有界扰动多变量Hammerstein系统输入到 状态稳定模型预测控制

考虑具有状态和控制约束的有界未知扰动多变量Hammerstein系统,提出一种具有输入到状态稳定和有限L_2增益性能的鲁棒非线性模型预测控制策略.基于多变量线性子系统H_∞控制律,滚动预测非线性代数方程的解算误差,继而在线优化计算满足系统约束条件的预测控制量.利用输入到状态稳定性概念和L_2增益思想,建立闭环系统关于该扰动信号具有鲁棒稳定性和L_2增益的充分条件,使闭环系统不仅满足系统约束,而且对不确定扰动输入和解算误差具有鲁棒性.最后以工业聚丙烯多牌号切换过程控制为例,仿真验证本文算法的有效性.     

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.     

基于鲁棒控制Lyapunov 函数的非线性预测控制

针对一类约束不确定性非线性仿射系统,提出一种可保证闭环系统鲁棒镇定的非线性模型预测控制算法.利用鲁棒控制Lyapunov函数得到改进的Sontag公式,并以此为基础,构造一种计算有效的单自由度鲁棒预测控制器.以Matlab语言为仿真工具,对一开环不稳定振荡器进行了仿真研究,结果表明,利用该控制算法得到的闭环系统不仅渐近稳定于原点,而且所得控制量和系统状态都满足系统约束,从而验证了控制算法的有效性.     

基于收缩约束模型预测控制的无人车辆路径跟踪

针对存在有界扰动的非线性无人驾驶车辆避障过程中最优路径规划跟踪问题,提出一种基于预测时域内系统输入输出收缩约束(PIOCC)的模型预测控制(MPC)方法.首先在构建目标函数时,为扩大可行性解的范围引入软约束思想,将最优规划路径的跟随问题转化为对模型预测控制优化问题的求解;其次为避免短预测时域造成闭环系统发散而导致在约束条件限定下出现无可行性解的情况,采用预测时域内系统输入输出收缩约束的方法,设计模型预测控制器;再次基于Lyapunov稳定性理论证明所设计的模型预测闭环控制系统是渐近稳定的;最后通过仿真实例验证了所提出基于PIOCC的控制策略在解决扩大可行解范围和避免闭环系统发散问题时的有效性,实现了无人驾驶车辆在路径跟踪时具有良好的快速性和稳定性.     

基于反步设计的构造性非线性预测控制算法

针对具有状态和输入约束的严格反馈非线性系统,提出一种反步设计构造性非线性预测控制算法.利用反步设计法离线构造系统的控制李亚普诺夫函数,进而得到系统的镇定可调控制器即稳定控制类.基于性能指标,滚动优化控制器可调参数,计算满足系统约束的预测控制量.进一步,运用控制李亚普诺大函数的性质建立闭环系统的稳定性.最后,应用轮式移动机器人的优化控制验证本文结果的有效性.     

约束Hammerstein系统输出反馈非线性预测控制

针对具有状态、输入和中间变量约束的Hammerstein系统,采用两步法控制策略,给出一种新的可保证闭环系统指数稳定的输出反馈非线性模型预测控制算法.基于Hammerstein系统的特殊结构,结合状态观测器给出无约束线性环节的输出反馈最优控制律,通过滚动优化一有限时域的约束优化问题计算实际控制量.给出保证闭环系统指数稳定的充分条件.以工业双环管聚丙烯装置牌号切换控制为例进行仿真,仿真结果验证该算法的有效性和实用性.     

多输入/多输出系统动态矩阵控制鲁棒稳定性

研究了基于脉冲响应模型的动态矩阵预测控制(DMC)算法,针对多输入、多输出(MIMO)系统脉冲响应模型的特点,利用脉冲响应系数误差矩阵范数平方和定义预测模型的模型误差,以线性矩阵不等式(LMI)的形式提出了DMC闭环鲁棒稳定充要条件,将DMC算法闭环稳定问题转换为一类线性矩阵不等式的可解问题.并且研究了模型误差与闭环系统稳定性之间的关系,给出了保证系统稳定条件下模型误差界的求取方法,通过求解一个线性矩阵不等式约束的凸优化问题得到保证闭环系统稳定的误差界.最后,利用算例对本文方法的有效性进行了验证.     

具有不确定性的非线性切换系统的约束预测控制

针对一类具有不确定性和变量约束的非线性切换系统, 提出了一种基于Lyapunov函数的预测控制方法, 其中状态约束分为两种情况: 1)要求状态变量在所有时刻都满足约束(称为硬约束); 2)允许状态在某些时刻超出约束(称为软约束). 主要思想是: 对切换系统的每一个子系统, 在输入和状态均受约束的情况下, 设计基于Lyapunov函数的有界控制器和预测控制器, 在两者之间适当切换, 得到初始稳定区域的描述并使得子闭环系统保持稳定. 对整个切换系统, 设计适当的切换律以保证: 1)在切换时刻, 闭环系统的状态处在切入系统的稳定区域内; 2)切入模块的Lyapunov函数是非增的, 从而可保证稳定性. 在状态变量的约束是软约束时, 对每一子模块首先设计一个控制策略, 尽快将状态控制到初始稳定区域, 然后再利用稳定区域内的控制律使系统稳定.     

约束Hammerstein系统输出反馈非线性预测控制

针对具有状态、输入和中间变量约束的Hammerstein系统,采用两步法控制策略,给出一种新的可保证闭环系统指数稳定的输出反馈非线性模型预测控制算法。基于Hammerstein系统的特殊结构,结合状态观测器给出无约束线性环节的输出反馈最优控制律,通过滚动优化一有限时域的约束优化问题计算实际控制量。给出保证闭环系统指数稳定的充分条件。以工业双环管聚丙烯装置牌号切换控制为例进行仿真,仿真结果验证该算法的有效性和实用性。     

广义准无限时域非线性预测控制

将准无限时域非线性预测控制方法推广到更一般的情况, 并给出了闭环约束系统的稳定性条件及最优解的存在条件. 基于反馈线性化技术讨论了广义准无限时域非线性预测控制的实现及较大终端域的获取. 该方法能显著减少在线优化所需的时间.     

Conditions under which suboptimal nonlinear MPC is inherently robust

We address the inherent robustness properties of nonlinear systems controlled by suboptimal model predictive control (MPC), i.e., when a suboptimal solution of the (generally nonconvex) optimization problem, rather than an element of the optimal solution set, is used for the control. The suboptimal control law is then a set-valued map, and consequently, the closed-loop system is described by a difference inclusion. Under mild assumptions on the system and cost functions, we establish nominal exponential stability of the equilibrium, and with a continuity assumption on the feasible input set, we prove robust exponential stability with respect to small, but otherwise arbitrary, additive process disturbances and state measurement/estimation errors. These results are obtained by showing that the suboptimal cost is a continuous exponential Lyapunov function for an appropriately augmented closed-loop system, written as a difference inclusion, and that recursive feasibility is implied by such (nominal) exponential cost decay. These novel robustness properties for suboptimal MPC are inherited also by optimal nonlinear MPC. We conclude the paper by showing that, in the absence of state constraints, we can replace the terminal constraint with an appropriate terminal cost, and the robustness properties are established on a set that approaches the nominal feasibility set for small disturbances. The somewhat surprising and satisfying conclusion of this study is that suboptimal MPC has the same inherent robustness properties as optimal MPC.     

约束非线性系统理想点多目标安全预测控制

考虑具有状态和控制约束的仿射非线性系统多目标安全控制问题,本文提出一种保证安全和稳定的多目标安全模型预测控制(MOSMPC)策略.首先通过理想点逼近方法解决多个控制目标的冲突问题.其次,利用控制李雅普诺夫障碍函数(CLBF)参数化局部控制律,并确定系统不安全域.在此基础上,构造非线性系统的参数化双模控制器,减少在线求解模型预测控制(MPC)优化问题的计算量.进一步,应用双模控制原理和CLBF约束,建立MOSMPC策略的递推可行性和闭环系统的渐近稳定性,并保证闭环系统状态避开不安全域.最后,以加热系统的多目标控制为例,验证了本文策略的有效性.     

输入非线性系统的两步法预测控制的鲁棒稳定性

针对具有不确定性和输入饱和约束的Hammerstein模型，采用两步法预测控制器，首先不考虑约束、非线性和不确定性，得到一个期望的中间变量．然后通过求解非线性代数方程组来处理非线性并通过解饱和来满足约束．采用Lyapunov方法得到了指数稳定条件，并给出了吸引域的计算和调整方法．最后通过仿真实例验证了稳定性结果．     

Predictive proportional nonlinear control for stable-target tracking of a mobile robot: an experimental study

Two new types of control method have been developed based on model predictive control for stable-target tracking of a nonholonomic mobile robot. One method (Method 1) is a new nonlinear control method. This was developed based on model predictive control (predictive nonlinear control) to predict the next position of a mobile robot using the current velocities of the right and left wheels. This technique uses a tuning guideline in predictive nonlinear control. The other method (Method 2) is a combination of Method 1 and proportional control (predictive proportional nonlinear control). Method 2 involves a tuning guideline not only in a predictive nonlinear controller, but also in a proportional controller. In this technique, the selection of a tuning guideline in the proportional controller is enhanced, and thereby increases the control action in closed-loop responses. In Method 1, the nonlinear controller is derived from Liapunov stability theory, and is used to control the linear and angular velocities for locomotion control. Tuning parameters in the nonlinear controller (in Method 1) are selected to satisfy various design criteria, such as stability, performance, and robustness. Method 1 has certain limitations that result in a decrease of the performance criteria specified. Strong nonlinearities in the mobile robot system result in accumulated errors. To enhance performance further, we developed Method 2 as the solution for decreasing cumulative errors. Hence, the proportional controller is added to Method 1 in the closed-loop form in order to eliminate errors. The advantage of Method 2 is that it can cope with strong nonlinearities in the mobile vehicle system. The results of the performances of Method 1 and Method 2 are shown to demonstrate the effectiveness of both methods, and also the better performance of Method 2. The two new methods are effective in stable-target tracking, yielding an increase in performance and stability.     

基于混合逻辑的非线性系统多模型预测控制

针对已有的多模型预测控制算法在模型预测过程中采用局部线性模型进行预测而产生的预测误差较大这一问题, 本文将非线性过程的多模型描述与输出预测之间的因果关系以约束条件的形式引入到模型预测控制的设计中, 将非线性过程描述成为一个混合逻辑动态系统模型, 模型切换规则以先验知识的形式引入到多模型预测过程中, 该模型可以全局地表征非线性过程的特性, 从而解决了多模型约束非线性预测控制的模型预测与模型切换问题.     

基于保辛算法的绳系卫星系统闭环反馈控制问题求解

应用非线性系统滚动时域控制的保辛算法求解绳系卫星系统子星释放和回收过程的闭环反馈控制问题.通过第二类Lagrange方程推导出二体绳系卫星系统的动力学方程;通过拟线性化方法将绳系卫星系统闭环反馈控制问题转化为线性非齐次Hamilton系统两端边值问题的迭代求解;通过保辛算法将线性非齐次Hamilton两端边值问题转化为线性方程组的求解;通过递进更新时间步的状态变量和控制变量,完成绳系卫星系统的闭环反馈控制.数值仿真表明:相对于Legendre伪谱方法,用保辛算法求解绳系卫星系统的闭环反馈控制问题的计算速度和收敛速度较快.绳系卫星系统的开环控制和闭环反馈控制问题数值仿真结果表明:在绳系卫星的初始状态存在偏差的情况下,使用开环控制会导致系统在终端无法达到稳定状态,而使用闭环反馈控制则能在一段时间内抵消初始状态向量偏差对系统产生的影响,最终达到稳定状态.     

On the stability of receding-horizon LQ control with zero-stateterminal constraint

Receding-horizon control with zero state terminal constraint for linear time-varying discrete systems is considered. It is shown that uniform controllability suffices to ensure closed-loop exponential stability thus relaxing the reversibility and/or detectability requirements made in the existing literature. The result has interesting implications in the design of predictive controllers with guaranteed closed-loop stability     

Handling communication disruptions in distributed model predictive control

In this work, we study distributed model predictive control (DMPC) of nonlinear systems subject to communication disruptions - communication channel noise and data losses - between distributed controllers. Specifically, we focus on a DMPC architecture in which one of the distributed controllers is responsible for ensuring closed-loop stability while the rest of the distributed controllers communicate and cooperate with the stabilizing controller to further improve the closed-loop performance. To handle communication disruptions, feasibility problems are incorporated in the DMPC architecture to determine if the data transmitted through the communication channel is reliable or not. Based on the results of the feasibility problems, the transmitted information is accepted or rejected by the stabilizing MPC. In order to ensure the stability of the closed-loop system under communication disruptions, each model predictive controller utilizes a stability constraint which is based on a suitable Lyapunov-based controller. The theoretical results are demonstrated through a nonlinear chemical process example.