On the Differentiability of Projected Trajectories and the Robust Convergence of Non-Convex Anti-Windup Gradient Flows

Hauswirth, Adrian; Dörfler, Florian; Teel, Andrew R.

doi:10.1109/lcsys.2020.2988515

Cited by 11 publications

(3 citation statements)

References 24 publications

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“…The key aspect in (47) is the fact that ∇ Φ is evaluated at P U (u) rather than at u. In Hauswirth et al (2020d) it was shown that trajectories u(t) of (47) converge in the sense that P U (u(t)) converges to the set of KKT points of the optimization problem minimize Φ(u) subject to u ∈ U .…”

Section: Input Saturation Via Projection and Anti-windupmentioning

confidence: 99%

Optimization Algorithms as Robust Feedback Controllers

Hauswirth¹,

Bolognani²,

Hug³

et al. 2021

Preprint

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Mathematical optimization is one of the cornerstones of modern engineering research and practice. Yet, throughout all application domains, mathematical optimization is, for the most part, considered to be a numerical discipline. Optimization problems are formulated to be solved numerically with specific algorithms running on microprocessors. An emerging alternative is to view optimization algorithms as dynamical systems. While this new perspective is insightful in itself, liberating optimization methods from specific numerical and algorithmic aspects opens up new possibilities to endow complex real-world systems with sophisticated self-optimizing behavior. Towards this goal, it is necessary to understand how numerical optimization algorithms can be converted into feedback controllers to enable robust "closed-loop optimization". In this article, we review several research streams that have been pursued in this direction, including extremum seeking and pertinent methods from model predictive and process control. However, our primary focus lies on recent methods under the name of "feedback-based optimization". This research stream studies control designs that directly implement optimization algorithms in closed loop with physical systems. Such ideas are finding widespread application in the design and retrofit of control protocols for communication networks and electricity grids. In addition to an overview over continuous-time dynamical systems for optimization, our particular emphasis in this survey lies on closed-loop stability as well as the enforcement of physical and operational constraints in closed-loop implementations. We further illustrate these methods in the context of classical problems, namely congestion control in communication networks and optimal frequency control in electricity grids, and we highlight one potential future application in the form of autonomous reserve dispatch in power systems.

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Section: Input Saturation Via Projection and Anti-windupmentioning

confidence: 99%

Optimization Algorithms as Robust Feedback Controllers

Hauswirth¹,

Bolognani²,

Hug³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…This leads to algorithms similar to sequential quadratic programming schemes [49]. Another possibility are anti-windup approximations [30,31] which serve to implement projected dynamical systems as the closed-loop behavior of feedback control loops that are subject to input saturation in feedback-based optimization [10,18,29].…”

Section: Stability Of Projected Gradient Flowsmentioning

confidence: 99%

Projected Dynamical Systems on Irregular, Non-Euclidean Domains for Nonlinear Optimization

Hauswirth¹,

Bolognani²,

Dörfler³

2021

SIAM J. Control Optim.

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“…Convergence and stability analysis for regulation of linear time-invariant systems towards the optimal solution of a time-varying convex optimisation problem is studied in [16]. Constraints are included in [17], [18] and [19] extends to non-linear systems and non-convex problems.…”

Section: Introductionmentioning

confidence: 99%

Distributed Feedback Optimisation for Robotic Coordination

Sylvain¹,

Perez²,

Badyn³

et al. 2021

Preprint

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Feedback optimisation is an emerging technique aiming at steering a system to an optimal steady state for a given objective function. We show that it is possible to employ this control strategy in a distributed manner. Moreover, we prove asymptotic convergence to the set of optimal configurations. To this scope, we show that exponential stability is needed only for the portion of the state that affects the objective function. This is showcased by driving a swarm of agents towards a target location while maintaining a target formation. Finally, we provide a sufficient condition on the topological structure of the specified formation to guarantee convergence of the swarm in formation around the target location.

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On the Differentiability of Projected Trajectories and the Robust Convergence of Non-Convex Anti-Windup Gradient Flows

Cited by 11 publications

References 24 publications

Optimization Algorithms as Robust Feedback Controllers

Optimization Algorithms as Robust Feedback Controllers

Projected Dynamical Systems on Irregular, Non-Euclidean Domains for Nonlinear Optimization

Distributed Feedback Optimisation for Robotic Coordination

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