# Dual Stochastic MPC for Systems with Parametric and Structural Uncertainty

arXiv: https://arxiv.org/abs/1912.10114 · HTML: https://mlsanity.com/paper/1912.10114/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2019.

## Built on by (most cited first, 2 of 2)

- [Active Uncertainty Reduction for Safe and Efficient Interaction Planning: A Shielding-Aware Dual Control Approach](https://mlsanity.com/paper/2302.00171/) (2023)
- [Active Uncertainty Reduction for Human-Robot Interaction: An Implicit Dual Control Approach](https://mlsanity.com/paper/2202.07720/) (2022)

## Abstract (arXiv)

Designing controllers for systems affected by model uncertainty can prove to be a challenge, especially when seeking the optimal compromise between the conflicting goals of identification and control. This trade-off is explicitly taken into account in the dual control problem, for which the exact solution is provided by stochastic dynamic programming. Due to its computational intractability, we propose a sampling-based approximation for systems affected by both parametric and structural model uncertainty. The approach proposed in this paper separates the prediction horizon in a dual and an exploitation part. The dual part is formulated as a scenario tree that actively discriminates among a set of potential models while learning unknown parameters. In the exploitation part, achieved information is fixed for each scenario, and open-loop control sequences are computed for the remainder of the horizon. As a result, we solve one optimization problem over a collection of control sequences for the entire horizon, explicitly considering the knowledge gained in each scenario, leading to a dual model predictive control formulation.