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

By Moritz Diehl, Hans Georg Bock, Johannes P. Schlöder. SIAM Journal of Control and Optimization, 2005

614 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/05644bba98565e0c493b88eb80c35743e3dbd670

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Citations in the corpus

Incorporating a class of constraints into the dynamics of optimal control problems (2009, methodology): “Current research concerns the application of the proposed methodology to real-time trajectory optimization, in particular in the context of real-time iteration schemes [25].”
Viability and predictive control for safe locomotion (2008, positive): “Of course, more complex models means more computational demands, but there exist extremely fast numerical algorithms for solving Nonlinear MPC problems [6], and the increase in computations is in no way comparable to what appears with brute force approaches.”
An auto-generated real-time iteration algorithm for nonlinear MPC in the microsecond range (2011, background): “Note that for the above real-time iteration scheme, local asymptotic closed-loop stability can be guaranteed assuming suitable end weights in combination with other regularity conditions [11,12,15].”
The advanced-step NMPC controller: Optimality, stability and robustness (2009, background): “Under mild conditions, if the sensitivity approximation is used to warm-start the next problem, the background problem can be converged in a few iterations (Diehl et al., 2005).”
Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation (2009, background): “Error bounds and closed loop stability of the scheme have been established for shrinking horizon problems in [15] and for NMPC with shifted and non-shifted initializations in [18] and [17].”
Fast Direct Multiple Shooting Algorithms for Optimal Robot Control (2005, background): “The scheme’s theoretical contraction properties have been investigated in [21] for the variant described in this paper, and in [22, 19] for other variants.”
From linear to nonlinear MPC: bridging the gap via the real-time iteration (2020, methodology): “One of the most successful and largely used approaches to fast NMPC is arguably based on the Real-Time Iteration (RTI) [13] and its predecessors [35, 38].”
Optimization‐based autonomous racing of 1:43 scale RC cars (2015, background): “Hence the convergence properties that are known for the real-time iteration [29] hold also for the MPCC problem (13).”
Whole-Body Nonlinear Model Predictive Control Through Contacts for Quadrupeds (2017, positive): “Furthermore, it allows to separate the algorithm into a feedback and a preparation phase [29], which helps to minimize the latency between state-measurement and control policy update.”