Blatt, M.; Schittkowski, K. Optimal control of one-dimensional partial differential algebraic equations with applications. (English) Zbl 0977.49001 Ann. Oper. Res. 98, 45-64 (2000). Summary: We present an approach to compute optimal control functions in dynamic models based on one-dimensional partial differential algebraic equations (PDAE). By using the method of lines, the PDAE is transformed into a large system of usually stiff ordinary differential algebraic equations and integrated by standard methods. The resulting nonlinear programming problem is solved by the sequential quadratic programming code NLPQL. Optimal control functions are approximated by piecewise constant, piecewise linear or bang-bang functions. Three different types of cost functions can be formulated. The underlying model structure is quite flexible. We allow break points for model changes, disjoint integration areas with respect to spatial variable, arbitrary boundary and transition conditions, coupled ordinary and algebraic differential equations, algebraic equations in time and space variables, and dynamic constraints for control and state variables. The PDAE is discretized by difference formulae, polynomial approximations with arbitrary degrees, and by special update formulae in case of hyperbolic equations. Two application problems are outlined in detail. We present a model for optimal control of transdermal diffusion of drugs, where the diffusion speed is controlled by an electric field, and a model for the optimal control of the input feed of an acetylene reactor given in form of a distributed parameter system. Cited in 2 Documents MSC: 49J20 Existence theories for optimal control problems involving partial differential equations 93C20 Control/observation systems governed by partial differential equations 65K05 Numerical mathematical programming methods 65M20 Method of lines for initial value and initial-boundary value problems involving PDEs 90C30 Nonlinear programming Keywords:optimal control; partial differential equations; numerical methods; transdermal systems; acetylene reactors Software:PDEFIT; PCOMP; NLPQLP PDFBibTeX XMLCite \textit{M. Blatt} and \textit{K. Schittkowski}, Ann. Oper. Res. 98, 45--64 (2000; Zbl 0977.49001) Full Text: DOI