A Technique for the Direct Optimization of Dynamic Systems Described by Differential-Algebraic Equations

Abstract

This paper presents a method for the optimization of dynamic systems described by index-1 differential-algebraic equations (DAE). The class of problems addressed include optimal control problems and parameter identification problems. Here, the controls are parameterized using piecewise constant inputs on a grid in the time interval of interest. In addition, the differential-algebraic equations are approximated using a Rosenbrock-Wanner (ROW) method. In this way the infinite dimensional optimal control problem is transformed into a finite dimensional nonlinear programming problem (NLP). The NLP is solved using a sequential quadratic programming technique. The paper shows that the ROW method discretization of the DAE leads to (i) a relatively small NLP problem, and (ii) an efficient technique for evaluation the function, constraints and gradients associated with the NLP problem. The paper also investigates a state mesh refinement technique that ensures a sufficiently accurate representation of the optimal state trajectory. Two nontrivial examples are used to illustrate the effectiveness of the proposed method.