Robust control algorithms for Markovian jumping parameters: application to flexible manufacturing systems

现代控制系统必须满足性能要求，并保持可接受的行为，即使在其动态的突然变化，例如，由于随机组件故障或维修。具有这种行为的系统可以被建模为混合系统，即在连续状态变量上附加一个称为模式或状态的离散随机变量。该模式描述了系统参数的随机跳变和不连续性的发生。马尔可夫跳变系统是一类重要的混合系统，它的模式过程是一个在有限集中取值的连续时间离散状态马尔可夫过程。柔性制造系统（FMS）是这类系统的一个很好的例子，它们构成了目前制造业中技术最先进的生产工具。FMS构成了一个重要的工程和数学挑战，鉴于复杂的功能组合：灵活性，大规模互联系统，随机事件，如机器故障，操作员缺席和波动的市场等，这种困难的组合是我们希望在本研究建议的应用部分，相信FMS系统计划和调度方法的发展可以提高生产率，显著增强加拿大在国际市场上的竞争力。我在本研究计划中的目标是：1。理论：针对存在不确定性的MJS系统（线性、线性时滞、非线性）开发鲁棒控制和估计算法; 2.适用范围：开发鲁棒的生产和维护（校正和预防）调度算法，并提出数值方法来解决相应的最优性条件。利用无穷小扰动分析法估计FMS流量控制问题的最优阈值。适应FMS的自适应控制形式。我在这个研究计划中使用的方法是一个用于控制理论和优化，其中包括确定性和随机最优控制，递阶控制，随机动态规划和博弈论。

Modern control systems must meet performance requirements and maintain acceptable behavior even in the presence of abrupt changes in their dynamic due, for instance, to random component failures or repairs. Sys- tems with this behavior may be modelled as hybrid ones, that is, to the continuous state variable, a discrete random variable called the mode, or regime is appended. The mode describes the random jumps of the system parameters and the occurrence of the discontinuities. One of the most important hybrid class of systems is the one called Markovian jumping systems (MJS), in which the mode-process is a continuous-time discrete-state Markov process taking values in a finite set. Flexible manufacturing systems (FMS) are a good example of this class of systems and they constitute at the present time, the technologically most sophisticated production tool in manufacturing. FMS constitue an important engineering and mathematical challenge in view of a combina- tion of complex features: flexibility, large scale interconnected systems, random events such as machine failu- res, operator absence and fluctuating markets, etc. This combination of difficulties is what we wish to address in the present research proposal for the application part, with the conviction that the development of a systema- tic planning and scheduling methodology for FMS could improve productivity, significantly enhance the com- petitivity of Canada on international markets. My objectives in this research proposal are: 1. Theory: develop robust algorithms for control and estimation for the class of systems with MJS (linear, linear with time delay, nonlinear) in the presence of uncertainties; 2. Application: develop robust production and maintenance (correc- tive and preventive) scheduling algorithms and propose numerical methods to solve the corresponding optimality conditions. Use the infenitesimal perturbation analysis to estimate the optimal threshold value for the flow control problem in FMS. Adapt the formalism of adaptive control for FMS. The methodology I use in this research proposal is the one used in control theory and optimization, which includes deterministic and stochastic optimal control, hierarchical control, stochastic dynamic programming and game theory.