Optimal Control for Nonlinear Interconnected Large-scale Systems: A Successive Approximation Approach

The optimal control problem for nonlinear interconnected large-scale dynamic systems is considered. A successive approximation approach for designing the optimal controller is proposed with respect to quadratic performance indexes. By using the approach, the high order, coupling,nonlinear two-point boundary value (TPBV) problem is transformed into a sequence of linear decoupling TPBV problems. It is proven that the TPBV problem sequence uniformly converges to the optimal control for nonlinear interconnected large-scale systems. A suboptimal control law is obtained by using a finite iterative result of the optimal control sequence.

Decentralized Iterative Learning Controllers for Nonlinear Large-scale Systems to Track Trajectories with Different Magnitudes

在为大规模工业进程的层次不变的优化编程，一种可行技术是使用真实系统的信息以便修改基于模型的最佳。在这种情形，有不同大小的步功能类型控制决定的一个序列被计算，由哪个真实系统连续地被刺激。在这份报纸，一套反复的学习控制器为大规模非线性的工业过程的一个班在分散的模式被嵌进层次不变的优化的过程。为每个分系统的控制器被用来产生升级的控制信号的一个序列以便与不同规模承担顺序的步骤控制决定的责任。学习控制设计的目的是连续地精制系统的短暂性能。借助于卷绕旋转积分的 Hausdorff 年轻的不平等，更新的规则的集中在 Lebesgue-p 标准的意义被分析。集中上的非线性和相互作用的发明被讨论。建议控制计划的有效性和有效性被一些模拟表明。

Optimal tracking control for nonlinear large-scale systems with persistent disturbances

This paper studies the optimal control with zero steady-state error problem for nonlinear large-scale systems affected by external persistent disturbances.The nonlinear large-scale system is transformed into N nonlinear subsystems with interconnect terms.Based on the internal model principle,a disturbance compensator is constructed such that the ith subsystem with external persistent disturbances is transformed into an augmented subsystem without disturbances.According to the sensitivity approach,the optimal tracking control law for the ith nonlinear subsystem can be obtained.The optimal tracking control law for the nonlinear large-scale systems can be obtained.A numerical simulation shows that the method is effective.

ROBUST OBSERVER DESIGN FOR A CLASS OF UNCERTAIN NONLINEAR LARGE SCALE SYSTEMS *

In this paper, a mathematic description of a class of uncertain nonlinear large scale systems based on some practical application is given. A designing method to construct observers for such kind of nonlinear composite systems is developed. The unknown parameters and disturbances are assumed to be neither linear nor matched. A numerical example is used to illustrate the efficiency of our results.

An Adaptive Sliding Mode Tracking Controller Using BP Neural Networks for a Class of Large-scale Nonlinear Systems

A new type controller, BP neural-networks-based sliding mode controller is developed for a class of large-scale nonlinear systems with unknown bounds of high-order interconnections in this paper. It is shown that decentralized BP neural networks are used to adaptively learn the uncertainty bounds of interconnected subsystems in the Lyapunov sense, and the outputs of the decentralized BP neural networks are then used as the parameters of the sliding mode controller to compensate for the effects of subsystems uncertainties. Using this scheme, not only strong robustness with respect to uncertainty dynamics and nonlinearities can be obtained, but also the output tracking error between the actual output of each subsystem and the corresponding desired reference output can asymptotically converge to zero. A simulation example is presented to support the validity of the proposed BP neural-networks-based sliding mode controller.

A two scaled numerical method for global analysis of high dimensional nonlinear systems

This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems, which regard state space respectively as continuous and discrete ones. On basis of this understanding it then points out that the previously proposed method of point mapping under cell reference (PMUCR), has laid a frame work for the development of a two scaled numerical method suitable for the global analysis of high dimensional nonlinear systems, which may take the advantages of both classes of single scaled methods but will release the difficulties induced by the disadvantages of them. The basic ideas and main steps of implementation of the two scaled method, namely extended PMUCR, are elaborated. Finally, two examples are presented to demonstrate the capabilities of the proposed method.

Robust non-fragile control for discrete-delay nonlinear large-scale systems

Time-delays,due to the information transmission between subsystems,naturally exist in large-scale systems and the existence of the delay is frequently a source of instability. This paper considers the problems of robust non-fragile fuzzy control for a class of uncertain discrete nonlinear large-scale systems with time-delay and controller gain perturbations described by T-S fuzzy model. An equivalent T-S fuzzy model is represented for discrete-delay nonlinear large-scale systems. A sufficient condition for the existence of such non-fragile controllers is further derived via the Lyapunov function and the linear matrix inequality( LMI) approach. Simulation results demonstrate the feasibility and the effectiveness of the proposed design and the proper stabilization of the system in spite of controller gain variations and uncertainties.

ADAPTIVE TRACKING CONTROL FOR A CLASS OF NONLINEAR COMPOSITE SYSTEMS *

In this paper, the problem of adaptive tracking control for a class of nonlinear large scale systems with unknown parameters entering linearly is discussed. Based on the theory of input output linearization of nonlinear systems, direct adaptive control schemes are presented to achieve bounded tracking. The proposed control schemes are robust with respect to the uncertainties in interconnection structure as well as subsystem dynamics. A numerical example is given to illustrate the efficiency of this method.

Observer-based Adaptive Optimal Control for Unknown Singularly Perturbed Nonlinear Systems With Input Constraints

This paper introduces an observer-based adaptive optimal control method for unknown singularly perturbed nonlinear systems with input constraints. First, a multi-Time scales dynamic neural network MTSDNN observer with a novel updating law derived from a properly designed Lyapunov function is proposed to estimate the system states. Then, an adaptive learning rule driven by the critic NN weight error is presented for the critic NN, which is used to approximate the optimal cost function. Finally, the optimal control action is calculated by online solving the Hamilton-Jacobi-Bellman HJB equation associated with the MTSDNN observer and critic NN. The stability of the overall closed-loop system consisting of the MTSDNN observer, the critic NN and the optimal control action is proved. The proposed observer-based optimal control approach has an essential advantage that the system dynamics are not needed for implementation, and only the measured input U+002F output data is needed. Moreover, the proposed optimal control design takes the input constraints into consideration and thus can overcome the restriction of actuator saturation. Simulation results are presented to confirm the validity of the investigated approach. © 2014 Chinese Association of Automation.

H_∞tracking design for a class of decentralized nonlinear systems via fuzzy adaptive observer

A novel H∞ tracking-based decentralized indirect adaptive output feedback fuzzy controller for a class of uncertain large-scale nonlinear systems is developed. By virtue of the proper filtering of the observation error dynamics, the observer-based decentralized indirect adaptive fuzzy control scheme is presented for a class of large-scale nonlinear systems using the combination of H∞ tracking technique, a fuzzy adaptive observer and fuzzy inference systems. The output feedback and adaptation mechanisms are both robust and implementable indeed owing to their freedom from the unavailable observation error vector. All the signals of the closed-loop largescale system are guaranteed to stay uniformly bounded and the output errors take on H∞ tracking performance. Simulation results substantiate the effectiveness of the proposed scheme.

COMPUTER COMPUTATION OF THE METHOD OF MULTIPLE SCALES-DIRICHLET PROBLEM FOR A CLASS OF SYSTEM OF NONLINEAR DIFFERENTIAL EQUATIONS

The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations . The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales .

HARMONIC, SUBHARMONIC, SUPERHARMONIC, SIMULTANEOUS SUB/SUPER HARMONIC AND COMBINATION RESONANCES OF SELF-EXCITED TWO COUPLED SECOND ORDER SYSTEMS TO MULTI-FREQUENCY EXCITATION

Harmonic, subharmonic, superharmonic, simultaneous sub/super harmonic, and combination resonances of the additive type of self-excited two coupled-second order systems to multi-frequency excitation are investigated. The theoretical results are obtained by the multiple-scales method. The steady state amplitudes for each resonance are plotted, showing the influence of the different parameters. Analysis for each figure is given. Approximate solution corresponding to each type of resonance is determined. Stability analyses are carried out for each case.

Multi-time scale dynamics in power electronics-dominated power systems

Electric power infrastructure has recently undergone a comprehensive transformation from electromagnetics to semiconductors. Such a development is attributed to the rapid growth of power electronic converter applications in the load side to realize energy conservation and on the supply side for renewable generations and power transmissions using high voltage direct current transmission. This transformation has altered the fundamental mechanism of power system dynamics, which demands the establishment of a new theory for power system control and protection. This paper presents thoughts on a theoretical framework for the coming semiconducting power systems.

Study on Variation of Parameters Formula and Stability for Impulsive Time－Delay Nonlinear Large Scale Systems

This work concerns the representation and stability properties of impulsive solutions for a class of time-delay and measure nonlinear large scale systems. On the basis of fundamental solution of the correspollding ordinary time-delay nonlinear large scale systems is established.By lumped Picard and Gauss-Seidel iteration methods which avoided the difficulties of constructing lyapunov functin, the explicit algebraic criteria of exponential stability for the impulsive and time-delay system are obtained.

STATIONARY OSCILLATIONS OF LARGE-SCALE NONLINEAR TIME-DELAY SYSTEMS

In this paper,we discuss the existence of stationary oscillations of certain large-scale nonlinear time-delay systems by weighted vector Liapunov functions and obtain a simple sufficiency criterion,which is independent of delays.

基于多尺度法的多机非线性强迫振荡机理研究

随着高比例新能源电网的发展,电力系统呈现出更明显的非线性特征,可以采用多尺度法展示二次非线性对多机系统强迫振荡的影响。首先,建立多机系统强迫振荡模型,将系统数学模型进行多次恒等变换并进行简化,与单机系统相比,多机系统有着更广泛的适用性。然后,利用多尺度法导出了非线性强迫振动稳态响应的幅频特性曲线和动态响应的近似一阶解析表达式,并分析关键参数对非线性强迫荡的影响。最后,以三机系统为例,验证了所提方法的准确性,并对由非线性引起的频率偏移和跳跃的现象做出了解释。

基于合理边界的更高速动车组多专业设计优化

考虑到非光滑与大位移两大非线性影响,作为大型复杂非线性系统的更高速动车组多专业设计优化需回归到合理的轮轨匹配边界条件。文章结合国内外高铁运维实践特殊性,以德国ICE3系列转向架为基础,提出更高速动车组转向架自适应改进方案,并针对该方案下的车体不稳定问题提出半主动车减振技术;通过构建三车组列车多体动力学仿真模型,验证了仅凭半主动车间减振技术即可解决车体不稳定问题;在不同工况下,验证更高速动车组转向架对轨道线路的适应性。结果表明:钢轨专业具备实施低锥度均匀磨耗策略的能力;车辆专业可改善对中央凹陷踏面磨耗的自清理能力;客运专业通过最优交路规划,有条件满足经济镟修要求。

有界窄带激励下手臂系统主共振分析

应用多尺度法,对随机窄带激励下人体手臂与振动机械耦合系统的第1阶主共振进行分析,建立手臂系统的二自由度非线性动力学方程。依次求解系统第1阶主共振的幅频响应方程和Ito随机微分方程。为研究随机振动下变量的分布规律,使用矩估计法计算第1阶主共振随机均方响应期望和均方值的近似表达式。通过数值分析得到人体手臂系统内参数对主共振的影响。结果表明,第1阶主共振的均方响应曲线与它们的幅频响应曲线结构相近具有拓扑关系,增大外激励的幅值主共振振幅的均方值和共振区域均增大,而系统阻尼的增大则会使均方值和共振区域减小。非线性刚度系数的改变对系统影响很小。

一类非线性大系统的动态递阶输出反馈镇定

本文应用递阶控制方法研究一类非线性大系统的输出反馈镇定问题.与分散控制不同,递阶控制包含一个系统,它根据所有子系统信息协调各子系统的本地控制.本文设计由各子系统输出驱动的动态中心协调系统,产生的协调信号被用于设计各子系统的状态观测器;然后,基于协调信号和观测器设计各子系统的反馈控制器.各子系统控制器经协调信号互相关联、协作,实现非线性大系统的镇定控制;最后,以仿真实例验证本文结论.

基于再分配伪逆的复合翼无人机飞行控制

复合翼无人机具有固定翼和旋翼无人机的气动构型,兼有两种无人机的飞行模态.在由旋翼模式向固定翼模式的过渡过程中,气动特性复杂,操控方式变化大,操控机构耦合性强,对飞行控制的鲁棒性提出了更高的要求.本文基于再分配伪逆控制算法和增量反演控制理论,研究了一种复合翼无人机全包线飞行姿态控制方法.针对飞行过程中气动特性变化大的问题,提出了一种基于增益调度理论的增量反演姿态控制方法,能够根据飞行过程的模态特性对增量反演控制器的控制器参数进行自适应调整,并从理论上分析了所研究方法的稳定性.为解决由旋翼机模式向固定翼模式过渡中操控机构转换的问题,提出了一种缩放再分配伪逆法的操控结构最优分配方法,提高了飞行过程对于控制指令的跟踪能力.仿真结果表明,本文所提出的基于再分配伪逆的增量反演控制方法相较于直接分配的反演法能以更高飞行品质实现飞行控制,过渡飞行过程姿态跟踪误差减少39%,高度跟踪误差减少87%.