TY - JOUR
T1 - A Framework for Time-Consistent, Risk-Sensitive Model Predictive Control
T2 - Theory and Algorithms
AU - Singh, Sumeet
AU - Chow, Yinlam
AU - Majumdar, Anirudha
AU - Pavone, Marco
N1 - Funding Information:
Manuscript received April 26, 2018; accepted September 3, 2018. Date of publication October 8, 2018; date of current version June 26, 2019. This work was supported by Office of Naval Research under the Science of Autonomy Program under Contract N00014-15-1-2673. Recommended by Associate Editor Mazen Alamir. (Corresponding author: Sumeet Singh.) S. Singh and M. Pavone are with the Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305 USA (e-mail:, ssingh19@stanford.edu; pavone@stanford.edu).
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2019/7
Y1 - 2019/7
N2 - In this paper, we present a framework for risk-sensitive model predictive control (MPC) of linear systems affected by stochastic multiplicative uncertainty. Our key innovation is to consider a time-consistent, dynamic risk evaluation of the cumulative cost as the objective function to be minimized. This framework is axiomatically justified in terms of time-consistency of risk assessments, is amenable to dynamic optimization, and is unifying in the sense that it captures a full range of risk preferences from risk neutral (i.e., expectation) to worst case. Within this framework, we propose and analyze an online risk-sensitive MPC algorithm that is provably stabilizing. Furthermore, by exploiting the dual representation of time-consistent, dynamic risk measures, we cast the computation of the MPC control law as a convex optimization problem amenable to real-Time implementation. Simulation results are presented and discussed.
AB - In this paper, we present a framework for risk-sensitive model predictive control (MPC) of linear systems affected by stochastic multiplicative uncertainty. Our key innovation is to consider a time-consistent, dynamic risk evaluation of the cumulative cost as the objective function to be minimized. This framework is axiomatically justified in terms of time-consistency of risk assessments, is amenable to dynamic optimization, and is unifying in the sense that it captures a full range of risk preferences from risk neutral (i.e., expectation) to worst case. Within this framework, we propose and analyze an online risk-sensitive MPC algorithm that is provably stabilizing. Furthermore, by exploiting the dual representation of time-consistent, dynamic risk measures, we cast the computation of the MPC control law as a convex optimization problem amenable to real-Time implementation. Simulation results are presented and discussed.
KW - Markov processes
KW - optimization
KW - predictive control
KW - risk analysis
UR - http://www.scopus.com/inward/record.url?scp=85054474868&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85054474868&partnerID=8YFLogxK
U2 - 10.1109/TAC.2018.2874704
DO - 10.1109/TAC.2018.2874704
M3 - Article
AN - SCOPUS:85054474868
SN - 0018-9286
VL - 64
SP - 2905
EP - 2912
JO - IRE Transactions on Automatic Control
JF - IRE Transactions on Automatic Control
IS - 7
M1 - 8485726
ER -