TY - JOUR
T1 - Second-Order Switching Time Optimization for Switched Dynamical Systems
AU - Stellato, Bartolomeo
AU - Ober-Blöbaum, Sina
AU - Goulart, Paul J.
N1 - Funding Information:
Manuscript received January 31, 2017; accepted April 10, 2017. Date of publication April 24, 2017; date of current version September 25, 2017. This work was supported by the People Programme (Marie Curie Actions) of the European Unions Seventh Framework Programme (FP7/2007-2013) under REA Grant Agreement 607957 (TEMPO). Recommended by Associate Editor Z. Sun. (Corresponding author: Bartolomeo Stellato.) The authors are with the University of Oxford, Oxford OX1 3PJ, U.K. (e-mail: bartolomeo.stellato@eng.ox.ac.uk; sina.ober-blobaum@ eng.ox.ac.uk; paul.goulart@eng.ox.ac.uk).
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2017/10
Y1 - 2017/10
N2 - Switching time optimization arises in finite-horizon optimal control for switched systems where, given a sequence of continuous dynamics, one minimizes a cost function with respect to the switching times. We propose an efficient method for computing the optimal switching times for switched linear and nonlinear systems. A novel second-order optimization algorithm is introduced where, at each iteration, the dynamics are linearized over an underlying time grid to compute the cost function, the gradient, and the Hessian efficiently. With the proposed method, the most expensive operations at each iteration are shared between the cost function and its derivatives, thereby greatly reducing the computational burden. We have implemented the algorithm in the Julia package SwitchTimeOpt, allowing users to easily solve switching time optimization problems. In the case of linear dynamics, many operations can be further simplified and benchmarks show that our approach is able to provide optimal solutions in just a few millisecond. In the case of nonlinear dynamics, our method provides optimal solutions with up to two orders of magnitude time reductions over state-of-the-art approaches.
AB - Switching time optimization arises in finite-horizon optimal control for switched systems where, given a sequence of continuous dynamics, one minimizes a cost function with respect to the switching times. We propose an efficient method for computing the optimal switching times for switched linear and nonlinear systems. A novel second-order optimization algorithm is introduced where, at each iteration, the dynamics are linearized over an underlying time grid to compute the cost function, the gradient, and the Hessian efficiently. With the proposed method, the most expensive operations at each iteration are shared between the cost function and its derivatives, thereby greatly reducing the computational burden. We have implemented the algorithm in the Julia package SwitchTimeOpt, allowing users to easily solve switching time optimization problems. In the case of linear dynamics, many operations can be further simplified and benchmarks show that our approach is able to provide optimal solutions in just a few millisecond. In the case of nonlinear dynamics, our method provides optimal solutions with up to two orders of magnitude time reductions over state-of-the-art approaches.
KW - Hybrid systems
KW - optimal control
KW - optimal switching times
KW - optimization algorithms
KW - switched systems
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U2 - 10.1109/TAC.2017.2697681
DO - 10.1109/TAC.2017.2697681
M3 - Article
AN - SCOPUS:85031028617
SN - 0018-9286
VL - 62
SP - 5407
EP - 5414
JO - IRE Transactions on Automatic Control
JF - IRE Transactions on Automatic Control
IS - 10
M1 - 7908990
ER -