SGER: Discrete Markov Chain Modeling of Nonlinear Dynamic Systems

Cleveland State University, Cleveland OH

Investigators

Abstract

PI: Sridhar Ungarala Institution: Cleveland State University Proposal Number: 0433527 Research The 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 Impact The broad societal impact lies in the potential for improving the efficiency of US process industry through a better understanding of nonlinear processes.