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

## TL;DR

This paper introduces a novel risk-sensitive model predictive control framework for linear stochastic systems, ensuring time-consistency and stability, and providing a convex optimization-based algorithm for real-time implementation.

## Contribution

It develops a unified, time-consistent risk evaluation framework for MPC, with a provably stabilizing online algorithm and convex reformulation for practical use.

## Key findings

- The proposed MPC algorithm is provably stabilizing.
- The control law can be computed via convex optimization.
- Simulation results demonstrate effectiveness and stability.

## 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.