Optimal and Robust Operations of Complex Processes withNon-Gaussian Distributed Uncertain Variables under ChanceConstraints - Extension to Model Predictive Control of Parabolic Partial Differential Equation Systems

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Many engineering processes are modeled by partial differential equations (PDEs) with uncertainties both in model parameters and in operating conditions. Optimization of constrained PDEs under uncertainties remains a challenge due to its mathematical and numerical complexity.Optimization of stochastic PDE systems where chance constraints are to be imposed on spatially distributed output variables has not been properly investigated until now. The objective of this proposed project is to develop efficient approaches to chance constrained optimization of PDE systems with Gaussian and non-Gaussian distributed uncertainties. The firstchallenging task is to appropriately describe spatially distributed output variables through the input uncertainties. Consistent with chance constraints, proper sets of orthogonal polynomials will be constructed for the expansion of the constrained output variables into infinite sums.Dimension reduction strategies will be investigated to truncate the infinite dimensionality of the stochastic PDE model. The second target is to develop mathematical and numerical methods for efficient computation of chance constraints of the PDE systems. Multidimensional sparsegrid techniques will be developed for deterministic transformation of stochastic PDEs as well as for efficiently computing high-dimensional integrals of chance constraints and their gradients.In general, the evaluation of spatially distributed chance constraints poses enormous difficulties. Hence, we will design a tractable and monotonic analytic approximation for chance constraints which guarantees a priori feasibility. In order ameliorate computational burdens suitable strategiesfor parallel computing will be developed and implemented. The overall theoretical and numerical development will be demonstrated through case studies on optimization of thermodynamic processes with endogenous and exogenous uncertainties.