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Robust Self-Tuning Control Design under Probabilistic Uncertainty using Polynomial Chaos Expansion-based Markov Models

机译：基于多项式混沌扩展的马尔可夫模型的概率不确定性鲁棒自调整控制设计

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摘要

A robust adaptive controller is developed for a chemical process using a generalized Polynomial Chaos (gPC) expansion-based Markov decision model, which can account for time-invariant probabilistic uncertainty and overcome computational challenge for building Markov models. To calculate the transition probability, a gPC model is used to iteratively predict probability density functions (PDFs) of system’s states including controlled and manipulated variables. For controller tuning, these PDFs and controller parameters are discretized to a finite number of discrete states for building a Markov model. The key idea is to predict the transition probability of controlled and manipulated variables over a finite future control horizon, which can be further used to calculate an optimal sequence of control actions. This approach can be used to optimally tune a controller for set point tracking within a finite future control horizon. The proposed method is illustrated by a continuous stirred tank reactor (CSTR) system with stochastic perturbations in the inlet concentration. The efficiency of the proposed algorithm is quantified in terms of control performance and transient decay.
机译：使用基于广义多项式混沌（gPC）展开的马尔可夫决策模型为化学过程开发了鲁棒的自适应控制器，该控制器可解决时不变概率不确定性并克服了构建马尔可夫模型的计算难题。为了计算转移概率，使用gPC模型来迭代预测系统状态（包括受控变量和受控变量）的概率密度函数（PDF）。对于控制器调整，这些PDF和控制器参数被离散化为有限数量的离散状态，以建立马尔可夫模型。关键思想是预测有限的未来控制范围内受控变量和受控变量的转移概率，该概率可以进一步用于计算最佳的控制动作序列。该方法可用于在有限的未来控制范围内优化控制器的设置点跟踪。连续搅拌釜反应器（CSTR）系统在入口浓度中具有随机扰动，说明了所提出的方法。所提出算法的效率通过控制性能和瞬态衰减进行量化。

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