series of homogeneous output feedback controllers are constructed recursively for each subsystem and the closed‐loop system is rendered semi‐globally asymptotically stable.     

Direct data‐driven control of linear time‐delay systems

This paper presents an extension of the Virtual Reference Feedback Tuning (VRFT) methodology dedicated to linear time‐delay systems with known delay and unknown dynamics. The standard VRFT is not well suited for systems with dominant time‐delay as it yields high order controllers. The proposed direct approach, relying on a Smith Predictor structure, guarantees the same level of performance as the standard VRFT but with lower order controllers. The joint direct data‐driven design of the controller and the predictor is facilitated by the introduction of an ad‐hoc optimization initialization. Effectiveness and robustness to uncertainty in the time‐delay estimation are shown in a vehicle dynamics control problem. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Input‐to‐state stability of min‐max MPC scheme for nonlinear time‐varying delay systems

This paper studies the robustness problem of the min–max model predictive control (MPC) scheme for constrained nonlinear time‐varying delay systems subject to bounded disturbances. The notion of the input‐to‐state stability (ISS) of nonlinear time‐delay systems is introduced. Then by using the Lyapunov–Krasovskii method, a delay‐dependent sufficient condition is derived to guarantee input‐to‐state practical stability (ISpS) of the closed‐loop system by way of nonlinear matrix inequalities (NLMI). In order to lessen the online computational demand, the non‐convex min‐max optimization problem is then converted to a minimization problem with linear matrix inequality (LMI) constraints and a suboptimal MPC algorithm is provided. Finally, an example of a truck‐trailer is used to illustrate the effectiveness of the proposed results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Direct adaptive fuzzy control with membership function tuning

In this paper, a direct self‐structured adaptive fuzzy control is introduced for the class of nonlinear systems with unknown dynamic models. Control is accomplished by an adaptive fuzzy system with a fixed number of rules and adaptive membership functions. The reference signal and state errors are used to tune the membership functions and update them instantaneously. The Lyapunov synthesis method is also used to guarantee the stability of the closed loop system. The proposed control scheme is applied to an inverted pendulum and a magnetic levitation system, and its effectiveness is shown via simulation. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Feedback predictive control for constrained fuzzy systems with Markovian jumps

In this paper, a feedback model predictive control method is presented to tackle control problems with constrained multivariables for uncertain discrete‐time nonlinear Markovian jump systems. An uncertain Markovian jump fuzzy system (MJFS) is obtained by employing the Takagi‐Sugeno (T‐S) fuzzy model to represent a discrete‐time nonlinear system with norm bounded uncertainties and Markovain jump parameters. To achieve more generality, the transition probabilities of the Markov chain are assumed to be partly unknown and partly accessible. The predictive formulation adopts an on‐line optimization paradigm that utilizes the closed‐loop state feedback controller and is solved using the standard semi‐definite programming (SDP). To reduce the on‐line computational burden, a mode independent control move is calculated at every sampling time based on a stochastic fuzzy Lyapunov function (FLF) and a parallel distributed compensation (PDC) scheme. The robust mean square stability, performance minimization and constraint satisfaction properties are guaranteed under the control move for all admissible uncertainties. A numerical example is given to show the efficiency of the developed approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

An analytical and numerical study of the two-dimensional Bratu equation

Bratu's problem, which is the nonlinear eigenvalue equationu+ exp(u)=0 withu=0 on the walls of the unit square and as the eigenvalue, is used to develop several themes on applications of Chebyshev pseudospectral methods. The first is the importance ofsymmetry: because of invariance under the C₄ rotation group and parity in bothx andy, one can slash the size of the basis set by a factor of eight and reduce the CPU time by three orders of magnitude. Second, the pseudospectral method is ananalytical as well as a numerical tool: the simple approximation3.2A exp(–0.64A), whereA is the maximum value ofu(x, y), is derived via collocation with but a single interpolation point, but is quantitatively accurate for small and moderateA. Third, the Newton-Kantorovich/Chebyshev pseudospectral algorithm is so efficient that it is possible to compute good numerical solutions—five decimal places—on amicrocomputer inbasic. Fourth, asymptotic estimates of the Chebyshev coefficients can be very misleading: the coefficients for moderately or strongly nonlinear solutions to Bratu's equations fall off exponentially rather than algebraically withv untilv is so large that one has already obtained several decimal places of accuracy. The corner singularities, which dominate the behavior of the Chebyshev coefficients in thelimit v, are so weak as to be irrelevant, and replacing Bratu's problem by a more complicated and realistic equation would merely exaggerate the unimportance of the corner branch points even more.     

基于样本熵与时频分析的手部抓握运动意图预测

针对上肢外骨骼控制信号产生与外部设备响应存在时间滞后导致脑机接口(BCI)系统实时性差的问题,采集被试手部自主抓握前运动相关皮质电位(MRCP) ,提出基于非线性复杂度特征样本熵 (SampEn)与线性幅值特征融合算法的手部运动意图预测方法. 从时频、神经复杂度分析不同大脑状态之间存在的差异,通过特征融合实现对手部抓握运动意图的预测. 基于特征融合意图离线预测准确率最高可达88.46%,可以在人体手部自主运动发生时刻?1 400 ms实现对手部运动预测. 与平静时期手部静止状态相比,被试产生手部抓握运动意图时脑电信号的功率谱与复杂度均产生明显变化,为基于手部运动意图预测提前驱动机器人实现人机协同提供控制策略.     

基于观测器摩擦补偿的机电系统高精度控制

针对机电作动系统在低速阶段摩擦非线性明显且同时存在其他干扰,易导致系统跟踪精度、稳定性下降这一问题,设计基于非线性观测器摩擦补偿的自适应鲁棒控制器. 针对摩擦非线性,利用LuGre摩擦模型描述系统的摩擦现象,提出非线性观测器对模型的内部摩擦状态进行观测. 针对系统摩擦系数、转动惯量及其他不确定性参数,设计参数自适应律进行估计. 利用前馈补偿的方法,对摩擦非线性和参数不确定性进行补偿,设计鲁棒项克服系统的其他扰动. 利用Lyapunov稳定性定理证明了提出的控制器在存在扰动的情况下可以实现系统的有界稳定性. 实验结果表明,提出的控制器具有较高的控制精度与较强的鲁棒性,跟踪精度较传统的PID控制器提高了一个数量级.