基于满意优化的非线性预测控制

对多约束的非线性系统建立T—S模糊模型,采用局部线性化方法在每个采样点对非线性系统进行线性化,从而得到系统的线性化模型。针对传统的优化方法无法直接处理带有一定模糊不确定性的优化问题,该文在广义预测控制滚动优化的机制下把具有模糊边界约束的有限预测时域的优化问题,转化为等价的确定性规划问题,通过模糊规划方法来求解多约束的目标函数,从而用满意优化取代传统的二次型性能指标来求解模糊约束条件的预测控制。仿真结果表明了该方法的有效性。     

一种求解非线性约束优化全局最优的新方法

本文提出了一种求解非线性约束优化的全局最优的新方法—它是基于利用非线性互补函数和不断增加新的约束来重复解库恩-塔克条件的非线性方程组的新方法。因为库恩-塔克条件是非线性约束优化的必要条件,得到的解未必是非线性约束优化的全局最优解,为此,本文首次给出了通过利用该优化问题的先验知识,不断地增加约束来限制全局最优解范围的方法,一些仿真例子表明提出的方法和理论有效的,并且可行的。     

非线性分离法广义预测控制稳态特性分析

对具有输入饱和约束和Harnmerstein非线性的系统,采用“非线性分离法广义预测控制(GPC)”策略,即采用线性GPC时先不考虑Hammerstein非线性,然后采用解非线性代数方程的方法处理该非线性。根据处理饱和约束和解方程的不同顺序,可得到两种“两步法GPC”和一种“非线性移去法GPC”,分析了这些方法的稳态特性,并通过仿真进行了验证。     

非线性约束系统H∞鲁棒预测控制

针对一类具有状态约束和控制约束的离散非线性系统，本文采用有限维参数化方法提出了一种基于闭环优化的H∞鲁棒预测控制算法．这种算法把预测控制的滚动优化机制同微分对策理论和非线性H∞控制理论做了有机结合；在闭环优化中通过有限维参数化方法把控制变量参数化为多项式控制变量，并且引入被控系统的过渡平衡点．这样算法不但可以处理不确定系统，而且降低了在线闭环优化的计算复杂度．进一步，证明了算法的可行性和对有界不确定性系统的鲁棒稳定性．最后，用数值仿真验证了算法的有效性．     

一类非线性不确定时滞系统时滞依赖鲁棒干扰抑制

针对一类范数有界非线性不确定状态时滞系统，讨论其时滞依赖鲁棒干扰抑制问题．非线性不确定性无需满足任何匹配条件，采用将非线性不确定性转换为线性不确定性的方法来完成上述设计．基于LMI技术设计的时滞依赖无记忆状态反馈控制律，可保证闭环系统的鲁棒稳定性且能优化二次型干扰抑制水平．计算机仿真算例表明了该方法的有效性．     

不确定多通道奇异大系统分散鲁棒H∞控制

研究不确定多通道奇异系统的鲁棒分散H_∞控制问题,假定不确定性是时不变、范数有界,且存在于系统和控制输入矩阵中．主要考虑分散H_∞输出反馈控制问题．推导出了使不确定多通道奇异系统能鲁棒稳定且满足一定的性能指标的充分必要条件,没有等式约束的非线性矩阵不等式条件,采用两步同伦法迭代来求解非线性矩阵不等式(NMI),首先,通过逐步对控制器的系数矩阵加上结构限制,计算出当确定性不存在时的标称系统的分散H_∞控制器．然后,逐步改变标称系统分散控制器的系数,计算出不确定性参数存在时的分散鲁棒控制器．在每一阶段,每一次迭代过程中,通过交替固定NMI的一个变量,使NMI转变为线性矩阵不等式(LMI)．数值例子说明了本文提出的方法的有效性．     

全航速升力反馈减摇鳍控制策略研究

提出全航速减摇鳍控制策略,对低航速和中航速切换策略进行研究．采用升力反馈封装鳍角到升力的不确定性,避免在零航速和低航速下复杂的控制规律;同时,基于T-S模型将横摇非线性不确定系统转化为线性时变系统,并将控制中的约束非线性优化问题转化为二次规划问题,避免了预测控制中的非线性优化在线求解．以某船为例,给出了低中航速的切换控制策略,仿真结果表明了该方法可以使减摇鳍满足全航速减摇要求．     

非线性系统具有圆盘极点约束的鲁棒模糊控制

针对一类具有范数有界时变参数不确定性的离散非线性系统,研究其具有圆盘极点约束的鲁棒模糊控制问题．采用T—S模糊模型逼近实际的离散非线性系统,结合并行分布补偿法和二次型性能指标,导出了保证闭环系统鲁棒稳定且所有极点配置在预先指定圆盘中的二次圆域稳定保性能控制器的存在条件,并将最优保性能控制器的设计问题可归结为求解一个线性矩阵不等式的凸优化问题．最后的仿真结果验证了设计方法的有效性．     

基于反步法的一类非线性切换系统控制器设计

研究一类子系统是纯反馈非线性系统的切换系统控制器设计问题．基于多Lyapunov函数和反步法,提出一种状态反馈控制律及切换规则设计方法。通过递推设计可得到使非线性切换系统稳定的反馈控制律和切换规则．将所提出的方法应用于该类非线性切换系统含有不确定性的情形,仿真算例结果表明了所提出方法的有效性．     

基于非线性电路的复杂交通网路径规划

分析比较了单行机动车道与非线性二极管单向导电之间的类似特性．对禁止左转路口及其关联道路进 行拓扑结构变换,在电路地图基础上建立了复杂城市交通网的电路网络模型,并提出一种基于非线性电路的车辆最 优路径规划方法．这种方法从根本上解决了城市复杂交通环境下具有单行约束路段与左转约束路口的最优路径规划 问题．通过对非线性电子器件伏安特性进行分段线性化处理,并且改进迭代过程中的控制策略,使得路径规划方法 的计算效率得到提高．复杂性分析与仿真实验证明了本方法的有效性与可行性．     

基于Popov定理的输入非线性广义预测控制系统的稳定性分析

对存在输入饱和约束和输入可逆静态非线性的系统,采用两步法广义预测控制策略. 首先用线性广义预测控制策略得到中间变量,代表期望的控制作用,然后用解方程方法补偿可逆 静态非线性并用解饱和方法满足饱和约束,得到实际的控制作用.两步法计算简单,特别适用于 快速控制的场合.将该控制系统闭环结构转化为静态非线性增益反馈结构,利用Popov定理分 析了该系统的闭环稳定性,得到了稳定的充分条件,并具体给出了有效的控制器参数确定算法使 得稳定性结论具备实用的价值.给出了算例验证了稳定条件.     

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.     

Absolute stability analysis of discrete-time systems with composite quadratic Lyapunov functions

A generalized sector bounded by piecewise linear functions was introduced in a previous paper for the purpose of reducing conservatism in absolute stability analysis of systems with nonlinearity and/or uncertainty. This paper will further enhance absolute stability analysis by using the composite quadratic Lyapunov function whose level set is the convex hull of a family of ellipsoids. The absolute stability analysis will be approached by characterizing absolutely contractively invariant (ACI) level sets of the composite quadratic Lyapunov functions. This objective will be achieved through three steps. The first step transforms the problem of absolute stability analysis into one of stability analysis for an array of saturated linear systems. The second step establishes stability conditions for linear difference inclusions and then for saturated linear systems. The third step assembles all the conditions of stability for an array of saturated linear systems into a condition of absolute stability. Based on the conditions for absolute stability, optimization problems are formulated for the estimation of the stability region. Numerical examples demonstrate that stability analysis results based on composite quadratic Lyapunov functions improve significantly on what can be achieved with quadratic Lyapunov functions.     

Economic plant-wide control design with backoff estimations using internal model control

Economic optimal operation typically involves operating as close as possible to the active constraints. However, in the presence of disturbances it is necessary to back-off from the constraints in order to avoid violating them. The backoff approach aims at selecting the control structure that minimizes the economic loss associated with the required constraint backoffs. This paper revisits the backoff approach and proposes a framework for estimating the constraint backoffs based on well-known elements of internal model control (IMC) theory, such as an automatic procedure for tuning the IMC low-pass filters, a stability condition, and an uncertainty representation based on diagonal input multiplicative uncertainty. Since the constraint backoffs are estimated using a linear dynamic model, the inclusion of input multiplicative uncertainty allows introducing conservatism in the estimation of the backoffs, which is required in order to avoid constraint violations. A forced-circulation evaporator benchmark problem is used to illustrate the approach.     

Zames-Falb Multipliers for Quadratic Programming

In constrained linear model predictive control, a quadratic program must be solved on-line at each control step, and this constitutes a nonlinearity. If zero is a feasible point for this quadratic program then the resultant nonlinearity is sector bounded. We show that if the nonlinearity is static then it is also monotone and slope restricted; hence, we show the existence of Zames-Falb multipliers for such a nonlinearity. The multipliers may be used in a general and versatile analysis of the robust stability of input constrained model predictive control.     

Efficient robust constrained model predictive control with a time varying terminal constraint set

An efficient robust constrained model predictive control algorithm with a time varying terminal constraint set is developed for systems with model uncertainty and input constraints. The approach is novel in that it off-line constructs a continuum of terminal constraint sets and on-line achieves robust stability by using a relatively short control horizon (even N=0) with a time varying terminal constraint set. This algorithm not only dramatically reduces the on-line computation but also significantly enlarges the size of the allowable set of initial conditions. Moreover, this control scheme retains the unconstrained optimal performance in the neighborhood of the equilibrium. The controller design is illustrated through a benchmark problem.     

Nonlinear Robust Adaptive Deterministic Control for Flexible Hypersonic Vehicles in the Presence of Input Constraint

A nonlinear deterministic robust control scheme is developed for a flexible hypersonic vehicle with input saturation. Firstly, the model analysis is conducted for the hypersonic vehicle model via the input‐output linearized technique. Secondly, the sliding mode manifold is designed based on homogeneity theory. Then an adaptive high order sliding mode control scheme is proposed to achieve tracking for the step change in altitude and velocity for hypersonic vehicles where the uncertainty boundary is unknown. Furthermore, the control input constraint is investigated and another new adaptive law is proposed to estimate the uncertainties and to guarantee the stability of the system with input saturation. Finally, the simulation results are provided to demonstrate the effectiveness of the proposed method.     

最优控制L1自适应在重装空投纵向控制器设计中的应用

为保证空投过程中载机的姿态和高度稳定,采用结合最优控制的L_1自适应控制方法设计了飞机纵向控制器.利用最优控制产生线性控制信号并确定匹配参考模型,在此基础上将系统非线性转化为L_1自适应控制结构中的匹配和非匹配不确定性实现姿态保持,结合外环PID高度控制器完成整个飞控系统的设计.仿真验证了控制器的强鲁棒性,可以抑制高自适应增益下输入信号中的高频抖振.     

压水堆功率跟踪自适应保性能控制器设计

针对压水堆动态模型的高度非线性和不确定性特点,本文提出一种自适应保性能跟踪控制器(adaptive guaranteed cost control,AGCC)设计方法.首先以堆芯的点堆方程为基础,引入功率跟踪误差的积分项,构造反应堆的增广状态空间模型,再结合线性参数变化(linear parameter varying,LPV)理论,建立了堆芯系统的多胞LPV模型.该控制器的控制输入由状态反馈控制和不确定性补偿组成,结合保性能控制理论和多胞模型理论,求解线性矩阵不等式得到变增益状态反馈矩阵,确保闭环系统全局渐近稳定;利用李亚普诺夫稳定理论得到不确定性参数的自适应律,实现对系统不确定性的动态补偿.仿真结果表明,该控制器不仅对系统不确定项具有自适应性,而且有较好的负荷跟踪性能.