分片线性规划及应用

提出通过分片线性逼近和分片线性规划,将非线性优化问题转化为一系列的线性规划进行求解的方法。讨论了分片线性规划的性质,证明了分片线性规划问题可以通过有限次线性规划得到求解,同时,给出了分片线性规划问题局部最优解的充要条件,并基于此构造了求解分片线性规划问题的下降算法。该算法与自适应链接超平面模型相结合,成功地对离心式冷水机组的工作点进行了优化。通过优化,机组的能耗比之当前工作点有了明显的下降,表明通过分片线性规划求解非线性优化问题的有效性。     

基于堆叠自适应链接超平面模型的间歇过程批次间优化控制

间歇过程优点多且应用广泛,但自动化水平较低。针对间歇过程产品质量控制问题,提出一种基于堆叠自适应链接超平面(stacked-AHH)模型的批次间优化控制策略。为克服间歇过程机理建模的困难,选择基于过程数据的经验模型。分片线性(PWL)模型作为经验模型的一种能够很好的拟合非线性函数。因其在定义域不同子区域都为线性函数的特点,所以能够避免优化过程中因模型线性化所带来的误差。在多种PWL模型中,AHH模型相对其他PWL模型具有精度高、模型质量好等优点。同时为提高模型的泛化能力和鲁棒性,对AHH模型进行了堆叠。由于存在模型误差和未知干扰,基于模型计算的最优控制输入在应用到实际过程时往往不是最优的。间歇过程具备重复性,因此可以利用当前和过去批次的信息来改善下一批次的操作,使跟踪误差随批次增加逐渐减小。通过仿真实验验证了策略的有效性。     

基于Pareto解集分段预测策略的动态多目标进化算法

针对现有的动态多目标优化算法种群收敛速度慢、多样性难以保持等问题,提出了一种基于Pareto解集分段预测策略的动态多目标进化算法BPDMOP。当检测到环境变化时,对前一时刻进化得到的Pareto最优解根据任一子目标函数进行排序,并按照该子目标的大小均分为3段,分别计算出每一段Pareto解集中心点的移动方向;对每一段Pareto子集进行系统抽样得到Pareto前沿面的特征点,利用线性模型分段预测下一代种群;根据优化问题的难易程度,自适应地在预测的种群周围产生随机个体来增加种群的多样性。通过对3类标准测试函数的实验表明了该算法能够有效求解动态多目标优化问题。     

基于ADEMO/D-ENS的飞控系统性能指标分配方法

针对目前飞行控制系统设计中部件/组件性能参数的确定存在反复多次迭代的问题,对飞控系统性能指标的分配进行了研究。通过对性能指标分配过程进行建模,确定了分配过程属于多目标优化问题。基于Tchebycheff方法将多目标优化问题转化为单目标优化子问题集合,基于自适应差分进化算法得到的单目标优化子问题集合的最优解即为多目标优化问题Pareto最优解,同时采用惩罚因子保持差分进化算法种群的多样性。通过仿真与性能指标未分配的系统进行对比,结果表明分配后的系统具有更好的动态性和跟踪性,说明所提出的分配方法是正确的、可行的,并能够为工程应用提供一定的理论指导。     

基于多Hammerstein模型及APSO的预测控制策略

研究了基于多Hammerstein模型的非线性预测控制问题,提出了基于多模型融合的非线性预测控制方法,根据实际对象不同的工作点建立了非线性系统的多Hammerstein模型表示,以此模型集合作为实际对象的预测模型,兼顾预测控制处理各类约束的优点,以计算量较小的自适应粒子群算法(APSO)作为预测控制的滚动优化方法计算最优控制序列,避免了传统粒子群算法易早熟和算法后期粒子易在全局最优解附近"振荡"的缺点,并给出相应的模型切换策略,pH中和反应的仿真结果说明了此方法的有效性,同时也为菲线性预测控制提供了一种新方法.     

基于分片线性化方法的非线性系统多模型自适应控制

基于分片线性化方法辨识一类非线性系统 ,给出了非线性系统的多线性模型表示。基于线性模型建立多个控制器 ,基于最大最小指标切换函数构成多模型自适应控制器。给出了非线性系统多模型自适应控制算法的优化模型集建立方法 ,解决了多模型自适应控制模型多、计算量大的问题。仿真结果证明了算法的有效性     

面向多目标优化问题的自适应差分进化算法

针对多目标优化得到一个最优解集和解之间难以比较的问题,对单目标优化中的自适应策略进行了改进,提出一种面向多目标优化问题的自适应差分进化算法,在已有方法自适应改变交叉率的基础上,设定缩放因子有三种不同的分布模型,通过统计一定代数内个体的优劣来自适应选择合适的模型并生成相应取值,从而控制了搜索长度,防止新个体陷入在最优解集的部分区域。该算法还提出利用第三方解集和优胜累积量的概念来处理最优解之间的比较问题。通过5个标准优化问题的测试结果以及与其他几种算法的对比研究表明,所提出的改进算法性能更好,其在IGD指标上减小了0.0031~0.0669,在IH指标上最多减小了0.0821。     

自适应迁移预测的动态多目标差分演化算法

针对动态多目标优化环境下寻找并跟踪变化的Pareto最优前沿和Pareto最优解集的难题,提出两个策略：自适应迁移策略和预测策略。自适应迁移策略是根据环境的变化自适应地插入迁移个体来提高算法种群的多样性,从而提高算法对动态环境的适应能力。预测策略是通过时间序列并加上一定的扰动来产生预测种群,来预测环境变化之后的Pareto最优解集,以达到对其快速跟踪的目的。通过两个策略在多目标差分演化算法上的应用来解决动态多目标优化问题。实验过程中,通过平均最优解集分布均匀度和平均决策空间世代距离等指标表明,基于自适应迁移策略和预测策略的多目标差分演化算法能够很好适应变化的环境,并能够快速找到Pareto最优解集。     

基于分片线性化方法的非系统性系统多模型自适应控制

基于分片线性化方法辨识一类非线性系统，给出了非线性系统的多线性模型表示。基于线性模型建立多个控制器，基于最大最小指标切换函数构成多模型自适应控制器。给出了非线性系统多模型自适应控制算法的优化模型集建立方法，解决了多模型自适应控制模型多、计算最大的问题。仿真结果证明了算法的有效性。     

自适应分片算法研究

论文提出了一个自适应磁盘分片算法。首先,利用M/G/1排队理论对单个文件和整个阵列的平均存储响应时间建模,并提出了最优分片宽度理论计算公式;考虑到访问流之间的竞争,论文提出了一个磁盘分片的启发算法,它同时计算没有背景负荷和有背景负荷下访问流对应的磁盘优化分片,最终的磁盘分片是两者的结合;模拟试验表明自适应分片算法在四种分片算法中的性能最佳。     

Adaptive hinging hyperplanes and its applications in dynamic system identification

The model of adaptive hinging hyperplanes (AHH) is proposed in this paper. It is based on multivariate adaptive regression splines (MARS) and generalized hinging hyperplanes (GHH) and shares attractive properties of the two. By making a modification to the basis function of MARS, AHH shows linear property in each subregion. The AHH model is actually a special case of the GHH model, which has a universal representation capability for continuous piecewise linear functions. The approximation ability of the AHH model is proved. The AHH algorithm is developed similar to the MARS algorithm. It is adaptive and can be executed efficiently, hence has power and flexibility to model unknown relationships. The AHH procedure is applied to identifying two dynamic systems and its potential is illustrated.     

一类双线性系统的广义预测控制研究

双线性模型预测控制的研究表明,采用一般双线性模型的预测控制将涉及非线性优化问题,在线处理相当困难,而采用线性近似模型的预测控制又会带来较大的偏差.针对一类输入一输出双线性系统,提出了一种双线性系统的广义预测控制算法.该算法将基于输入-输出模型双线性系统中的双线性项和线性项合并,建立了一种类似于线性系统的ARIMA模型,并充分利用多步最优预测信息,由递推近似实现多步预测.控制律具有解析形式,避免了一般非线性寻优的复杂计算,并能适用于非最小相位双线性系统.仿真实验表明该算法具有良好的控制效果.     

Model predictive control based on adaptive hinging hyperplanes model

The model of adaptive hinging hyperplanes (AHH) is used in model predictive control (MPC). The nonlinear dynamic system is approximated by the continuous piecewise affine (CPWA) model AHH and the controller design problem becomes a continuous piecewise quadratic programming. The necessary and sufficient conditions for a point to be locally optimal for such a problem are established, based on which, a descent algorithm is developed to find a local optimum. Issues concerning feasibility and stability are also discussed. Simulations are conducted to confirm the effectiveness of the proposed MPC strategy.     

Unscented model predictive control of chance constrained nonlinear systems

This paper introduces an unscented model predictive approach for the control of constrained nonlinear systems under uncertainty. The main contribution of this paper is related to incorporation of statistical linearization, rather than commonly used analytical linearization, of the process and measurement models to provide a closer approximation of belief space propagation. Specifically, the state transition is approximated using an unscented transform to obtain a Gaussian belief space. This approximation allows for realization of closed-form solutions, which are otherwise available to linear systems only. Subsequently, the proposed approach is used to develop a model predictive motion control scheme that yields optimal control policies in presence of nonholonomic constraints as well as state estimation and collision avoidance chance constraints. As an example, successful kinematic control of a two-wheeled mobile robot is demonstrated in unstructured environments. Finally, the superiority of the proposed unscented model predictive control (MPC) over the traditional linearization-based MPC is discussed.     

基于小波变换的非线性广义预测控制

提出了基于小波变换的非线性广义预测控制算法。预测模型采用Hammerstein模型,对于其静态非线性部分采用小波网络来辨识,动态线性部分用最小二乘法来辨识。这种辨识方法比传统的多项式拟合的模型误差要小得多。基于这种预测模型广义预测控制器弥补了传统广义预测控制的模型失配问题。以CSTR为例对所设计的控制器进行仿真研究,结果表明控制器能够取得良好的控制效果。     

饱和非线性时滞系统约束预测控制

针对一类具有执行器饱和与输出约束的离散非线性时滞系统,提出新的模糊预测控制方法。首先,采用T-S模糊模型来逼近实际非线性系统,运用平行分步补偿（PDC）原理将该系统转化为一系列线性系统的凸组合。其次,通过每个采样时刻优化无穷时域的“min-max”性能指标来求解状态反馈预测控制器,得到系统满足Lyapunov渐近稳定的充分条件,并进一步将该条件转化为基于线性矩阵不等式（LMI）技术的半正定规划（SDP）问题。最后,通过数值仿真验证该方法的有效性。     

Model predictive control using reduced order models: Guaranteed stability for constrained linear systems

The problem of controlling a high-dimensional linear system subject to hard input and state constraints using model predictive control is considered. Applying model predictive control to high-dimensional systems typically leads to a prohibitive computational complexity. Therefore, reduced order models are employed in many applications. This introduces an approximation error which may deteriorate the closed loop behavior and may even lead to instability. We propose a novel model predictive control scheme using a reduced order model for prediction in combination with an error bounding system. We employ the explicit time and input dependent bound on the model order reduction error to achieve design conditions for constraint fulfillment, recursive feasibility and asymptotic stability for the closed loop of the model predictive controller when applied to the high-dimensional system. Moreover, for a special choice of design parameters, we establish local optimality of the proposed model predictive control scheme. The proposed MPC approach is assessed via examples demonstrating that a good trade-off between computational efficiency and conservatism can be achieved while guaranteeing constraint satisfaction and asymptotic stability.     

Online correction MPC strategy for spatially-distributed system based on PCA method

In this paper, the online correction model predictive control (MPC) strategy is presented for partial dif- ferential equation (PDE) unknown spatially-distributed systems (SDSs). The low-dimensional MIMO models are obtained using principal component analysis (PCA) method from the high-dimensional spatio-temporal data. Though the linear low- dimensional model is easy for control design, it is a linear approximation for nonlinear SDSs. Thus, the MPC strategy is proposed based on the online correction low-dimensional models, where the state at a previous time is used to correct the output of low-dimensional models and the spatial output is correct by the average deviation of the historical data. The simulations demonstrated show the accuracy and efficiency of the proposed methodologies.     

Design of an RMPC with a time‐varying terminal constraint set for tracking problem

This paper presents a robust model predictive control algorithm with a time‐varying terminal constraint set for systems with model uncertainty and input constraints. In this algorithm, the nonlinear system is approximated by a linear model where the approximation error is considered as an unstructured uncertainty that can be represented by a Lipschitz nonlinear function. A continuum of terminal constraint sets is constructed off‐line, and robust stability is achieved on‐line by using a variable control horizon. This approach significantly reduces the computational complexity. The proposed robust model predictive controller with a terminal constraint set is used in tracking set‐points for nonlinear systems. The effectiveness of the proposed method is illustrated with a numerical example. Copyright © 2015 John Wiley & Sons, Ltd.     

Min-max model predictive control for constrained nonlinear systems via multiple LPV embeddings

A min-max model predictive control strategy is proposed for a class of constrained nonlinear system whose trajectories can be embedded within those of a bank of linear parameter varying (LPV) models. The embedding LPV models can yield much better approximation of the nonlinear system dynamics than a single LTV model. For each LPV model, a parameter-dependent Lyapunov function is introduced to obtain poly-quadratically stable control law and to guarantee the feasibility and stability of the original nonlinear system. This approach can greatly reduce computational burden in traditional nonlinear predictive control strategy. Finally a simulation example illustrating the strategy is presented. Supported by the National Natural Science Foundation of China (Grant Nos. 60774015, 60825302, 60674018), the National High-Tech Research & Development Program of China (Grant No. 2007AA041403), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20060248001), and partly by Shanghai Natural Science Foundation (Grant No. 07JC14016)