Uniform modeling of parameter dependent nonlinear systems

This paper addresses the problem of approximating parameter dependent nonlinear systems in a unified framework. This modeling has been presented for the first time in the form of parameter dependent piecewise affine systems. In this model, the matrices and vectors defining piecewise affine systems are affine functions of parameters. Modeling of the system is done based on distinct spaces of state and parameter, and the operating regions are partitioned into the sections that we call ’multiplied simplices’. It is proven that this method of partitioning leads to less complexity of the approximated model compared with the few existing methods for modeling of parameter dependent nonlinear systems. It is also proven that the approximation is continuous for continuous functions and can be arbitrarily close to the original one. Next, the approximation error is calculated for a special class of parameter dependent nonlinear systems. For this class of systems, by solving an optimization problem, the operating regions can be partitioned into the minimum number of hyper-rectangles such that the modeling error does not exceed a specified value. This modeling method can be the first step towards analyzing the parameter dependent nonlinear systems with a uniform method.     

基于深度神经网络的高位滑坡范围预测

以贵州尖山营滑坡为工程背景,通过对深度学习的总结与分析,建立多层感知器模型以对该滑坡危险区范围进行非线性预测研究。通过对深度神经网络算法的优化,构建64-128-32-1四层多层感知器模型,并以滑坡最大高差、滑坡体积、滑源区坡度、坡脚坡度、地层倾角作为输入量,以滑坡最大水平运动距离作为输出量对该模型进行训练,实现影响因素与运动距离的非线性映射。根据对贵州省尖山营滑坡调查和研究,尖山营滑坡区域面积约648 700 m2,体积约1 200万 m3,属于特大型滑坡。依据最优模型对该滑坡进行滑距预测,滑坡平面直线距离1 769 m区域内为危险区域。     

Robust pole assignment for incomplete nonlinear decoupling applied to robots

A robustness analysis and synthesis for incomplete nonlinear decoupling for a class of nonlinear systems is discussed. Rigid and elastic-joint robot models belong to this class. For the elastic case, a transformation facilitates the robustness analysis under a weak assumption. Charts with H ₁- and H - norms of closed-loop disturbance transfer functions of the nonlinear-decoupled system are presented for a robust pole assignment.     

基于D-FNN的混沌铁磁谐振系统非线性补偿控制方法

针对电网混沌铁磁谐振系统产生的混沌现象,提出基于动态模糊神经网络的混沌铁磁谐振系统非线性补偿控制方法。该方法采用动态模糊神经网络来逼近系统的非线性部分,消除了过电压的混沌现象,将系统稳定到目标位置,实现了对系统的非线性补偿控制。Matlab仿真结果表明,基于动态模糊神经网络的非线性补偿控制方法控制结果正确,响应快速。     

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 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     

On the use of the WLF model in polymers and foods.

The validity of the WLF model with fixed "universal" coefficients was tested against that of the model original form with variable coefficients using published coefficients of polymers and amorphous sugars crystallization and viscosity data. The disagreement between the two versions of the model is particularly large at temperature ranges starting about 20 to 30 degrees K above the glass transition or reference temperature, excluding the former from being a model of general applicability. Because the WLF model mathematical structure entails the existence of an almost linear region near the reference temperature, establishment of its validity as a kinetic model and meaningful determination of its constants requires data spread over an extended temperature range, especially when the experimental results have a scatter.