On reducing the number of decision variables for dynamic optimization

This paper presents an input parameterization for dynamic optimization that allows reducing the number of decision variables compared to traditional direct methods. A small number of decision variables is likely to be beneficial for various applications such as global optimization and real-time optimization in the presence of plant-model mismatch. The procedure consists of three steps: (i) adjoint-free optimal control laws are computed for all arc types that may be present in the solution, and a finite set of plausible arc sequences is postulated; (ii) the sensitivity-seeking arcs are either described by analytical control laws or approximated by cubic splines, which results in a parsimonious input parameterization that represents the optimal inputs using only a few parameters, namely, switching times and initial conditions for the sensitivity-seeking arcs; and (iii) for each arc sequence, optimal parameter values are computed via numerical optimization, and the sequence with the best cost is optimal. The procedure is illustrated via the simulated examples of a semibatch reactor and a distillation column.