A Splitting Method for Optimal Control

B. O'Donoghue, G. Stathopoulos, and S. Boyd

IEEE Transactions on Control Systems Technology, 21(6):2432-2442, November 2013.

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 so 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.