Reliable Solution to Dynamic Optimization Problems using Integrated Residual Regularized Direct Collocation

Abstract: Direct collocation is a widely used method for solving dynamic optimization problems (DOPs), but its implementation simplicity and computational efficiency are limited for challenging problems like those involving singular arcs. In this paper, we introduce the direct transcription method of integrated residual regularized direct collocation (IRR-DC). This method enforces dynamic constraints through a combination of explicit constraints and penalty terms within discretized DOPs. This method retains the implementation simplicity of direct collocation while significantly improving both solution accuracy and efficiency, particularly for challenging problem types. Through the examples, we demonstrate that for difficult problems where traditional direct collocation results in excessive fluctuations or large errors between collocation points, IRR-DC effectively suppresses oscillations and yields solutions with greater accuracy (several magnitudes lower in various error metrics) compared to other regularization alternatives.