Optimal control approach for nonlinear chemical processes with uncertainty and application to a continuous stirred-tank reactor problem

Abstract

Practical chemical process is usually a dynamic process including uncertainty. Stochastic constraints can be used to chemical process modeling, where constraints cannot be strictly satisfied or need not be fully satisfied. Thus, optimal control of nonlinear systems with stochastic constraints can be available to address practical nonlinear chemical process problems. This problem is hard to cope with due to the stochastic constraints. By introducing a novel smooth and differentiable approximation function, an approximation-based approach is proposed to address this issue, where the stochastic constraints are replaced by some deterministic ones. Following that, the stochastic constrained optimal control problem is converted into a deterministic parametric optimization problem. Convergence results show that the approximation function and the corresponding feasible set converge uniformly to that of the original problem. Then, the optimal solution of the deterministic parametric optimization problem is guaranteed to converge uniformly to the optimal solution of the original problem. Following that, a computation approach is proposed for solving the original problem. Numerical results, obtained from a nonlinear continuous stirred-tank reactor problem including stochastic constraints, show that the proposed approach is less conservative compared with the existing typical methods and can obtain a stable and robust performance when considering the small perturbations in initial system state.