# Adaptive MPC under Time Varying Uncertainty: Robust and Stochastic

arXiv: https://arxiv.org/abs/1909.13473 · HTML: https://mlsanity.com/paper/1909.13473/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2019.

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

- [Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guarantees](https://mlsanity.com/paper/2111.00411/) (2021)
- [Online Learning for Predictive Control with Provable Regret Guarantees](https://mlsanity.com/paper/2111.15041/) (2021)
- [Probabilistic Symmetry for Multi-Agent Dynamics](https://mlsanity.com/paper/2205.01927/) (2022)
- [Reinforcement Learning Compensated Model Predictive Control for Off-road Driving on Unknown Deformable Terrain](https://mlsanity.com/paper/2408.09253/) (2024)
- [Dynamic Tube MPC: Learning Tube Dynamics with Massively Parallel Simulation for Robust Safety in Practice](https://mlsanity.com/paper/2411.15350/) (2024)
- [Actor-Critic Cooperative Compensation to Model Predictive Control for Off-Road Autonomous Vehicles Under Unknown Dynamics](https://mlsanity.com/paper/2503.00577/) (2025)

## Abstract (arXiv)

This paper deals with the problem of formulating an adaptive Model Predictive Control strategy for constrained uncertain systems. We consider a linear system, in presence of bounded time varying additive uncertainty. The uncertainty is decoupled as the sum of a process noise with known bounds, and a time varying offset that we wish to identify. The time varying offset uncertainty is assumed unknown point-wise in time. Its domain, called the Feasible Parameter Set, and its maximum rate of change are known to the control designer. As new data becomes available, we refine the Feasible Parameter Set with a Set Membership Method based approach, using the known bounds on process noise. We consider two separate cases of robust and probabilistic constraints on system states, with hard constraints on actuator inputs. In both cases, we robustly satisfy the imposed constraints for all possible values of the offset uncertainty in the Feasible Parameter Set. By imposing adequate terminal conditions, we prove recursive feasibility and stability of the proposed algorithms. The efficacy of the proposed robust and stochastic Adaptive MPC algorithms is illustrated with detailed numerical examples.