A tutorial for applying DMOC to solve optimization control problems

This paper presents a detailed procedure to apply newly-proposed DMOC (Discrete Mechanics and Optimal Control) methodology to solve optimal control problems. DMOC is based on a direct discretization of Lagrange-d´Alembert principle for a system. First, this tutorial explains the principle of DMOC, and how to formulate the problem in DMOC. Next the steps are shown about how to install and configure nonlinear programming solver IPOPT, and how to use the modeling language AMPL. In particular, the user-defined function is involved with AMPL to solve a more complicated problem. Furthermore, a glider example is provided in this tutorial to solve optimal control problem with the user-defined 2D time-varying B-spline ocean current model. The ocean current original data was collected by HF-Radar stations located around Monterey Bay, CA in August 2000. Practically, this tutorial is shown how to use DMOC to solve optimal control problems with IPOPT and AMPL as the components. The possible users are robotic researchers, control system engineers, operations management researchers, and so on.