Real-Time Iterations for Nonlinear Optimal Feedback Control

An efficient Newton-type scheme for the approximate on-line solution of optimization problems as they occur in optimal feedback control is presented. The scheme allows a fast reaction to disturbances by delivering approximations of the exact optimal feedback control which are iteratively refined during the runtime of the controlled process. The approximation errors of this real-time iteration scheme can be bounded and the solution contracts towards the optimal feedback control. The robustness and excellent real-time performance of the method is demonstrated in a numerical experiment, the control of an unstable system, namely an airborne kite that shall fly loops. This paper is a short version of an article that appeared recently in the SIAM Journal on Control and Optimization [1].