Dynamic optimization of stochastic systems using in situ adaptive tabulation

The problem of efficient formulations for the optimization of stochastic dynamical systems modeled by timestep-per based descriptions is investigated. The issue of computational requirements for the system evolution is circumvented by extending the notion of in situ adaptive tabulation to stochastic systems. Conditions are outlined that allow unbiased estimation of the mapping gradient matrix and, subsequently, expressions to compute the ellipsoid of attraction are derived. The proposed approach is applied towards the solution of dynamic optimization problems for a bistable reacting system describing catalytic oxidation of CO and an illustrative homogeneous chemically reacting system describing dimerization of a monomer. The dynamic evolution of both systems is modeled using kinetic Monte Carlo simulations. In both cases, tabulation resulted in significant reduction in the solution time of the optimization problem