基于不变集的Markov跳变系统的预测控制研究

发布时间：2018-02-17 05:25

本文关键词： Markov 跳变系统模型预测控制不变集硬约束概率软约束时滞类周期系统　出处：《上海交通大学》2015年博士论文　论文类型：学位论文

【摘要】：Markov跳变系统是指结构发生随机性突变的系统,如经济系统、飞行器控制系统、通信系统以及太阳能加热系统中都会出现这样的情况,它是一类非常重要的系统。在Markov跳变系统中,由于物理限制的存在或者经济、性能的要求总是不可避免地存在约束。在处理约束时,模型预测控制由于其独特的滚动时域运行机制,相比于其他控制方法通常更有优势。因此Markov跳变系统的模型预测控制是一个非常有意义的研究课题。约束的存在给Markov跳变系统预测控制器的设计带来了困难。在约束存在的情形下设计具有递归可行性保证以及良好控制性能的预测控制器是Markov跳变系统预测控制研究的一个关键问题。本论文针对以上问题,对Makrov跳变系统不同情形下约束预测控制器的设计展开研究,主要内容和成果如下。?针对加性扰动的约束Markov跳变系统,给出了求解该系统最大允许集的高效算法。?针对具有硬约束的Markov跳变系统,基于椭圆集给出了无约束、约束多步控制器的设计,证明了算法的递归可行性和闭环系统的均方稳定性。为了提高算法的在线计算效率,进一步给出了降低其在线计算量的预测控制器设计。?针对具有硬约束的Markov跳变系统,为了克服上面算法不能有效处理非对称约束的缺点,基于最大允许集(多面体集)给出了一般插值、具有线性目标和基于精确约束处理的插值预测控制器设计,证明了算法的递归可行性和闭环系统的均方稳定性。?针对具有概率软约束的Markov跳变系统,分两种情形:扰动能量有界和持续扰动的情形,基于最大允许集给出了相应的预测控制器的设计,证明了算法的递归可行性和闭环系统的均方稳定性。?针对时滞建模为Markov链的结构不确定系统,采用状态增广的方式将系统转化为标准的结构不确定时滞Markov跳变系统,给出了预测控制器的设计,并给出了降低其在线计算量的预测控制器设计。?针对具有类周期特性和期望约束的Markov跳变系统,分别给出了鲁棒控制器、随机控制器以及预测控制器的设计。证明了在以上控制器作用下的约束满足性以及闭环系统的稳定性。
[Abstract]:Markov jump systems are systems in which the structure changes at random, such as economic systems, aircraft control systems, communications systems, and solar heating systems. It is a very important system. In Markov jump system, because of the existence of physical limitation or economy, the performance requirement inevitably exists. Model Predictive Control (MPC), due to its unique rolling time-domain operation mechanism, Compared with other control methods, the model predictive control of Markov jump system is a very meaningful research topic. The existence of constraints makes the design of predictive controller for Markov jump system difficult. The design of predictive controller with recursive feasibility and good control performance is a key problem in the study of predictive control for Markov jump systems. The design of constrained predictive controller for Makrov jump system under different conditions is studied. The main contents and results are as follows. For an additive perturbed constrained Markov jump system, an efficient algorithm for solving the maximum allowable set of the system is presented. For Markov jump systems with hard constraints, the design of unconstrained and constrained multistep controllers based on elliptic sets is presented. The recursive feasibility of the algorithm and the mean square stability of closed loop systems are proved. Furthermore, the design of a predictive controller to reduce the amount of on-line calculation is given. For Markov jump systems with hard constraints, in order to overcome the disadvantage that the above algorithm can not deal with asymmetric constraints effectively, a general interpolation method based on the maximum allowable set (polyhedron set) is presented. The design of interpolation predictive controller with linear target and precise constraint processing proves the recursive feasibility of the algorithm and the mean square stability of the closed-loop system. For Markov jump systems with probabilistic soft constraints, the corresponding predictive controllers are designed on the basis of the maximum allowable set. The recursive feasibility of the algorithm and the mean square stability of the closed-loop system are proved. For structured uncertain systems with time-delay modeling as Markov chains, the system is transformed into a standard structured uncertain time-delay Markov jump system by state expansion, and the design of predictive controller is presented. The design of a predictive controller to reduce the amount of calculation on line is also given. The design of robust controller, stochastic controller and predictive controller for Markov jump systems with quasi-periodic characteristics and expected constraints are presented, and the constraint satisfaction and the stability of closed-loop systems are proved.
【学位授予单位】：上海交通大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O211.62;O231

【参考文献】