# Time-varying Projected Dynamical Systems with Applications to Feedback Optimization of Power Systems

arXiv: https://arxiv.org/abs/1809.07288 · HTML: https://mlsanity.com/paper/1809.07288/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2018.

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

- [Predictability and Fairness in Load Aggregation with Deadband](https://mlsanity.com/paper/2305.17725/) (2023)

## Abstract (arXiv)

This paper is concerned with the study of continuous-time, non-smooth dynamical systems which arise in the context of time-varying non-convex optimization problems, as for example the feedback-based optimization of power systems. We generalize the notion of projected dynamical systems to time-varying, possibly non-regular, domains and derive conditions for the existence of so-called Krasovskii solutions. The key insight is that for trajectories to exist, informally, the time-varying domain can only contract at a bounded rate whereas it may expand discontinuously. This condition is met, in particular, by feasible sets delimited via piecewise differentiable functions under appropriate constraint qualifications. To illustrate the necessity and usefulness of such a general framework, we consider a simple yet insightful power system example, and we discuss the implications of the proposed conditions for the design of feedback optimization schemes.