Multiple-shooting strategy for Optimal Control System Design of Differential-Algebraic equations systems

Optimal design and operation of complex chemical processes often require the solution of intricate dynamic optimization problems. Dynamic process optimization has become increasingly important in this context over the past decade, because there has been a renaissance of batch processes (e.g. in the still emerging field of biochemical engineering), and even for processes which are normally operated at steady-state, process dynamics must now be taken into account quite frequently (e.g. in order to satisfy specific requirements during start-up or shut-down operations). Dynamic processes are normally modeled via ordinary (ODE) or differential-algebraic (DAE) equations systems, and to more complicated (partial-) integro-differential equations. The objective of this paper is to investigate the performance of a particular branch of dynamic optimization method, namely, multiple shooting via MATLAB. Using a case study of a simple batch reactor process, the off-line fixed horizon dynamic optimization via multiple-shooting strategy is carried out using MATLAB ODE solver and optimization routine. The MATLAB performance is benchmarked against the commercial software g-PROMS. It is found that the multiple-shooting strategy is fairly robust to different initial guesses with increasing number of intervals specified. However, the convergence time is highly dependent on the initial guesses and the number of intervals selected. In general, MATLAB takes more than 300 times longer to converge to the same optimal solution compared to g-PROMS.