# Risk-averse risk-constrained optimal control

## TL;DR

This paper introduces a decomposition approach for multistage risk-averse optimal control problems with nested risk mappings, enabling more efficient solutions and accounting for uncertainty propagation over time.

## Contribution

It presents a novel decomposition method for complex nested risk-averse control problems and introduces a new form of risk constraints considering temporal uncertainty propagation.

## Key findings

- Enables efficient numerical solutions for nested risk-averse control problems.
- Introduces a new risk constraint form that accounts for uncertainty over time.
- Improves robustness of control strategies against low-probability events.

## Abstract

Multistage risk-averse optimal control problems with nested conditional risk mappings are gaining popularity in various application domains. Risk-averse formulations interpolate between the classical expectation-based stochastic and minimax optimal control. This way, risk-averse problems aim at hedging against extreme low-probability events without being overly conservative. At the same time, risk-based constraints may be employed either as surrogates for chance (probabilistic) constraints or as a robustification of expectation-based constraints. Such multistage problems, however, have been identified as particularly hard to solve. We propose a decomposition method for such nested problems that allows us to solve them via efficient numerical optimization methods. Alongside, we propose a new form of risk constraints which accounts for the propagation of uncertainty in time.