约束非线性系统构造性模型预测控制

研究了连续时间约束非线性系统模型预测控制设计. 利用控制 Lyapunov函数离线构造单变量可调预测控制器,再根据性能指标在线优化可调参数,其中该参数近似于闭环系统的,衰减率,同时,控制 Lyapunov函数保证了算法的可行性和闭环系统的稳定性 .最后通过数值仿真验证了该算法的有效性.

     

指令跟踪自适应广义预测控制及其应用

现有的广义预测控制系统其闭环性能受可调参数影响较大,它的目标函数无法直接规定 闭环性能.该文提出一种具有独立跟踪和调节目标的新型自适应广义预测控制算法,并将其 应用于快速时变的导弹控制系统设计中.这种算法利用参考模型规定对指令信号的跟踪性 能,减少了可调参数对闭环性能的影响.仿真结果证实了该算法的有效性.     

存在环境约束的机器人自适应迭代学习控制

针对存在不确定性和外界干扰的受限机器人系统提出一种自适应迭代学习控制律.不确定性参数被估计在时间域内,同时重复性外界干扰在迭代域内得到补偿.通过引入饱和学习函数,保证了闭环系统所有信号有界.借助Lyapunov复合能量函数法,证明了系统渐进收敛到期望轨迹的同时,能够保证力跟踪误差有界可调.     

网络控制系统的自整定PID 控制器设计

结合广义预测控制（GPC）方法和PID反馈结构,设计了一种具有预测功能的PID控制器,PID参数根据未来时刻的预计输出误差进行整定.控制器导出多步控制序列,置于执行器端的延迟补偿器根据网络时延从控制序列中选择控制信息并作用于控制对象,从而对时延进行补偿,使控制性能得到极大改善.控制器结合了PID控制和预测控制的优点,具有较强的鲁棒性和工程意义.最后通过构造Lyapunov函数对闭环系统的稳定性进行了分析,并通过仿真验证了该算法的有效性.     

船舶航向非线性系统的多滑模自适应模糊控制

针对参数未知的船舶航向非线性控制系统数学模型,在考虑舵机伺服机构特性的情况下,船舶航向控制问题就成为一个虚拟控制系数未知的非匹配不确定非线性控制问题.基于多滑模设计方法和模糊逻辑系统的逼近能力,提出了一种多滑模自适应模糊控制算法,通过引入非连续投影算法和积分型Lyapunov函数,提高了系统在抑制参数漂移、控制器奇异等方面的能力.借助Lyapunov函数证明了所设计控制器使最终的闭环非匹配不确定船舶运动非线性系统中的所有信号有界,且跟踪误差收敛到零.仿真研究表明:该算法与传统的PID控制相比,具有较好的跟踪能力和自适应能力.     

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.     

控制方向未知的全状态约束非线性系统的鲁棒自适应跟踪控制

针对一类控制方向未知的含有时变不确定参数和未知时变有界扰动的全状态约束非线性系统,本文提出了一种基于障碍Lyapunov函数的反步自适应控制方法.障碍Lyapunov函数保证了系统状态在运行过程中始终保持在约束区间内;Nussbaum型函数的引入解决了系统控制方向未知的问题;光滑投影算法确保了不确定时变参数的有界性.障碍Lyapunov函数、Nussbaum型函数及光滑投影算法与反步自适应方法的有效结合首次解决了控制方向未知的全状态约束非线性系统的跟踪控制问题.所设计的自适应鲁棒控制器能在满足状态约束的前提下确保闭环系统的所有信号有界.通过恰当地选取设计参数,系统的跟踪误差将收敛于0的任意小的邻域内.仿真结果表明了控制方案的可行性.     

未知不确定非线性系统的直接自校正滑模控制

针对一类具有未知不确定性的非线性系统,提出一种参数直接自校正滑模控制方法.将系统的非线性、参数变化和外部干扰都视作系统不确定性,控制器的设计无需不确定项的上下界等信息:为改善跟踪性能与减小输入抖振,控制器设计中引入可调边界层厚度的双极性sigmoid函数与可变滑模切换增益,推导出控制增益和边界层厚度的直接自校正律,并基于Lyapunov判据给出了闭环系统稳定性证明.仿真实例证明了该方法的有效性和正确性.     

考虑摩擦力影响精密伺服系统的鲁棒自适应控制

针对具有摩擦力扰动的精密伺服系统提出了一种鲁棒自适应控制方法.首先,对基于 bristle模型的动态摩擦力模型进行了线性参数化,该线性参数化过程包含了对stribeck效应的 线性参数化处理;然后,基于构造的Lyapunov函数设计全局渐近稳定自适应控制律,并对闭环 系统的跟踪性能进行了严格的理论分析.仿真实验验证了算法的有效性.     

网络环境下非线性切换系统的固定时间控制

本文针对一类不确定非线性切换系统, 在控制系数和量化器参数未知的情况下, 研究系统的自适应固定时间控制问题. 首先, 文章利用增加幂次积分法和共同Lyapunov函数设计带有可调参数的自适应控制器. 然后, 基于改进的固定时间控制理论, 文章提出有效的参数调节律, 从而实现闭环系统的固定时间稳定性. 最后, 通过仿真实验验证所提控制算法的有效性     

Fuzzy Constrained Min-Max Model Predictive Control Based on Piecewise Lyapunov Functions

This paper proposes two novel stable fuzzy model predictive controllers based on piecewise Lyapunov functions and the min-max optimization of a quasi-worst case infinite horizon objective function. The main idea is to design state feedback control laws that minimize the worst case objective function based on fuzzy model prediction, and thus to obtain the optimal transient control performance, which is of great importance in industrial process control. Moreover, in both of these predictive controllers, piecewise Lyapunov functions have been used in order to reduce the conservatism of those existent predictive controllers based on common Lyapunov functions. It is shown that the asymptotic stability of the resulting closed-loop discrete-time fuzzy predictive control systems can be established by solving a set of linear matrix inequalities. Moreover, the controller designs of the closed-loop control systems with desired decay rate and input constraints are also considered. Simulations on a numerical example and a highly nonlinear benchmark system are presented to demonstrate the performance of the proposed fuzzy predictive controllers.     

Adaptive control Lyapunov function based model predictive control for continuous nonlinear systems

A design of adaptive model predictive control (MPC) based on adaptive control Lyapunov function (aCLF) is proposed in this article for nonlinear continuous systems with part of its dynamics being unknown at the starting time. Specifically, to guarantee the convergence of the closed-loop system with online predictive model updating, a stability constraint is designed. It limits the aCLF of the system under the MPC to be less than that under an online updated auxiliary adaptive control. The auxiliary adaptive control which implements in a sampling-hold fashion can guarantee the convergence of the controlled system. The sufficient conditions that guarantee the states to be steered to a small region near the equilibrium by the proposed MPC are provided. The calculation of the proposed algorithm does not depend on the model mismatch at the starting time. And it does not require the Lyapunov function of the state of the real system always to be reduced at each time. These provide the potential to improve the performance of the closed-loop system. The effectiveness of the proposed method is illustrated through a chemical process example.     

Predictive control of switched nonlinear systems with scheduled mode transitions

In this work, a predictive control framework is proposed for the constrained stabilization of switched nonlinear systems that transit between their constituent modes at prescribed switching times. The main idea is to design a Lyapunov-based predictive controller for each constituent mode in which the switched system operates and incorporate constraints in the predictive controller design which upon satisfaction ensure that the prescribed transitions between the modes occur in a way that guarantees stability of the switched closed-loop system. This is achieved as follows: For each constituent mode, a Lyapunov-based model predictive controller (MPC) is designed, and an analytic bounded controller, using the same Lyapunov function, is used to explicitly characterize a set of initial conditions for which the MPC, irrespective of the controller parameters, is guaranteed to be feasible, and hence stabilizing. Then, constraints are incorporated in the MPC design which, upon satisfaction, ensure that: 1) the state of the closed-loop system, at the time of the transition, resides in the stability region of the mode that the system is switched into, and 2) the Lyapunov function for each mode is nonincreasing wherever the mode is reactivated, thereby guaranteeing stability. The proposed control method is demonstrated through application to a chemical process example.     

具有零动态仿射非线性系统控制Lyapunov函数的构造

研究具有零动态仿射非线性系统控制Lyapunov函数的构造问题.提出通过求解一个Lyapunov方程获得可线性化部分的二次型控制Lyapunov函数.由可线性部分的控制Lyapunov函数和零动态部分的Lyapunov函数,通过构造一个正定函数,得到了整个系统的控制Lyapunov函数,且设计了可半全局镇定整个闭环系统的控制律.仿真实例说明了所提出方法的有效性.     

Stability analysis of a multi-model predictive control algorithm with application to control of chemical reactors

We study a stabilizing multi-model predictive control strategy for controlling nonlinear process at different operating conditions. The control algorithm is a receding horizon scheme with a quasi-infinite horizon objective function that has finite and infinite horizon cost components. The finite horizon cost consists of free input variables that direct the system towards a terminal region which contains the desired operating point. The infinite horizon cost has an upper bound and steers the system to the desired operating point. The system is represented by a sequence of piecewise linear models. Based on the condition of the system states, the sequence of piecewise linear models is updated and the controller’s objective function switches form quasi-infinite to infinite horizon objective function. This results in a hybrid control structure. A recent approach in the analysis of hybrid systems that uses multiple Lyapunov functions is employed in the stability analysis of the closed-loop system. The stabilizing hybrid control strategy is illustrated on two examples and their closed-loop stability properties are studied.     

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.     

A Lyapunov's direct method for the global robust stabilization of nonlinear cascaded systems

The global robust stabilization problem of cascaded systems with dynamic uncertainty has been approached by the small gain theorem. This method, however, does not produce an explicit Lyapunov function for the closed-loop system. In this paper, we develop a Lyapunov's direct method based recursive approach to solving the global robust stabilization problem for the mentioned systems. This method also produces an explicit Lyapunov function for the closed-loop system which is a superposition of those of individual subsystems. This Lyapunov function is indispensable when the adaptive control of the same class of systems is further considered.     

DoS攻击下网络化控制系统基于观测器的记忆型事件触发预测控制

本文研究了DoS攻击下网络化控制系统记忆型事件触发预测补偿控制问题. 首先, 由于网络带宽资源有限 和系统状态不完全可观测性, 引入了记忆型事件触发函数, 为观测器提供离散事件触发传输方案. 然后, 分析了网络 传输通道上发生的DoS攻击. 结合上述记忆型事件触发方案, 在控制节点设计一类新颖的预测控制算法, 节省网络 带宽资源并主动补偿DoS攻击. 同时, 建立了基于观测器的记忆型事件触发预测控制的闭环系统, 并且分析稳定性. 通过线性矩阵不等式(LMI)和Lyapunov稳定性理论, 建立了控制器、观测器和记忆型事件触发矩阵的联合设计方案, 并验证了该方案的可行性. 仿真结果表明, 该方案结合记忆型事件触发机制可以有效补偿DoS攻击, 节约网络带宽 资源.     

基于最小二乘支持向量机的双模控制

提出一种保证闭环系统稳定性的双模控制:采用预测控制将状态驱动到终端约束域,再利用局部线性控制将状态驱动到原点.在分析一类基于最小二乘支持向量机(LS-SVM)的预测控制的基础上,在常规的性能指标后附加了一个终端约束,并利用李亚普诺夫方法推导了确保闭环系统稳定性的4个充分条件.在此基础上,推导了基于最小二乘支持向量机的双模控制算法.仿真结果显示了算法的优越性.