10,913 research outputs found
Time-varying Projected Dynamical Systems with Applications to Feedback Optimization of Power Systems
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
Connections Between Adaptive Control and Optimization in Machine Learning
This paper demonstrates many immediate connections between adaptive control
and optimization methods commonly employed in machine learning. Starting from
common output error formulations, similarities in update law modifications are
examined. Concepts in stability, performance, and learning, common to both
fields are then discussed. Building on the similarities in update laws and
common concepts, new intersections and opportunities for improved algorithm
analysis are provided. In particular, a specific problem related to higher
order learning is solved through insights obtained from these intersections.Comment: 18 page
Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems
Development of robust dynamical systems and networks such as autonomous
aircraft systems capable of accomplishing complex missions faces challenges due
to the dynamically evolving uncertainties coming from model uncertainties,
necessity to operate in a hostile cluttered urban environment, and the
distributed and dynamic nature of the communication and computation resources.
Model-based robust design is difficult because of the complexity of the hybrid
dynamic models including continuous vehicle dynamics, the discrete models of
computations and communications, and the size of the problem. We will overview
recent advances in methodology and tools to model, analyze, and design robust
autonomous aerospace systems operating in uncertain environment, with stress on
efficient uncertainty quantification and robust design using the case studies
of the mission including model-based target tracking and search, and trajectory
planning in uncertain urban environment. To show that the methodology is
generally applicable to uncertain dynamical systems, we will also show examples
of application of the new methods to efficient uncertainty quantification of
energy usage in buildings, and stability assessment of interconnected power
networks
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