Application of gap metric to model bank determination in multilinear model approach

This paper presents a gap metric based method which aims to perform the operating range decomposition and the minimum linear model bank determination of a nonlinear system when multilinear model approach is employed to design a controller for this nonlinear system. For a prescribed distance level, the minimum linear model bank determined by the proposed method can provide sufficient information for multilinear model controller design of the nonlinear system. To illustrate the usefulness of the proposed method, two examples of nonlinear systems are presented. Moreover, a mixed logical dynamical model-based MPC (MLD–MPC) controller is designed based on the minimum model bank. Simulations confirm the method for selecting linear model bank in multilinear model approach.     

Multiple model bank selection based on nonlinearity measure and H-gap metric

This paper provides a systematic method for model bank selection in multi-linear model analysis for nonlinear systems by presenting a new algorithm which incorporates a nonlinearity measure and a modified gap based metric. This algorithm is developed for off-line use, but can be implemented for on-line usage. Initially, the nonlinearity measure analysis based on the higher order statistic (HOS) and the linear cross correlation methods are used for decomposing the total operating space into several regions with linear models. The resulting linear models are then used to construct the primary model bank. In order to avoid unnecessary linear local models in the primary model bank, a gap based metric is introduced and applied in order to merge similar linear local models. In order to illustrate the usefulness of the proposed algorithm, two simulation examples are presented: a pH neutralization plant and a continuous stirred tank reactor (CSTR).     

Correlation analysis based MIMO neuro-fuzzy Hammerstein model with noises

A novel identification algorithm for neuro-fuzzy based MIMO Hammerstein system with noises by using the correlation analysis method is presented in this paper. A special test signal that contains independent separable signals and uniformly random multi-step signal is adopted to identify the MIMO Hammerstein system, resulting in the identification problem of the linear model separated from that of nonlinear part. As a result, it can circumvent the problem of initialization and convergence of the model parameters encountered by the existing iterative algorithms used for identification of MIMO Hammerstein model. Moreover, least square method based parameter identification algorithms of dynamic linear part and static nonlinear part are proposed to avoid the influence of noise. Examples are used to illustrate the effectiveness of the proposed method.     

MIMO系统的多模型预测控制

针对非线性多变量系统提出一种多模型预测控制(MMPC)策略.首先给出一种多模型 辨识方法,利用模糊满意聚类算法将复杂非线性系统划分为若干子系统,并获得多个线性模型, 通过模型变换得出全局系统模型,接着对全局MIMO系统设计MMPC,并进行了系统的性能分 析,最后以pH中和过程为例,通过仿真研究验证了辨识和控制算法的有效性.     

The nonlinear model-predictive control of a chemical plant using multiple neural networks

A combination of multiple neural networks (NNs) is selected and used to model nonlinear multi-input multi-output (MIMO) processes with time delays. An optimisation procedure for a nonlinear model-predictive control (MPC) algorithm based on this model is then developed. The proposed scheme has been applied and evaluated for two example problems, including the MPC of a multi-component distillation column.     

Efficient routing redundancy design over lossy networks

In this paper, a wireless networked control system is made robust with respect to packet losses by exploiting routing redundancy. Multiple copies of sensing and actuation data are sent via different routing paths, associated to possibly different delays. Similar to linear network coding, such data are recombined as a weighted linear combination. A MIMO output‐feedback architecture is considered. A methodology that takes into account both the network parameters and the plant dynamics is proposed to set up an optimization problem to design network weights to satisfy a robustness metric based on the notion of asymptotic mean‐square stability. Such metric induces either an objective or a constraint function that is nonlinear. For this reason, an efficient suboptimal design methodology is also proposed. Finally, the solutions are compared with the optimal choice from the communication designer point of view, which is based on the minimization of the quadratic error induced by the network on the actuation signal. The suboptimal methodology is shown, by means of a nontrivial example, to give results extremely close to the optimum with a strongly reduced computation time. It is also shown that the optimal choice from the communication design point of view, which neglects the plant dynamics, does not guarantee stochastic stability.     

A gap metric based weighting method for multimodel predictive control of MIMO nonlinear systems

A novel weighting method is proposed for multimodel predictive control of nonlinear systems with multiple scheduling variables (MIMO nonlinear systems), in which the gap metric is employed to formulate weighting functions for local controller combination. Compared to existent weighting functions, the proposed weighting method has two major advantages: firstly, there is only one tuning parameter, which makes it simpler. Secondly, the weights depend only on the scheduling vector and can be calculated off-line and stored in a look-up table. Therefore, the computational load can be reduced, especially for nonlinear systems with multiple scheduling variables. A MIMO CSTR system is studied to demonstrate the effectiveness of the proposed weighting method.     

基于增强蚁群优化的海量规模MIMO系统快速检测算法

大规模MIMO系统的符号向量检测算法计算复杂度较高,对此结合粒子群优化与蚁群优化提出一种低计算复杂度的海量规模MIMO系统快速检测算法。首先,推导出一种新的概率搜索模型,将基于距离的蚁群搜索与基于速度的粒子搜索结合;然后,将ACO距离指标与PSO的方向、速度指标结合生成一种新的概率指标,将ACO的信息素更新步骤变为PSO速度的更新;最终,将MIMO检测问题建模为路径寻找问题,寻找MIMO符号检测问题的次优解。对比仿真实验结果表明,本算法的检测性能优于部分传统算法以及其他新颖的MIMO检测算法,在获得与最大似然估计检测法接近的误码率性能下,具有极快的计算速度,适用于海量规模的MIMO系统。     

Iterative performance improvement of fuzzy control systems for three tank systems

This paper suggests the performance improvement of fuzzy control systems (FCSs) for three tank systems using iterative feedback tuning (IFT). The stable design of Takagi–Sugeno–Kang fuzzy controllers is guaranteed by means of a stability theorem based on LaSalle’s global invariant set theorem formulated for a class of multi input-multi output (MIMO) nonlinear processes. An IFT algorithm characterized by setting the step size to guarantee the FCS stability is proposed. The theoretical approaches are applied in a case study that deals with the IFT-based stable design of fuzzy controllers dedicated to the level control of a cylindrical three tank system as a representative MIMO system. A set of experimental results for a laboratory setup illustrates the performance improvement.     

A novel neural internal model control for multi-input multi-output nonlinear discrete-time processes

An internal model-based neural network control is proposed for unknown non-affine discrete-time multi-input multi-output (MIMO) processes in nonlinear state space form under model mismatch and disturbances. Based on the neural state-space model built for an unknown nonlinear MIMO state space process, an approximate internal model and approximate decoupling controllers are derived simultaneously. Thus, the learning of the inverse process dynamics is not required. A neural network model-based extended Kalman observer is used to estimate the states of a nonlinear process as not all states are accessible. The proposed neural internal model control can work for open-loop unstable processes with its closed-loop stability derived analytically. The application to a distributed thermal process shows the effectiveness of the proposed approach for suppressing nonlinear coupling and external disturbances and its feasibility for the control of unknown non-affine nonlinear discrete-time MIMO state space processes.     

Structured Set Membership identification of nonlinear systems with application to vehicles with controlled suspension

This paper considers an iterative algorithm for the identification of structured nonlinear systems. The systems considered consist of the interconnection of a MIMO linear systems and a MIMO nonlinear system. The considered interconnection structure can represent as particular cases Hammerstein, Wiener or Lur’e systems. A key feature of the proposed method is that the nonlinear subsystem may be dynamic and is not assumed to have a given parametric form. In this way the complexity/accuracy problems posed by the proper choice of the suitable parametrization of the nonlinear subsystem are circumvented. Moreover, the simulation error of the overall model is shown to be a nonincreasing function of the number of algorithm iteration. The effectiveness of the algorithm is tested on the problem of identifying a model for vertical dynamics of vehicles with controlled suspensions from both simulated and experimental data.     

基于预测窗的轮式移动机器人最优避障避碰算法

针对非线性轮式移动机器人的避障以及多机器人间的相互避碰问题,提出了一种基于预测窗的避障避碰算法.首先为了便于预测碰撞的发生,通过反馈线性化将非线性的机器人运动学模型转化成线性模型;然后根据线性模型预测会导致机器人发生碰撞的所有相对虚拟加速度变化量集合,称之为加速度变化障碍.基于此,为每个机器人构造既能躲避障碍物又能相互避碰的可行加速度变化集合.然后通过优化指标函数求得最优虚拟加速度变化量,最后将其转换成机器人的实际控制量.这种算法与现有的相比,可使机器人在避障或避碰过程中的行驶方向角、线速度的变化幅值更小,角速度和线加速度的变化更为平顺,而且运行所用的平均时间更短.仿真结果演示了所提出算法的有效性和相对于已有方法的优势.     

含有色噪声的神经模糊Hammerstein模型分离辨识

针对实际工业过程中普遍存在的有色噪声,本文提出一种基于递推增广最小二乘算法的神经模糊Hammerstein模型辨识方法,突破了传统的Hammerstein模型迭代分离算法.首先,利用多信号源实现Hammerstein模型中静态非线性环节和动态线性环节的分离,大大简化了辨识过程,提高了串联环节参数的分离精度.其次,利用长除法将噪声模型用有限脉冲响应模型逼近,采用增广递推最小二乘法进行线性环节的参数估计.最后,采用神经模糊模型拟合静态非线性环节,同时设计了神经模糊模型参数的非迭代优化算法,改善了模型的使用范围.该方法保证了模型的预测精度,对含有色噪声的非线性系统具有较好的拟合效果.仿真结果验证了上述方法的有效性.     

A gap metric based multiple model approach for nonlinear switched systems

Many applications in chemical engineering often exhibit a switching character due to the presence of discrete modes in the course of their operation. First principles models of such systems constructed using process simulators are far too complex for use in online applications, especially in model-based control. For such systems, numerous control-relevant modeling approaches have been reported in the literature such as mixed logic dynamical (MLD) models [1] and piece wise affine (PWA) [2] models among others. These models describe the evolution of states in each discrete mode using linear equations. Fewer control-relevant models have been reported that address the nonlinear behavior of switched systems. To model nonlinear hybrid systems, Nandola and Bhartiya [3] proposed a multiple linear model approach wherein multiple linear models are used to describe the dynamic behavior in each mode of the hybrid system. However, no guidelines were provided to select the number of models necessary in each mode and their region of validity. In this work, we address these lacunae by presenting a systematic multiple model approach to describe nonlinear switched systems. The method involves a trajectory based linearization and employs a model bank with a set of local linear models for each discrete operational mode. The model bank is generated by linearizing the first principles model across a carefully designed trajectory based on accuracy of multi-step ahead predictions. The numerous models thus obtained are clustered using the gap metric as the distance measure and representative models are selected. The selected linear models are aggregated using Bayesian or Fuzzy approaches to obtain the global model for the nonlinear switched system. A simulation case study of spherical two-tank system and an experimental case study of a benchmark problem consisting of three tanks are used to validate the proposed modeling strategy.     

Rao-Blackwellized粒子势均衡多目标多伯努利滤波器

由于多伯努利滤波器直接近似递推了多目标状态的后验概率密度,使得多目标跟踪问题在基于随机有限集理论框架下的求解及目标状态的估计显得更为直观.本文针对一个状态可分解(线性/非线性)的状态空间模型,分析基于Rao-Blackwell定理的滤波估计方法,结合噪声的去相关构造线性状态的滤波方程.文中详细推导并提出Rao-Blackwellized粒子势均衡多目标多伯努利滤波器的一般实现形式,包括给出多伯努利非线性状态粒子滤波的实现形式,并结合非线性滤波结果给出多伯努利线性状态的递推滤波公式.本文提出的滤波器实现方法能够在更低维的状态空间上进行采样,滤波器的整体跟踪性能得到提高.多目标跟踪的仿真实验结果验证了该算法的有效性.     

A rapid learning and dynamic stepwise updating algorithm for flatneural networks and the application to time-series prediction

A fast learning algorithm is proposed to find an optimal weights of the flat neural networks (especially, the functional-link network). Although the flat networks are used for nonlinear function approximation, they can be formulated as linear systems. Thus, the weights of the networks can be solved easily using a linear least-square method. This formulation makes it easier to update the weights instantly for both a new added pattern and a new added enhancement node. A dynamic stepwise updating algorithm is proposed to update the weights of the system on-the-fly. The model is tested on several time-series data including an infrared laser data set, a chaotic time-series, a monthly flour price data set, and a nonlinear system identification problem. The simulation results are compared to existing models in which more complex architectures and more costly training are needed. The results indicate that the proposed model is very attractive to real-time processes.     

Variable selection algorithm for the construction of MIMO operatingpoint dependent neurofuzzy networks

An input variable selection procedure is introduced for the identification and construction of multi-input multi-output (MIMO) neurofuzzy operating point dependent models. The algorithm is an extension of a forward modified Gram-Schmidt orthogonal least squares procedure for a linear model structure which is modified to accommodate nonlinear system modeling by incorporating piecewise locally linear model fitting. The proposed input nodes selection procedure effectively tackles the problem of the curse of dimensionality associated with lattice-based modeling algorithms such as radial basis function neurofuzzy networks, enabling the resulting neurofuzzy operating point dependent model to be widely applied in control and estimation. Some numerical examples are given to demonstrate the effectiveness of the proposed construction algorithm     

多变量非线性系统的变阶采样迭代学习控制

针对存在初态误差的情形, 提出多变量非线性系统的变阶采样迭代学习控制方法. 相对固定阶迭代学习算法, 变阶算法可有效降低跟踪误差. 对变阶采样迭代学习算法进行了收敛性分析, 推导出收敛充分条件. 给出了变阶学习的两种实现策略-DD (Direct division)和DIP (Division in phases)策略. 数值仿真表明, 基于DIP策略的变阶采样迭代学习算法在获得较高的控制精度的同时, 具有较快的收敛速度.     

Document Classification via Nonlinear Metric Learning

Learning a proper distance metric is an important problem in document classification, because the similarities of samples in many problems are usually measured by distance metric. In this paper, we address the nonlinear metric leaning problem with applying in the document classification. First, we propose a new representation about nonlinear metric by using a linear combination of some basic kernels. Second, we give a linear metric learning method by a triplet constraint and k-nearest neighbors, and then we develop it to a nonlinear method based on multiple kernel by above nonlinear metric. Further, the corresponding problem can be rewritten as an unconstrained optimization problem on positive definite matrices groups. At last, to ensure the learned distance matrix must be a positive definite matrix, we provide an improved intrinsic steepest descent algorithm with adaptive step-size to solve this unconstrained optimization. The experimental results show that our proposed method is effective on some document classification problems.     

Robust identification and fault diagnosis based on uncertain multiple input–multiple output linear parameter varying parity equations and zonotopes

We present a robust fault diagnosis method for uncertain multiple input–multiple output (MIMO) linear parameter varying (LPV) parity equations. The fault detection methodology is based on checking whether measurements are inside the prediction bounds provided by the uncertain MIMO LPV parity equations. The proposed approach takes into account existing couplings between the different measured outputs. Modelling and prediction uncertainty bounds are computed using zonotopes. Also proposed is an identification algorithm that estimates model parameters and their uncertainty such that all measured data free of faults will be inside the predicted bounds. The fault isolation and estimation algorithm is based on the use of residual fault sensitivity. Finally, two case studies (one based on a water distribution network and the other on a four-tank system) illustrate the effectiveness of the proposed approach.