Optimal Nonlinear Estimation and Control - Bayesian Solutions with Markov Chains

摘要：Sridhar Ungarala机构：Cleveland State UniversityProposal Number：0522864题目：Optimal Nonlinear Estimation and Control-Bayesian Solutions with Markov Chains优化交互和引导过程实现其指定目标的能力取决于尽可能可靠地观察、建模和操纵动态的能力。 大多数化学过程的非线性性质提出了具有挑战性的操作问题，并由动态的不确定性和数据中的错误加剧。 线性建模、估计和控制技术对非线性系统在宽范围条件下的运行造成了许多限制。本研究的目的是推进非线性过程系统工程的概率建模，最优状态估计和最优控制问题的贝叶斯解决方案，使用有限状态马尔可夫链。 一个新的和一般的方法将开发建立离散时间有限状态马尔可夫链的轨迹模型在状态空间。 马尔可夫链将模拟随机激励下任何类型的非线性引起的状态概率分布函数的时间演化。从噪声数据中最优估计状态是系统工程中的一项关键任务。现有的方法使用线性高斯假设提出了易于处理的最小二乘优化问题，但不能有效地利用非线性数据。基于卡尔曼滤波器扩展到非线性系统的递归方法往往会由于非高斯PDF的汇总统计量上的递归关系的失败而发散。 一个一般的概率密度为基础的解决方案，称为细胞过滤器，将开发递归贝叶斯估计在离散空间中使用马尔可夫建模方法。通过处理非高斯过程和测量误差、过程约束和非加性误差，单元滤波器将为广泛的一类非线性过程提供最通用的估计策略。非线性最优控制策略将通过在离散空间中提出问题来实现。提出了一种求解非线性优化问题的单元迭代动态规划方法。马尔可夫模型的概率动力学，贝叶斯估计和动态规划相结合，可以有效地解决在线优化的非线性MPC.Intellectual优点：该研究提出了非线性过程系统工程的理解在一个基本的水平。使用pdf作为过程的状态，使用pdf上的线性算子作为过程模型，是状态空间思想的扩展。其优点在于，贝叶斯解决方案不仅推广了现有的方法，但减轻了许多与传统的非线性优化的解决方案相关联的实际困难。这些想法与初步的模拟结果，这将铺平道路的示范真实的过程。一个CSTR的案例研究表明，在所有三个领域的方法是更准确的比现有的方法和计算负荷是合理的低到中等dimensions.Broad影响：先进的非线性过程操作将被纳入先进的控制和数学选修课程。与自动化行业的合作将迅速将成果付诸实践。维护一个用于并行计算的Linux集群可以改进组织的计算基础设施。广泛的社会影响来自贝叶斯方法的应用，以提高美国过程工业的效率。最近贝叶斯方法在金融、制药和软件领域的商业成功表明了这一计划的及时性。

ABSTRACTPI: Sridhar Ungarala Institution: Cleveland State UniversityProposal Number: 0522864Title: Optimal Nonlinear Estimation and Control - Bayesian Solutions with Markov ChainsThe ability to optimally interact and guide a process towards its specified goals depends upon the capacity to observe, model and manipulate the dynamics as reliably as possible. The nonlinear nature of most chemical processes presents challenging operational problems, compounded by uncertainties in dynamics and errors in data. Linear techniques of modeling, estimation and control pose many limitations for nonlinear systems operating over wide ranging conditions. This research aims to advance nonlinear process systems engineering by formulating Bayesian solutions to problems in probabilistic modeling, optimal state estimation and optimal control with the use of finite state Markov chains. A new and general methodology will be developed to build discrete-time finite-state Markov chains from trajectory models in state space. The Markov chain will model the temporal evolution of state pdfs due to any type of nonlinearity under stochastic excitation.Optimal estimation of states from noisy data is a critical task in systems engineering. Existing methods use linear-Gaussian assumptions to pose tractable least squares optimization problems, but fail to utilize the nonlinear data efficiently. Recursive methods based on extensions of the Kalman filter to nonlinear systems tend to diverge due to the failure of recursive relationships on the summary statistics of non-Gaussian pdfs. A general probability density based solution, called the cell filter, will be developed for recursive Bayesian estimation using the Markov modeling approach in discrete space. By handling non-Gaussian process and measurement errors, process constraints and non-additive errors, the cell filter will provide the most general estimation strategy for a wide class of nonlinear processes. Nonlinear optimal control strategies will be developed by posing the problem in discrete space. A novel cell iterative dynamic programming approach is proposed for nonlinear optimization. The combination of Markov models of probabilistic dynamics, Bayesian estimation and dynamic programming can efficiently solve online optimization for nonlinear MPC.Intellectual Merit: The research advances the understanding of nonlinear process systems engineering at a fundamental level. The use of the pdf as the state of a process and linear operators on pdfs as process models is an extension of state space thinking. The merit lies in the fact that the Bayesian solutions not only generalize existing methods, but alleviate many of the practical difficulties associated with traditional nonlinear optimization based solutions. These ideas are substantiated with preliminary simulation results, which will pave the way for demonstrations on real processes. A CSTR case study shows that the methodology in all three areas is more accurate than existing methods and the computational load is reasonable for low to moderate dimensional systems.Broad Impact: Advanced in nonlinear process operations will be incorporated in elective courses in advanced control and mathematics. Collaborations with the automation industry will quickly bring the results into practice. Maintaining a Linux cluster for parallel computing improves the computational infrastructure of the organization. The broad societal impact comes from the application of Bayesian methods for improving the efficiency of US process industry. Recent commercial successes of the Bayesian approach in financial, pharmaceutical and software fields indicate the timeliness of this plan.