SGER: Discrete Markov Chain Modeling of Nonlinear Dynamic Systems

PI: Sridhar ungaralinstitution: Cleveland State university提案编号：0433527 research最佳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，建模和操纵过程动态的能力。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，经常与动力学的不确定性和测量误差相结合。在随机非线性系统中，过程状态的概率密度函数的确定是操作任务的核心。线性和线性化建模技术对需要在大范围条件下运行的非线性系统提出了限制。因此，现有的概率方法大多采用线性化动力学和简单的高斯密度函数，预测能力较差。这个探索性研究（SGER）项目将专注于开发从连续空间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变。该方法基于细胞间映射和测量理论。最终目标是开发新的方法来模拟非线性动态系统的概率特征，这将有助于解决系统工程中的贝叶斯问题。虽然广义贝叶斯解已经存在了很长时间，但由于缺乏概率模型，它们很少适用于非线性系统的实现。广泛的影响广泛的社会影响在于通过更好地理解非线性过程来提高美国过程工业效率的潜力。

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.