Rapid Solution of Optimal Control Problems by a Functional Spreadsheet Paradigm: A Practical Method for the Non-Programmer

Abstract

We devise a practical and systematic spreadsheet solution paradigm for general optimal control problems. The paradigm is based on an adaptation of a partial-parametrization direct solution method which preserves the original mathematical optimization statement, but transforms it into a simplified nonlinear programming problem (NLP) suitable for Excel NLP solver. A rapid solution strategy is implemented by a tiered arrangement of pure elementary calculus functions in conjunction with Excel NLP solver. With the aid of the calculus functions, a cost index and constraints are represented by equivalent formulas that fully encapsulate an underlining parametrized dynamical system. Excel NLP solver is then employed to minimize (or maximize) the cost index formula, by varying decision parameters, subject to the constraints formulas. The paradigm is demonstrated for several fixed and free-time nonlinear optimal control problems involving integral and implicit dynamic constraints with direct comparison to published results obtained by fundamentally different methods. Practically, applying the paradigm involves no more than defining a few formulas using basic Excel spreadsheet skills.