# Performative Control for Linear Dynamical Systems

arXiv: https://arxiv.org/abs/2410.23251 · HTML: https://mlsanity.com/paper/2410.23251/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2024.

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

- [Performative Reinforcement Learning with Linear Markov Decision Process](https://mlsanity.com/paper/2411.05234/) (2024)
- [Decision-Dependent Stochastic Optimization: The Role of Distribution Dynamics](https://mlsanity.com/paper/2503.07324/) (2025)
- [Performative Policy Gradient: Optimality in Performative Reinforcement Learning](https://mlsanity.com/paper/2512.20576/) (2025)
- [Independent Learning in Performative Markov Potential Games](https://mlsanity.com/paper/2504.20593/) (2025)
- [Online Multi-Agent Control with Adversarial Disturbances](https://mlsanity.com/paper/2506.18814/) (2025)
- [Towards Performatively Stable Equilibria in Decision-Dependent Games for Arbitrary Data Distribution Maps](https://mlsanity.com/paper/2509.02619/) (2025)

## Abstract (arXiv)

We introduce the framework of performative control, where the policy chosen by the controller affects the underlying dynamics of the control system. This results in a sequence of policy-dependent system state data with policy-dependent temporal correlations. Following the recent literature on performative prediction [21], we introduce the concept of a performatively stable control (PSC) solution. We first propose a sufficient condition for the performative control problem to admit a unique PSC solution with a problem-specific structure of distributional sensitivity propagation and aggregation. We further analyze the impacts of system stability on the existence of the PSC solution. Specifically, for almost surely strongly stable policy-dependent dynamics, the PSC solution exists if the sum of the distributional sensitivities is small enough. However, for almost surely unstable policy-dependent dynamics, the existence of the PSC solution will necessitate a temporally backward decaying of the distributional sensitivities. We finally provide a repeated stochastic gradient descent scheme that converges to the PSC solution and analyze its non-asymptotic convergence rate. Numerical results validate our theoretical analysis.