Simultaneous Constrained Model Predictive Control and Identification of DARX Processes

In this work, we formulate a new approach to simultaneous constrained model predictive control and identification (MPCI). The proposed approach relies on the development of a persistent excitation (PE) criterion for processes described by DARX models. That PE criterion is used as an additional constraint in the standard on-line optimization of MPC. The resulting on-line optimization problem of MPCI is handled by successively solving a series of semi-definite programming problems. Advantages of MPCI in comparison to other closed-loop identification methods are (a) Constraints on process inputs and outputs are handled explicitly, (b) Deterioration of output regulation is kept to a minimum, while closed-loop identification is performed. The applicability of the method is illustrated by a number of simulation studies. Theoretical and computational issues for further investigation are suggested.     

Stabilizing polynomial approximation of explicit MPC

A given explicit piecewise affine representation of an MPC feedback law is approximated by a single polynomial, computed using linear programming. This polynomial state feedback control law guarantees closed-loop stability and constraint satisfaction. The polynomial feedback can be implemented in real time even on very simple devices with severe limitations on memory storage.     

基于FPGA的非线性预测控制器设计

对于非线性程度较高的复杂对象,非线性模型预测控制（NonlinearModelPredictiveControl,NMPC）是一种有效的控制策略。为了实现对这类对象的有效控制,设计了一种基于FPGA（FieldProgrammableGateArray）的非线性预测控制器,该嵌入式控制器具有灵活性和高适应性等特点,能够应用于工业现场控制。为了满足工业控制的可行性和实时性要求,提出了一种序贯二次规划（SQP）算法的改进算法,在FPGA有限的计算资源下,保证每个采样间隔内都能得到NMPC优化问题的可行解。经仿真实验证明,采用非线性预测控制器在计算速度和精度上都能达到较好的性能。     

Set Membership identification of nonlinear systems

In the paper the problem of identifying nonlinear dynamic systems, described in nonlinear regression form, is considered, using finite and noise-corrupted measurements. Most methods in the literature are based on the estimation of a model within a finitely parametrized model class describing the functional form of involved nonlinearities. A key problem in these methods is the proper choice of the model class, typically realized by a search, from the simplest to more complex ones (linear, bilinear, polynomial, neural networks, etc.). In this paper an alternative approach, based on a Set Membership framework is presented, not requiring assumptions on the functional form of the regression function describing the relations between measured input and output, but assuming only some information on its regularity, given by bounds on its gradient. In this way, the problem of considering approximate functional forms is circumvented. Moreover, noise is assumed to be bounded, in contrast with statistical methods, which rely on assumptions such as stationarity, ergodicity, uncorrelation, type of distribution, etc., whose validity may be difficult to test reliably and is lost in presence of approximate modeling. In this paper, necessary and sufficient conditions are given for the validation of the considered assumptions. An optimal interval estimate of the regression function is obtained, providing its uncertainty range for any assigned regressor values. The set estimate allows to derive an optimal identification algorithm, giving estimates with minimal guaranteed L_p error on the assigned domain of the regressors. The properties of the optimal estimate are investigated and its worst-case L_p identification error is evaluated. The presented approach is tested and compared with other nonlinear methods on the identification of a water heater, a mechanical system with input saturation and a vehicle with controlled suspensions.     

Stability Analysis of Constrained Nonlinear Model Predictive Control with Terminal Weighting

This paper investigates stability of model predictive control (MPC) for nonlinear constrained systems. New stability results for the MPC algorithms with terminal weighting are proposed using the dynamic programming method, which gives new criteria for choosing state, control and terminal weighting in the performance index to achieve stability of MPC algorithms. Illustrative examples are given to show that by combining this condition with existing ones, much less conservative results can be generated.     

预测函数控制的内模控制理论

内模控制是一种基于过程数学模型进行控制器设计的新型控制策略,是研究预测控制重要的理论基础。预测函数控制是一种控制量计算方程简单,实时控制效果好的新型预测控制算法。本文用内模控制理论研究预测函数控制,分析了系统的鲁棒性和稳定性,最后进行了参数设计和仿真研究。     

基于非线性(Wiener)模型自适应预测函数控制

针对一类非线性对象提出了基于Wiener模型的非线性系统自适应预测函数控制方法。利用带遗忘因子的递推最小二乘算法在线辨识得到Wiener模型核参数,根据所得模型参数直接计算得到非线性预测函数控制律,而且使控制律计算容易,适用于具有一定非线性的被控对象,并能适应被控对象的环境变化。     

Hybrid Fuzzy Modelling for Model Predictive Control

Model predictive control (MPC) has become an important area of research and is also an approach that has been successfully used in many industrial applications. In order to implement a MPC algorithm, a model of the process we are dealing with is needed. Due to the complex hybrid and nonlinear nature of many industrial processes, obtaining a suitable model is often a difficult task. In this paper a hybrid fuzzy modelling approach with a compact formulation is introduced. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for the hybrid fuzzy modelling purposes is presented. An efficient method for identifying the hybrid fuzzy model is also proposed. A MPC algorithm suitable for systems with discrete inputs is treated. The benefits of the MPC algorithm employing the hybrid fuzzy model are verified on a batch-reactor simulation example: a comparison between the proposed modern intelligent (fuzzy) approach and a classic (linear) approach was made. It was established that the MPC algorithm employing the proposed hybrid fuzzy model clearly outperforms the approach where a hybrid linear model is used, which justifies the usability of the hybrid fuzzy model. The hybrid fuzzy formulation introduces a powerful model that can faithfully represent hybrid and nonlinear dynamics of systems met in industrial practice, therefore, this approach demonstrates a significant advantage for MPC resulting in a better control performance.     

Unified Set Membership theory for identification, prediction and filtering of nonlinear systems

The problem of making inferences from data measured on nonlinear systems is investigated within a Set Membership (SM) framework and it is shown that identification, prediction and filtering can be treated as specific instances of the general presented theory. The SM framework presents an alternative view to the Parametric Statistical (PS) framework, more widely used for studying the above specific problems. In particular, in the SM framework, a bound only on the gradient of the model regression function is assumed, at difference from PS methods which assume the choice of a parametric functional form of the regression function. Moreover, the SM theory assumes only that the noise is bounded, in contrast with PS approaches, which rely on noise assumptions such as stationarity, uncorrelation, type of distribution, etc. The basic notions and results of the general inference making theory are presented. Moreover, some of the main results that can be obtained for the specific inferences of identification, prediction and filtering are reviewed. Concluding comments on the presented results are also reported, focused on the discussion of two basic questions: what may be gained in identification, prediction and filtering of nonlinear systems by using the presented SM framework instead of the widely diffused PS framework? why SM methods could provide stronger results than the PS methods, requiring weaker assumptions on system and on noise?     

基于神经网络的迭代优化预测控制

针对时变的非线性系统,提出一种基于神经网络的迭代优化预测控制。它将传统的预测控制策略与神经网络逼近任息非线性函数的能力结合,预测系统未来输出,然后用迭代学习方法优化预测控制器,即通过一阶泰勒展开的方法,把非线性优化问题转化为线性优化问题。不仅简化计算,同时避免用神经网络优化控制器时,由于调节参数过多、涮前速度慢而导致系统闭环稳定性和鲁棒性差的问题。仿真结果表明,该控制方案具有良好的控制品质,并适应对象参数的变化,具有较强的鲁棒性和自适应性。     

基于神经网络Smith预估器的预测控制

针对非线性系统时滞问题,给出了一种新型的单神经元Smith预测控制算法.神经网络的预测控制器由不完全微分的单神经元自适应PID控制器和神经网络的Smith预估器组成.预估器对输出进行多步预测,控制器超前动作以消除时滞对系统的影响.不完全微分的单神经元自适应PID控制器通过改进的Hebb学习规则实现其权值调节,通过权系数的在线调整实现自适应控制.仿真实验证明了该方法具有较快的响应速度和较好的响应性能.     

Predictive switching supervisory control of persistently disturbed input-saturated plants

Predictive switching logic schemes are considered whereby a feedback-gain is switched-on at any time from a family of candidate feedback-gains so as to control a discrete-time input-saturated LTI system possibly subject to persistent bounded disturbances of unknown arbitrary magnitude. It is constructively shown that such schemes do exist which ensure, along with good tracking performance, global asymptotic and semi-global exponential stability in the noiseless case, as well as finite l_∞-induced gain to the disturbance-to-state map, whenever the structure of the disturbed plant can make such properties conceptually achievable, viz., the disturbance which enters an Asymptotically Null-Controllable with Bounded Input (ANCBI) system acts directly only on the stable modes, while the critically unstable ones are indirectly affected by the disturbance only via the feedback controls. More generally, in ANCBI systems general disturbances of suitably bounded magnitude can also be handled by the scheme, provided that the switching logic be equipped with an appropriate hysteresis facility.     

基于BP网络模型的非线性预测控制策略研究

提出了一种基于神经网络模型的非线性多步预测控制策略。预测器和控制器由一个BP网络构成。在整个过程中,首先利用一个BP网络构造一个非线性多步预测模型,根据被控对象输出与网络实际输出之间的误差采用改进的BP算法修改网络权值,以逐步建立合理的多步预测模型。然后,根据网络的多步预测输出序列与设定值序列的偏差构造性能指标函数,根据性能指标函数采用自适应变步长梯度法修改控制律。仿真结果表明了该策略的有效性。     

一种空间飞行器姿态控制非线性模型的预测控制新算法

空间飞行器的姿态控制受到诸如带时延的非线性动态特性、模型和参数的不确定性等因素的影响 ,其控制相当复杂。传统的控制技术 (如PID控制 )对控制对象的过程模型要求较高 ,且不能解决过程控制中非线性、时变、控制输入的约束性等因素的影响 ,其控制所能达到的性能和效率也远不够满足当前飞行器的控制要求。该文将介绍一种新型的基于控制输入的函数空间最优化的模型预测控制算法 ,称为函数空间模型预测控制 (F -MPC)。该法可用于线性和非线性系统 ,对过程模型要求不高 ,能在控制输入约束条件存在的情况下通过在线优化使系统很好地跟踪期望轨迹 ,并且解决了PID控制所遇到的问题。同时 ,将该算法用于空间飞行器的姿态控制仿真 ,仿真结果表明控制效果很好。     

Kernel shapes of fuzzy sets in fuzzy systems for function approximation

The shapes of if-part fuzzy sets affect the approximating capability of fuzzy systems. In this paper, the fuzzy systems with the kernel-shaped if-part fuzzy sets are built directly from the training data. It is proved that these fuzzy systems are universal approximators and their uniform approximation rates can be estimated in the single-input-single-output (SISO) case. On the basis of these rates, the relationships between the approximating capability and the shapes of if-part fuzzy sets are developed for the fuzzy systems. Furthermore, the sinc functions that serve as input membership functions are proved to have the almost best approximation property in a particular class of membership functions. The theoretical results are confirmed from the simulation data. In addition, the estimations of the uniform approximation rates are extended to the multi-input-single-output (MISO) case.     

神经网络预测控制及其在二级倒立摆中的仿真

本文介绍了一种基于神经网络的预测控制算法,考虑到算法中复杂性能指标的寻优难以找到全局最优解,提出了一种在工作点附近线性化得到对象的瞬时ARIX模型,再利用GPC(广义预测控制)算法求得近似解,最后以其为初值进行寻优获得全局最优解的方法,提高了算法的性能。最后的二级倒立摆仿真验证了算法的可靠性。     

采用集结的预测控制器仿真研究

集结策略在减少预测控制在线计算量同时也必然带来控制性能的下降,研究集结策略与控制器性能的关系,对于应用集结策略有着重要的意义.约束预测控制器不存在公式解,无法从理论上得到集结策略与控制器性能的关系.通过仿真研究的方法,结合定性分析,研究了集结阵维数和集结阵结构对控制器性能影响,以及衰减策略下不同衰减率的集结阵对控制器性能影响.仿真得到的结果能有效地指导实际系统中集结阵的选取,使集结预测控制器具有良好的性能.     

Affine and predictive control policies for a class of nonlinear systems

The input-state linear horizon (ISLH) for a nonlinear discrete-time system is defined as the smallest number of time steps it takes the system input to appear nonlinearly in the state variable. In this paper, we employ the latter concept and show that the class of constraint admissible N-step affine state-feedback policies is equivalent to the associated class of constraint admissible disturbance-feedback policies, provided that N is less than the system’s ISLH. The result generalizes a recent result in [Goulart, P. J., Kerrigan, E. C., Maciejowski, J. M. (2006). Optimization over state feedback policies for robust control with constraints. Automatica, 42(4), 523-533] and is significant because it enables one: (i) to determine a constraint admissible state-feedback policy by employing well-known convex optimization techniques; and (ii) to guarantee robust recursive feasibility of a class of model predictive control (MPC) policies by imposing a suitable terminal constraint. In particular, we propose an input-to-state stabilizing MPC policy for a class of nonlinear systems with bounded disturbance inputs and mixed polytopic constraints on the state and the control input. At each time step, the proposed MPC policy requires the solution of a single convex quadratic programme parameterized by the current system state.     

Symmetry between constrained reference tracking and constrained state estimation

This paper exposes a symmetry relationship between constrained output reference tracking and constrained state estimation problems. The symmetry, which is different from the traditional duality relationship between control and estimation, is provided by means of two tables that give a complete translation of all variables of one problem into the variables of the other. An example is provided to illustrate the behaviour of the optimal solutions to the reference tracking and state estimation problems. The symmetry relationship leads to interesting interpretations of several of the resulting trajectories.     

一种改进的神经网络非线性预测控制

从建立神经网络非线性预测模型出发,针对BP网络存在收敛速度慢,容易陷入局部最小的缺点,该文在BFGS拟牛顿法的基础上,提出了一种基于并行拟牛顿优化算法的并行拟牛顿神经网络。该并行拟牛顿优化算法采用两个含有不同参数的拟牛顿校正公式,在每次迭代过程中,利用这两个不同的校正公式得到相应的搜索方向,并通过不精确搜索法求取最优步长,最后根据一性能指标取最优的一个搜索方向和相应的步长对网络各层之间的权值进行修正。Matlab仿真结果表明,同BP神经网络和BFGS拟牛顿神经网络相比,该神经网络具有收敛速度快、模型精度高的特点,更适合于实时非线性控制。