Dynamic optimization of constrained chemical-engineering problems using dynamic-programming

In many chemical engineering process control applications, one frequently encounters differential-algebraic optimization problems. Such optimal control problems are difficult to solve, in general, because of the presence of singular arcs for systems whose Hamiltonian is linear with respect to the control variable. The authors propose the use of absolute error penalty functions in handling constrained optimal control problems in chemical engineering by posing the problem as a nonsmooth dynamic optimization problem. They show that iterative dynamic programming (IDP) is a very useful technique for solving constrained dynamic optimization problems without unduly increasing the dimension of the system or the computational burden. A move suppression criterion has been incorporated into the IDP algorithm in order to penalize excessive control moves. To show the efficacy of the method, an analytical (exact) solution of a simple problem is obtained using least squares control theory and compared with results obtained using IDP. Results obtained for other seemingly difficult optimal control problems in chemical enigneering compare very favorably with those reported in the optimization and optimal control literature.