A Framework for Time-Consistent, Risk-Sensitive Model Predictive Control: Theory and Algorithms
Abstract
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.
Cite
@article{arxiv.1703.01029,
title = {A Framework for Time-Consistent, Risk-Sensitive Model Predictive Control: Theory and Algorithms},
author = {Sumeet Singh and Yin-Lam Chow and Anirudha Majumdar and Marco Pavone},
journal= {arXiv preprint arXiv:1703.01029},
year = {2018}
}
Comments
Submitted to IEEE Transactions on Automatic Control. arXiv admin note: text overlap with arXiv:1511.06981; v2: clarified exposition, reduced review of dynamic risk theory, updated simulations with computation time