【作者】 李哲；

【导师】 李少远；

【作者基本信息】 上海交通大学 ， 控制科学与工程， 2016， 硕士

【摘要】 事件触发控制最早应用于资源有限的系统,通过设计与状态相关的触发条件并按照触发条件的满足与否进行信号传输与系统控制,从而使得系统资源可以得到有效利用,解决资源有限系统中计算资源(优化次数)与系统稳定性间的矛盾。在约束预测控制中,除了系统资源与稳定性的矛盾,还存在系统可行性、最优性与计算复杂度的基本矛盾,但这一矛盾可以通过根据系统状态合理地设计终端约束来解决。本文不仅通过设计与终端约束相关的事件触发条件,使系统在保持稳定性的情况下有效地减少优化次数,还将事件触发应用于控制器中,根据由终端约束设计的触发条件在线地设计终端约束,从而解决系统可行性、最优性与计算复杂度之间的矛盾。主要工作与创新点包括:1.集合序列事件触发预测控制:针对有约束的预测控制系统,构建了一个与闭环可行状态轨迹相关,又不依赖于此轨迹的集合序列。利用该序列的收敛性和可行性设计事件触发条件,在保证系统稳定性的前提下有效减少了优化次数。与其他有约束系统的事件触发相比,该方法的触发条件更简单,有效。2.基于集合序列的终端约束事件触发预测控制器设计:针对预测控制中可行域大小与计算复杂度的矛盾,利用上一章构建的集合序列中集合之间的i步集关系,创新性地将事件触发控制框架应用到控制器内部。利用状态终端约束构成的触发条件判断当前系统的可行性,并在事件触发后选择使系统可行的终端集,使系统在任意优化时域下始终具有最大的吸引域,剥离了可行域对优化时域的依赖。3.终端约束事件触发预测控制器设计:基于集合序列的方法需要线下计算一系列集合,求解过程会有些繁琐,并且系统最优性受限于集合序列中最小的集合。本章引入Minkowski泛函,将终端集参数化,从而将终端集合的线下计算、线上综合转化为完全的线上优化;提出可行裕量的概念,定量地描述当前系统的可行性情况。与基于集合序列的方法相比,该算法不用计算复杂的集合序列,具有更大的灵活性,并且可以得到更好的系统性能(最优性得到改善)。4.终端约束事件触发分布式预测控制:将终端约束事件触发预测控制扩展到分布式预测控制中,使得分布式预测控制中每个子系统始终都具有最大的可行域,保证了存在耦合时的各子系统的强可行性。结合定义在邻域的Lyapunov函数,保证了全局系统的稳定性,减小原有分布式系统稳定性约束的保守性。更多还原

【Abstract】 Event-trigger control is first applied in systems with limited resource.By designing state related trigger condition and transforming signals or commuting control actions according to the trigger condition,the system resources can be utilized effectively,which can resolve the contradiction between system resources(optimization times)and stability.In constrained system,there is a fundamental contradiction among feasibility,optimality and computational complexity,which can be solved by redesigning the terminal constraint set rationally.This paper designed a novel trigger condition based on the terminal constraint to reduce the optimization times while keeping the system stable.Additionally,the event-trigger scheme is firstly applied in controller to solve the contradiction among feasibility,optimality and computational complexity,in which,the trigger condition is based on the terminal constraint set.The solution is redesign the terminal set whenever the event is triggered.The main contributions can be summarized into following four parts:1.Event-triggered model predictive control for set trajectory: For control system with constraints,a contractive set trajectory is constructed,which is related to but not depends on a feasible closed-loop state trajectory.Its convergence property is used to design a novel trigger condition for event-trigger model predictive control.It is able to reduce the calculation times of the optimization while guarantee the stability of system.Compared to existed trigger conditions,it is easier to be obtained.2.Event-triggered model predictive control for terminal constraint with set trajectory: Since the set trajectory is able to characterize whether current system is feasible before the optimization problem is solved.A trigger condition based on set trajectory is newly applied inside the controller to arise the redesign of some controller parameter(terminal set).This scheme is able to make the domain of attraction not depend on the optimization horizon,i.e.it always has the largest domain of attraction with any optimization horizon.3.Event-triggered model predictive control for terminal constraint: The calculation of the set trajectory is complicated and the optimality of former controller is restricted to smallest set in the trajectory.Then Minkowski functional is introduced to parameterize the terminal constraint,which enables the redesign of terminal set is totally on-line.Additionally,a novel conception,feasibility margin,is proposed to characterize the feasibility of current system.It is more flexible than the one used set trajectory and has better control performance.4.Event-triggered Distributed Model Predictive Control for terminal constraint:The event-triggered model predictive control for terminal constraint is extended to distributed system.It enables to design stability guaranteed parameters more easily.Feasibility depends on event-triggered terminal set and global stability is guaranteed by Lyapunov functions defined in neighborhood,which is able to reduce the conservatism of stability constraint in traditional distributed model predictive control.更多还原