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

arXiv: https://arxiv.org/abs/1703.01029 · HTML: https://mlsanity.com/paper/1703.01029/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2017.

## Built on by (most cited first, 6 of 6)

- [STEP: Stochastic Traversability Evaluation and Planning for Risk-Aware Off-road Navigation](https://mlsanity.com/paper/2103.02828/) (2021)
- [Risk-averse autonomous systems: A brief history and recent developments from the perspective of optimal control](https://mlsanity.com/paper/2109.08947/) (2021)
- [Risk-Averse Stochastic Shortest Path Planning](https://mlsanity.com/paper/2103.14727/) (2021)
- [STL Robustness Risk over Discrete-Time Stochastic Processes](https://mlsanity.com/paper/2104.01503/) (2021)
- [Sample-Based Bounds for Coherent Risk Measures: Applications to Policy Synthesis and Verification](https://mlsanity.com/paper/2204.09833/) (2022)
- [Risk-Averse Decision Making Under Uncertainty](https://mlsanity.com/paper/2109.04082/) (2021)

## Abstract (arXiv)

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.