A Splitting Method for Optimal Control

Brendan O'Donoghue, Giorgos Stathopoulos, Stephen P. Boyd

Abstract: We apply an operator splitting technique to a generic linear-convex optimal control problem, which results in an algorithm that alternates between solving a quadratic control problem, for which there are efficient methods, and solving a set of single-period optimization problems, which can be done in parallel, and often have analytical solutions. In many cases, the resulting algorithm is division-free (after some off-line pre-computations) and can be implemented in fixed-point arithmetic, for example on a field-programmable gate array (FPGA). We demonstrate the method on several examples from different application areas.