Design of a General-Purpose Optimal Controller via the hp-Radau Collocation Method

The design of a controller is a considerable investment in any engineering project, and the ability to reuse a general-purpose controller represents a significant time- and cost-saving measure. This paper outlines the design of a system-independent optimal controller using the \textit{hp}-Radau collocation method. Given an arbitrary set of system dynamics and constraints, the controller can rapidly generate the optimal trajectory for the system with great accuracy. The theory behind classic optimal control is given, followed by a discussion of modern pseudospectral collocation methods used to solve optimal control problems numerically. The design of a software using these techniques in MATLAB is then outlined. Finally, this software is used to simulate the control of several dynamical systems - including the Bryson-Denham problem and a robotic arm - in order to demonstrate its efficacy.