TY - JOUR
T1 - Guaranteeing Constraints of Disturbed Nonlinear Systems Using Set-Based Optimal Control in Generator Space
AU - Schürmann, Bastian
AU - Althoff, Matthias
N1 - Publisher Copyright:
© 2017
PY - 2017/7
Y1 - 2017/7
N2 - We address the problem of finding an optimal solution for a nonlinear system for a set of initial states rather than just for a single initial state. In addition, we consider state and input constraints as well as a set of possible disturbances. While previous optimal control techniques typically ignore the fact that the current state of a system is not exactly known, future safety-critical systems demand that all uncertainties including the initial state are considered; this is required for e.g. automated vehicles, surgical robots, or human-robot interaction. We present a new method that obtains optimal control inputs by finding optimal weights for generators that span the space reachable by the considered system. This solution routine can be used not only for a single initial state but also for a set of initial states - this is not possible using classical optimization techniques. We ensure that all constraints are met by using reachability analysis, which provides formal bounds for all possible system trajectories. We demonstrate the applicability of our approach with an example from automated driving; for this example, the result is obtained within a few seconds and outperforms a classical LQR approach.
AB - We address the problem of finding an optimal solution for a nonlinear system for a set of initial states rather than just for a single initial state. In addition, we consider state and input constraints as well as a set of possible disturbances. While previous optimal control techniques typically ignore the fact that the current state of a system is not exactly known, future safety-critical systems demand that all uncertainties including the initial state are considered; this is required for e.g. automated vehicles, surgical robots, or human-robot interaction. We present a new method that obtains optimal control inputs by finding optimal weights for generators that span the space reachable by the considered system. This solution routine can be used not only for a single initial state but also for a set of initial states - this is not possible using classical optimization techniques. We ensure that all constraints are met by using reachability analysis, which provides formal bounds for all possible system trajectories. We demonstrate the applicability of our approach with an example from automated driving; for this example, the result is obtained within a few seconds and outperforms a classical LQR approach.
KW - Control of Constrained Systems
KW - Nonlinear Control
KW - Optimal Control
KW - Reach-Avoid Problems
KW - Reachability Analysis
KW - Robust Control
KW - Zonotopes
UR - http://www.scopus.com/inward/record.url?scp=85027060763&partnerID=8YFLogxK
U2 - 10.1016/j.ifacol.2017.08.1617
DO - 10.1016/j.ifacol.2017.08.1617
M3 - Article
AN - SCOPUS:85027060763
SN - 1474-6670
VL - 50
SP - 11515
EP - 11522
JO - IFAC Proceedings Volumes (IFAC-PapersOnline)
JF - IFAC Proceedings Volumes (IFAC-PapersOnline)
IS - 1
ER -