A Real-Time Iteration Scheme for Nonlinear Optimization in Optimal Feedback Control

Authors

Moritz Diehl, Hans Georg Bock, Johannes P. Schloeder

Year

2005

Journal Paper

Algorithm

Real-Time Iteration

Source

SIAM Journal on Control and Optimization

Identifiers

DOI 10.1137/S0363012902400713

Abstract¶

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 contractivity of this real-time iteration scheme is proven, and a bound on the loss of optimality - compared with the theoretical optimal solution - is given. 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.

Summary¶

This paper establishes the real-time iteration scheme for nonlinear optimal feedback control: one Newton/SQP-type update is performed per sampling instant while previous iterates warm-start the next online problem. It gives the key contractivity and optimality-loss results that justify RTI-based NMPC, and demonstrates the method on the now-classic airborne-kite benchmark.