Title: 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.