Optimal Nonlinear Estimation and Control - Bayesian Solutions with Markov Chains

摘要：Sridhar Ungarala研究所：克利夫兰州立大学提案编号：0522864标题：最优非线性估计和控制-带有马尔可夫链的贝叶斯解决方案能否以最佳方式交互并引导过程朝着其指定目标前进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特性带来了具有挑战性的操作问题，再加上动力学上的不确定性和数据上的错误。线性建模、估计和控制技术对运行在大范围条件下的非线性系统提出了许多限制。这项研究的目的是利用有限状态马尔可夫链对概率建模、最优状态估计和最优控制中的问题建立贝叶斯解决方案，从而推动非线性过程系统工程的发展。从状态空间的轨迹模型出发，提出了一种新的、通用的方法来构造离散时间有限状态马尔可夫链。在随机激励下，马尔可夫链可以模拟任意类型的非线性状态pdf的时间演化过程。现有的方法使用线性-高斯假设来提出容易处理的最小二乘优化问题，但不能有效地利用非线性数据。基于卡尔曼滤波扩展到非线性系统的递归方法由于非高斯pdf汇总统计量的递归关系的失败而倾向于发散。使用离散空间中的马尔可夫建模方法，将为递归贝叶斯估计开发一种基于概率密度的通用解决方案，称为单元过滤器。通过处理非高斯过程和测量误差、过程约束和非加性误差，单元滤波器将为一大类非线性过程提供最一般的估计策略。通过在离散空间中提出该问题，可以得到非线性最优控制策略。提出了一种新的求解非线性优化问题的元胞迭代动态规划方法。将概率动力学的马尔可夫模型、贝叶斯估计和动态规划相结合，可以有效地解决非线性过程主控问题的在线优化问题。使用pdf作为进程的状态，使用pdf上的线性运算符作为进程模型，是状态空间思想的扩展。其优点在于，贝叶斯解不仅推广了现有的方法，而且缓解了与传统的基于非线性优化的解相关的许多实际困难。这些想法得到了初步的模拟结果的证实，这将为实际过程的演示铺平道路。CSTR的案例研究表明，这三个领域的方法都比现有的方法更准确，对于中低维系统，计算量是合理的。广泛的影响：高级非线性过程操作将被纳入高级控制和数学的选修课。与自动化行业的合作将很快将结果付诸实践。维护用于并行计算的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，以提高美国流程工业的效率。贝叶斯方法最近在金融、制药和软件领域取得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.