Solving Optimal Control Problems using Simscape Models for State Derivatives

This technical report outlines an approach to calculate derivative functions for Simscape models and use them to solve optimal control problems. Although this approach is less efficient than analytic expression for the derivatives, not every problem will have these directly available due to a variety of reasons, including multidomain, multibody, large-scale, automatically generated, or proprietary models. A step-by-step procedure is presented to assist utilizing this approach. The canonical BrysonDenham state-constrained double integrator optimal control problem is used as a test optimal control problem. A number of control formulations are compared to demonstrate the computational expense of this approach compared to analytic expressions of the state derivatives and additional benefits including improved final solutions and execution time over more traditional formulations. In particular, direct transcription solutions are decidedly more efficient than the common shooting approach. Coupled with an optimal control toolbox, the user will no longer need to worry about expressing complex derivative equations or the implementation details of their optimal control problem, allowing the focus to be shifted towards solving more complex problems. ∗Ph.D pre-candidate in Systems and Entrepreneurial Engineering, Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, [email protected] ©2014 Daniel R. Herber