Hybrid stochastic optimization method for optimal control problems of chemical processes

In the paper, the optimal control problem of chemical process systems is considered. In general, it is very difficult to solve this problem analytically due to its nonlinear nature and the existence of control input constraints. To obtain the numerical solution, based on the time scaling transformation technology and the control parameterization method, the problem is transformed into a parameter optimization problem with some variable bounds, which can be efficiently solved using the improved conjugate gradient algorithm developed by us. However, in spite of the improved conjugate gradient algorithm is very efficient for local search, the solution obtained is usually a local extremum for non-convex optimal control problems. In order to escape from the local extremum, a novel stochastic search method is developed. A large number of numerical experiments show that the novel stochastic search method is excellent in exploration, while bad in exploitation. In order to improve the exploitation, we propose a hybrid stochastic optimization approach to solve the problem based on the novel stochastic search method and the improved conjugate gradient algorithm. Convergence results indicate that any global optimal solution of the approximate problem is also a global optimal solution of the original problem. Finally, four chemical process system optimal control problems illustrate that the hybrid numerical optimization algorithm proposed by us is low CPU time and obtains a better cost function value than the existing approaches. (C) 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.