A Framework for Time-Consistent, Risk-Sensitive Model Predictive Control: Theory and Algorithms

Sumeet Singh, Yinlam Chow, Anirudha Majumdar, Marco Pavone

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


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.

Original languageEnglish (US)
Article number8485726
Pages (from-to)2905-2912
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number7
StatePublished - Jul 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


  • Markov processes
  • optimization
  • predictive control
  • risk analysis


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