SGER: Discrete Markov Chain Modeling of Nonlinear Dynamic Systems

主要研究者：Sridhar Ungarala机构：Cleveland State UniversityProposal Number：0433527ResearchThe ability to optimally interact and guide a process towards its specified goals depends on the capacity to observe，model and manipulate the process dynamics as reliably as possible. 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，经常由动态和测量误差的不确定性加剧。 在随机非线性系统中，确定过程状态的概率密度函数是操作任务的核心。 线性和线性化建模技术对要求在宽范围条件下操作的非线性系统造成限制。 因此，大多数现有的概率方法假设线性化的动态和简单的高斯密度函数，往往具有较差的预测能力。 这个探索性研究（SGER）项目将专注于开发从连续空间中的轨迹模型构建离散时间有限状态马尔可夫链模型的方法，该模型将准确地模拟由于任何类型的非线性而导致的任何类型密度的时间演化。 该方法以胞映射和测度理论为基础，其最终目标是为非线性动态系统的概率特征建模提供新的方法，为系统工程中贝叶斯问题的求解提供帮助。 虽然广义贝叶斯解决方案已经有很长一段时间，他们很少适合在非线性系统中实施，由于缺乏概率models.Broad ImpactThe广泛的社会影响在于通过更好地了解非线性过程的潜力，提高美国过程工业的效率。

PI: Sridhar UngaralaInstitution: Cleveland State UniversityProposal Number: 0433527ResearchThe ability to optimally interact and guide a process towards its specified goals depends upon the capacity to observe, model and manipulate the process dynamics as reliably as possible. The nonlinear nature of most chemical processes presents challenging operational problems, frequently compounded by uncertainties in dynamics and errors in measurements. In stochastic nonlinear systems, the determination of a probability density function of the state of a process is central for operations tasks. Linear and linearized techniques of modeling pose limitations for nonlinear systems required to operate over wide ranging conditions. Therefore, most existing probabilistic methods assume linearized dynamics and simple Gaussian density functions, which tend to have poor predictive capability. This Small Grant for Exploratory Research (SGER) project will focus on developing methods that build discrete-time finite-state Markov chain models, from trajectory models in continuous space, which will accurately models the temporal evolution of any type of density due to any type of nonlinearity. The approach is based on cell-to-cell mapping and measure theory.The ultimate goal is to develop new means to model the probabilistic features of nonlinear dynamic systems, which should aid in solving Bayesian problems in systems engineering. While generalized Bayesian solutions have been available for a long time, they are seldom amenable for implementation in nonlinear systems due to the lack of probabilistic models.Broad ImpactThe broad societal impact lies in the potential for improving the efficiency of US process industry through a better understanding of nonlinear processes.