Solving optimal control problems using hp-version finite elements in time

A previously published temporal finite element method for optimal control p roblems is updated to include higher-order hierarchical shape functions. Th e accuracy and power of the analysis and corresponding code are illustrated on optimal control problems with nonlinear system dynamics, using interfac es based on symbolic mathematics to automatically generate the necessary de rivative expressions and nonlinear algebraic equations to be solved. The cl ass of problems includes those that can have free or fixed final time, mult iple phases, nonlinear/periodic boundary conditions, and control constraint s. This code has been tested on a variety of problems, culminating in a thr ee-phase, seven-state, two-control missile problem with nonlinear system dy namics, where accuracy was found to be significantly improved over h-versio n results, with potential order-of-magnitude reductions in CPU time and num bers of parameters for a given level of error.