An integral quadratic constraint framework for real-time steady-state optimization of linear time-invariant systems

Nelson, Zachary E.; Mallada, Enrique

doi:10.48550/arxiv.1710.10204

Cited by 1 publication

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“…The idea of "closing the loop" on a physical systems not just to control, but to optimize the state of a physical system with simple feedback controllers has recently emerged as a new frontier, combining ideas from optimization and control theory with notable applications in the operation and optimization of power systems [1]- [10]. The underlying premise of such autonomous (or feedback-based) optimization schemes as illustrated in Fig.…”

Section: Introductionmentioning

confidence: 99%

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

Hauswirth

Subotić

Bolognani

et al. 2018

2018 IEEE Conference on Decision and Control (CDC)

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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.Index Terms-Non-smooth analysis, nonlinear dynamical systems, power systems. arXiv:1809.07288v2 [math.OC]

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Section: Introductionmentioning

confidence: 99%