RBF-ARX model-based MPC strategies with application to a water tank system

A hybrid pseudo-linear RBF-ARX model that combines Gaussian radial basis function (RBF) networks and linear ARX model structure is utilized for representing the dynamic behavior of a class of smooth nonlinear and non-stationary systems. This model is locally linear at each working point and globally nonlinear within whole working range. Based on the structural characteristics of the RBF-ARX model, three receding horizon predictive control (RBF-ARX-MPC) strategies are designed: (1) the RBF-ARX-MPC algorithm based on single-point linearization (MPC-SPL); (2) the RBF-ARX-MPC algorithm based on multi-point linearization (MPC-MPL); and (3) the RBF-ARX-MPC algorithm based on globally nonlinear optimization (MPC-GNO). In the MPC-SPL, the future multi-step-ahead predictive output of the system is obtained based on the local linearization of the RBF-ARX model at only current working-point, while in the MPC-MPL the future long-term output prediction is obtained according to the future local characteristics from previous online optimization results of the RBF-ARX model based MPC. In the MPC-GNO, the globally nonlinear characteristics of the RBF-ARX model are fully used for online getting control variables of the MPC. Real-time control experiments for the three type MPCs are carried out on a water tank system, which are also compared with a classical PID control and a traditional linear ARX model-based MPC. The results verify that the modeling method and the model-based predictive control strategies are realizable and effective for the nonlinear and unstable system. Moreover, it is also shown that the MPC-GNO can obtain better control performance but need more computation time compared to the other MPCs, which makes it possible to be applied into some slowly varying processes.     

基于RBF-ARX模型的预测控制在液位系统中的应用

针对单容液位系统紊流时的非线性特征,研究了基于RBF-ARX模型预测控制策略控制单容液位系统;讨论RBF-ARX模型结构的选取,模型参数辨识,RBF参数优化,基于RBF-ARX模型的预测控制策略等问题;模型的仿真结果,证实了RBF-ARX模型在非线性系统建模和辨识中的有效性;同基于全局线性ARX模型的预测控制器和PID控制器相比较,基于此模型的预测控制取得了优异的控制效果。     

Nonlinear system modeling and robust predictive control based on RBF-ARX model

An integrated modeling and robust model predictive control (MPC) approach is proposed for a class of nonlinear systems with unknown steady state. First, the nonlinear system is identified off-line by RBF-ARX model possessing linear ARX model structure and state-dependent Gaussian RBF neural network type coefficients. On the basis of the RBF-ARX model, a combination of a local linearization model and a polytopic uncertain linear parameter-varying (LPV) model are built to approximate the present and the future system's nonlinear behavior, respectively. Subsequently, based on the approximate models, a min–max robust MPC algorithm with input constraint is designed for the output-tracking control of the nonlinear system with unknown steady state. The closed-loop stability of the MPC strategy is guaranteed by the use of parameter-dependent Lyapunov function and the feasibility of the linear matrix inequalities (LMIs). Simulation study to a NO_x decomposition process illustrates the effectiveness of the modeling and robust MPC approaches proposed in this paper.     

RBF-ARX模型在三容水箱液位控制系统建模中的应用

针对三容水箱液位系统的非线性，采用RBF-ARX模型对三容液位系统进行了离线动态特性建模的研究。着重讨论了RBF-ARX模型结构的选取、模型参数辨识、RBF参数优化等问题。RBF-ARX模型与ARX模型的一步预测输出比较的结果证实了RBF-ARX模型在非线性系统建模中的优越性。     

RBF-ARX模型在倒立摆系统建模中的应用

针对直线一级倒立摆控制系统的非线性特性,采用RBF-ARX模型对倒立摆系统的全局非线性动态特性进行建模.讨论了RBF-ARX模型结构的选取,模型参数辨识,RBF参数优化等问题.并且分别比较了该倒立摆系统的RBF-ARX模型与全局线性ARX模型,以及将RBF-ARX在某一工作点局部线性化后的模型与局部线性ARX模型的预测输出和模型误差,验证了RBF-ARX模型在倒立摆系统建模和辨识中的有效性.     

一种新的ARX模型在磁悬浮系统建模中的应用

采用一种新的ARX模型（RBF-ARX模型）对磁悬浮系统进行离线建模,讨论了RBF-ARX模型的原理、结构的选取、模型参数辨识和RBF参数优化等问题。文章分别采用不同的序列作为状态变量,分别建立RBF-ARX模型,并分析了各模型的性能及可靠性。模型的预测输出和仿真结果,证实了RBF-ARX模型在非线性系统建模和辨识中的有效性。通过与ARX模型的比较,证明了RBF-ARX模型在非线性系统建模中效果更好。     

RBF-ARX模型在液位系统建模中的应用

针对单容液位系统紊流时的非线性特征,采用RBF-ARX模型对单容液位系统进行离线动态特性建模的研究;分别在液位高中低三个工作点建立了其局部线性ARX模型,它们的单位阶跃响应存在巨大差异,证实了整个系统具有较强的非线性;讨论了RBF-ARX模型结构的选取,模型参数辨识,RBF参数优化等问题;模型的预测输出和仿真结果,证实了RBF-ARX模型在非线性系统建模和辨识中的有效性.     

Modeling and Control Approach to Coupled Tanks Liquid Level System Based on Function‐Type Weight RBF‐ARX Model

A multi‐input multi‐output (MIMO) FWRBF‐ARX model, which adopts radial basis function (RBF) neural networks with function‐type weights (FWRBF) to approximate the coefficients of the state‐dependent AutoRegressive model with eXogenous input variables (SD‐ARX), is utilized for describing the dynamics of a coupled tanks liquid system. Based on local linearization information of the MIMO FWRBF‐ARX model, a predictive control strategy is proposed. In the algorithm, the control actions of the model predictive control (MPC) are calculated based on the local linearization of the MIMO FWRBF‐ARX model at current working point. Real‐time control experiments are carried out on the coupled tanks liquid system. The detailed comparative experiments demonstrate the feasibility and effectiveness of the proposed modeling and model‐based control strategy for the coupled tanks plant.     

Nonlinear model predictive control using parameter varying BP-ARX combination model

A novel back-propagation AutoRegressive with eXternal input (BP-ARX) combination model is constructed for model predictive control (MPC) of MIMO nonlinear systems, whose steady-state relation between inputs and outputs can be obtained. The BP neural network represents the steady-state relation, and the ARX model represents the linear dynamic relation between inputs and outputs of the nonlinear systems. The BP-ARX model is a global model and is identified offline, while the parameters of the ARX model are rescaled online according to BP neural network and operating data. Sequential quadratic programming is employed to solve the quadratic objective function online, and a shift coefficient is defined to constrain the effect time of the recursive least-squares algorithm. Thus, a parameter varying nonlinear MPC (PVNMPC) algorithm that responds quickly to large changes in system set-points and shows good dynamic performance when system outputs approach set-points is proposed. Simulation results in a multivariable stirred tank and a multivariable pH neutralisation process illustrate the applicability of the proposed method and comparisons of the control effect between PVNMPC and multivariable recursive generalised predictive controller are also performed.     

An efficient algorithm for optimal control of PWA systems with polyhedral performance indices

We present an algorithm for the computation of explicit optimal control laws for piecewise affine (PWA) systems with polyhedral performance indices. The algorithm is based on dynamic programming (DP) and represents an extension of ideas initially proposed in Kerrigan and Mayne [(2003). Optimal control of constrained, piecewise affine systems with bounded disturbances. In Proceedings of the 41st IEEE conference on decision and control, Las Vegas, Nevada, USA, December], and Baoti? et al. [(2003). A new algorithm for constrained finite time optimal control of hybrid systems with a linear performance index. In Proceedings of European control conference, Cambridge, UK, September]. Specifically, we show how to exploit the underlying geometric structure of the optimization problem in order to significantly improve the efficiency of the off-line computations. An extensive case study is provided, which clearly indicates that the algorithm proposed in this paper may be preferable to other schemes published in the literature.     

A RBF-ARX model-based robust MPC for tracking control without steady state knowledge

A RBF-ARX modeling and robust model predictive control (MPC) approach to achieving output-tracking control of the nonlinear system with unknown steady-state knowledge is proposed. On the basis of the RBF-ARX model with considering the system time delay, a local linearization state-space model is obtained to represent the current behavior of the nonlinear system, and a polytopic uncertain linear parameter varying (LPV) state-space model is built to represent the future system’s nonlinear behavior. Based on the two models, a quasi-min–max MPC algorithm with constraint is designed for output-tracking control of the nonlinear system with unknown steady state knowledge. The optimization problem of the quasi-min–max MPC algorithm is finally converted to the convex linear matrix inequalities (LMIs) optimization problem. Closed-loop stability of the MPC strategy is guaranteed by the use of parameter-dependent Lyapunov function and feasibility of the LMIs. Two examples, i.e. the modeling and control of a continuously stirred tank reactor (CSTR) and a two tank system demonstrate the effectiveness of the RBF-ARX modeling and robust MPC approach.     

Efficient clustering of uncertain data streams

Clustering uncertain data streams has recently become one of the most challenging tasks in data management because of the strict space and time requirements of processing tuples arriving at high speed and the difficulty that arises from handling uncertain data. The prior work on clustering data streams focuses on devising complicated synopsis data structures to summarize data streams into a small number of micro-clusters so that important statistics can be computed conveniently, such as Clustering Feature (CF) (Zhang et al. in Proceedings of ACM SIGMOD, pp 103–114, 1996) for deterministic data and Error-based Clustering Feature (ECF) (Aggarwal and Yu in Proceedings of ICDE, 2008) for uncertain data. However, ECF can only handle attribute-level uncertainty, while existential uncertainty, the other kind of uncertainty, has not been addressed yet. In this paper, we propose a novel data structure, Uncertain Feature (UF), to summarize data streams with both kinds of uncertainties: UF is space-efficient, has additive and subtractive properties, and can compute complicated statistics easily. Our first attempt aims at enhancing the previous streaming approaches to handle the sliding-window model by using UF instead of old synopses, inclusive of CluStream (Aggarwal et al. in Proceedings of VLDB, 2003) and UMicro (Aggarwal and Yu in Proceedings of ICDE, 2008). We show that such methods cannot achieve high efficiency. Our second attempt aims at devising a novel algorithm, cluUS , to handle the sliding-window model by using UF structure. Detailed analysis and thorough experimental reports on synthetic and real data sets confirm the advantages of our proposed method.     

基于稳态非线性模型和线性ARX模型组合的非线性预测控制

通过点集映射来表示非线性系统的稳态模型,用系统的稳态增益来修正具有外界输入的线性自回归（AutoRegressive with eXternal input, ARX）模型的动态增益,提出了一种基于稳态非线性模型和线性ARX模型组合的非线性预测控制算法．该算法用递归最小二乘法在线辨识系统的动态模型参数,用序列二次规划算法求解目标函数．最后通过对典型化工非线性对象pH中和过程的仿真对本算法进行了验证．结果表明,本算法比广义预测控制算法具有更好的设定值跟踪性能和抗干扰能力．     

Model validation for control and controller validation in a prediction error identification framework—Part II: illustrations

In this paper, we illustrate our new results on model validation for control and controller validation in a prediction error identification framework, developed in a companion paper (Gevers et al., Automatica (2003) 39(3) pii: S005-1098(02)00234-0), through two realistic simulation examples, covering widely different control design applications. The first is the control of a flexible mechanical system (the Landau benchmark example) with a tracking objective, the second is the control of a ferrosilicon production process with a disturbance rejection objective.     

Comments and further improvements on “pth moment stability of stochastic neural networks with Markov volatilities”

In a very recent paper, Peng and Liu (Neural Comput Appl 20:543–547, 2011) investigated the pth moment stability of the stochastic Grossberg–Hopfield neural networks with Markov volatilities by Mao et al. (Bernoulli 6:73–90, 2000, Theorem 4.1). We should point out that Mao et al. (Bernoulli 6:73–90, 2000, Theorem 4.1) investigated the pth moment exponentially stable for a class of stochastic dynamical systems with constant delay; however, this theorem cannot apply to the case of variable time delays. It is also worthy to emphasize that Peng and Liu (Neural Comput Appl 20:543–547, 2011) discussed by Mao et al. (Bernoulli 6:73–90, 2000, Theorem 4.1) the pth moment exponentially stable for the Grossberg–Hopfield neural networks with variable delays, and therefore, there are some gaps between Peng and Liu (Neural Comput Appl 20:543–547, 2011, Theorem 1) and Mao et al. (Bernoulli 6:73–90, 2000, Theorem 4.1). In this paper, we fill up this gap. Moreover, a numerical example is also provided to demonstrate the effectiveness and applicability of the theoretical results.     

Learning functions using randomized genetic code-like transformations: probabilistic properties and experimentations

Inductive learning of nonlinear functions plays an important role in constructing predictive models and classifiers from data. We explore a novel randomized approach to construct linear representations of nonlinear functions proposed elsewhere [H. Kargupta (2001)], [H. Kargupta et al., (2002)]. This approach makes use of randomized codebooks, called the genetic code-like transformations (GCTs) for constructing an approximately linear representation of a nonlinear target function. We first derive some of the results presented elsewhere [H. Kargupta et al., (2002)] in a more general context. Next, it investigates different probabilistic and limit properties of GCTs. It also presents several experimental results to demonstrate the potential of this approach.     

A note on “Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm” by Jung-Bok Jo,Yinzhen Li,Mitsuo Gen,Computers & Industrial Engineering (2007)

In 2007, a spanning tree-based genetic algorithm approach for solving nonlinear fixed charge transportation problem proposed by Jo et al. [Jo, J. B., Li, Y., Gen, M. (2007). Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Computers & Industrial Engineering. doi:10.1016/j.cie.2007.06.022] was published in Computers & Industrial Engineering journal. In 2008, comments like calculation of total cost, indication of problem size were given by Kannan et al. [Kannan, G., Kumar, P. S., Vinay V. P. (2008). Comments on ‘‘Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm” by Jung-Bok Jo, Yinzhen Li, Mitsuo Gen, Computers & Industrial Engineering (2007). Computers & Industrial Engineering. doi:10.1016/j.cie.2007.12.019] for the published model of [Jo, J. B., Li, Y., Gen, M. (2007). Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Computers & Industrial Engineering.doi:10.1016/j.cie.2007.06.022]. In this note, as a response to the comments of Kannan et al., the formula for calculating the total cost of nonlinear fixed charge transportation problem is illustrated with examples, to which the near-optimal solutions are given.     

Solving the Beck and Wieland model with optimal experimentation in DualPC

Currently, there is a renewed interest in the use of optimal experimentation (adaptive control) in economics. Example are found in [Amman and Kendrick, 1999], [Amman and Kendrick, 2003], [Cosimano, in?press], [Cosimano and Gapen, 2005b], [Cosimano and Gapen, 2005a], [Cosimano and Gapen, 2006], [Tesfaselassie et?al., 2007], [Tucci, 1997], [Wieland, 2000a] and [Wieland, 2000b]. In this paper we present the Beck & Wieland model [Beck, G., & Wieland, V. (2002). Learning and control in a changing economic environment. Journal of Economic Dynamics and Control, 26, 1359-1378] and the methodology to solve this model with time-varying parameters using the various control methods described in [Kendrick, 1981] and [Kendrick, 2002]. Furthermore, we also provide numerical results using the DualPC software [Amman, H. M., & Kendrick, D. A. (1999). The DualI/DualPC software for optimal control models: User’s guide. Working paper, Austin, TX 78712, USA: Center for Applied Research in Economics, University of Texas] and show first evidence that optimal experimentation or Dual Control may produce better results than Expected Optimal Feedback.     

Mining non-derivable hypercliques

A hyperclique (Xiong et al. in Proceedings of the IEEE international conference on data mining, pp 387–394, 2003) is an itemset containing items that are strongly correlated with each other, based on a user-specified threshold. Hypercliques (HCs) have been successfully used in a number of applications, for example, clustering (Xiong et al. in Proceedings of the 4th SIAM international conference on data mining, pp 279–290, 2004) and noise removal (Xiong et al. in IEEE Trans Knowl Data Eng 18(3):304–319, 2006). Even though HC has been shown to respond well to datasets with skewed support distribution and low support threshold, it may still grow very large for dense datasets and lower h-confidence threshold. In this paper, we propose a new pruning method based on combining HCs and non-derivable itemsets (NDIs) (Calders and Goethals in Proceedings of the PKDD international conference on principles of data mining and knowledge discovery, pp 74–85, 2002) in order to substantially reduce the amount of generated HCs. Specifically, we propose a new collection of HCs, called non-derivable hypercliques (NDHCs). The NDHC collection is a lossless representation of HCs, that is, given the itemsets in NDHCs, we can generate the complete HC collection and their support, without additional scanning of the dataset. We present an efficient algorithm to mine all NDHC sets, NDHCMiner, and an algorithm to derive all HC sets and their support from NDHCs, NDHCDeriveAll. We experimentally compare our collection, NDHC with HC, with respect to runtime performance as well as total number of generated sets, using real and artificial data. We also show comparisons with another condensed representation of HCs, maximal hyperclique patterns (MHPs). Our experiments show that the NDHC collection offers substantial advantages over HCs, and even MHPs, especially for dense datasets and lower h-confidence values.