A hybrid evolutionary direct search technique for solving Optimal Control problems

Abstract

An Optimal Control is a set of differential equations describing the path of the control variables that minimize the cost functional (function of both state and control variables). Direct solution methods for optimal control problems treat them from the perspective of global optimization: perform a global search for the control function that optimizes the required objective. Invasive Weed Optimization (IWO) technique is used here for optimal control. However, the direct solution method operates on discrete n-dimensional vectors, not on continuous functions, and becomes computationally unmanageable for large values of n. Thus, a parameterization technique is required, which can represent control functions using a small number of real-valued parameters. Typically, direct methods using evolutionary techniques parameterize control functions with a piecewise constant approximation. This has obvious limitations, both for accuracy in representing arbitrary functions, and for optimization efficiency. In this paper a new parameterization is introduced, using Bézier curves, which can accurately represent continuous control functions with only a few parameters. It is combined with Invasive Weed Optimization into a new evolutionary direct method for optimal control. The effectiveness of the new method is demonstrated by solving a wide range of optimal control problems.