# Online convex optimization for constrained control of linear systems using a reference governor

arXiv: https://arxiv.org/abs/2211.09088 · HTML: https://mlsanity.com/paper/2211.09088/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2022.

## Built on by (most cited first, 1 of 1)

- [Predictive Linear Online Tracking for Unknown Targets](https://mlsanity.com/paper/2402.10036/) (2024)

## Abstract (arXiv)

In this work, we propose a control scheme for linear systems subject to pointwise in time state and input constraints that aims to minimize time-varying and a priori unknown cost functions. The proposed controller is based on online convex optimization and a reference governor. In particular, we apply online gradient descent to track the time-varying and a priori unknown optimal steady state of the system. Moreover, we use a λ-contractive set to enforce constraint satisfaction and a sufficient convergence rate of the closed-loop system to the optimal steady state. We prove that the proposed scheme is recursively feasible, ensures that the state and input constraints are satisfied at all times, and achieves a dynamic regret that is linearly bounded by the variation of the cost functions. The algorithm's performance and constraint satisfaction is illustrated by means of a simulation example.