Random convex approximations of ambiguous chance constrained programs

Tseng, Shih-Hao; Bitar, Eilyan; Tang, Ao

doi:10.1109/cdc.2016.7799224

Cited by 11 publications

(11 citation statements)

References 21 publications

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“…?, enforcing the robust constraints involves dealing with semiinfinite programming when the D has infinite cardinality. For those cases, one may instead enforce chance constraints and adopt sampling-based techniques as in [24]- [26].…”

Section: B General Formulation For Robust Controller Synthesismentioning

confidence: 99%

Realization-Stability Lemma for Controller Synthesis

Tseng¹

2021

Preprint

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We have witnessed the emergence of several controller parameterizations and the corresponding synthesis methods, including Youla, system level, inputoutput, and many other new proposals. Meanwhile, under the same synthesis method, there are multiple realizations to adopt. Different synthesis methods/realizations target different plants/scenarios. Also, various robust results are proposed to deal with different perturbed system structures. Except for some case-by-case studies, we don't currently have a unified framework to understand their relationships.To address the issue, we show that existing controller synthesis methods and realization proposals are all special cases of a simple lemma, the realization-stability lemma. The lemma leads to easier equivalence proofs among existing methods and robust stability conditions for general system analysis. It also enables the formulation of a general controller synthesis problem, which provides a unified foundation for controller synthesis, realization derivation, and robust stability analysis.

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Section: B General Formulation For Robust Controller Synthesismentioning

confidence: 99%

Realization-Stability Lemma for Controller Synthesis

Tseng¹

2021

Preprint

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“…Using the equivalent conditions in (26), we verify the satisfaction of the desired inequality in (25) in two separate cases: γ i = 0 and γ i < 0.…”

Section: B Proof Of Propositionmentioning

confidence: 99%

“…This follows from the fact that for any positive semidefinite matrix X, if the diagonal entry satisfies [X] mm = 0, then all offdiagonal entries in the correspoding row and column also satisfy [X] ml = [X] lm = 0, for all l ∈ [n]. In this case, (25) becomes equivalent to the first condition in (26), and we are done.…”

Section: B Proof Of Propositionmentioning

confidence: 99%

“…Under this paradigm, the underlying distribution is assumed to belong to a closed ball centered around a known distribution. An alternative treatment of ambiguous chance constraints is provided in [25]. In addition to the basic difficulty inherent to the identification of an accurate distributional model, chance constraints do not explicitly account for the magnitude of constraint violations when they occur-however small their a priori specified probability.…”

Section: Introductionmentioning

confidence: 99%

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Robust AC Optimal Power Flow

Louca

Bitar

2019

IEEE Trans. Power Syst.

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There is a growing need for new optimization methods to facilitate the reliable and cost-effective operation of power systems with intermittent renewable energy resources. In this paper, we formulate the robust AC optimal power flow (RAC-OPF) problem as a two-stage robust optimization problem with recourse. This problem amounts to a nonconvex infinitedimensional optimization problem that is computationally intractable, in general. Under the assumption that there is adjustable generation or load at every bus in the power transmission network, we develop a technique to approximate RAC-OPF from within by a finite-dimensional semidefinite program by restricting the space of recourse policies to be affine in the uncertain problem data. We establish a sufficient condition under which the semidefinite program returns an affine recourse policy that is guaranteed to be feasible for the original RAC-OPF problem. We illustrate the effectiveness of the proposed optimization method on the WSCC 9-bus and IEEE 14-bus test systems with different levels of renewable resource penetration and uncertainty.

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“…Despite its generality, solving this general formulation is challenging in general, and the major obstacle is to ensure the perturbed stability for all ∆ ∈ D. Except for some computationally tractable cases as those listed in Section IV, enforcing the robust constraints involves dealing with semiinfinite programming when the D has infinite cardinality. For those cases, one may instead enforce chance constraints and adopt sampling-based techniques as in [15]- [17].…”

Section: B General Formulation For Robust Controller Synthesismentioning

confidence: 99%

A General Approach to Robust Controller Analysis and Synthesis

Tseng

2021

2021 60th IEEE Conference on Decision and Control (CDC)

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Robust controller synthesis attracts reviving research interest, driven by the rise of learning-based systems where uncertainty and perturbation are ubiquitous. Facing an uncertain situation, a robustly stabilizing controller should maintain stability while operating under a perturbed system deviating from its nominal specification. There have been numerous results for robust controller synthesis in multiple forms and with various goals, including µ-synthesis, robust primal-dual Youla, robust input-output, and robust system level parameterizations. However, their connections with one another are not clear, and we lack a general approach to robust controller analysis and synthesis.To serve this purpose, we derive robust stability conditions for general systems and formulate the general robust controller synthesis problem. The conditions hinge on the realizationstability lemma, a recent analysis tool that unifies existing controller synthesis methods. Not only can the conditions infer a wide range of existing robust results, but they also lead to easier derivations of new ones. Together, we demonstrate the effectiveness of the conditions and provide a unified approach to robust controller analysis and synthesis.

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Random convex approximations of ambiguous chance constrained programs

Cited by 11 publications

References 21 publications

Realization-Stability Lemma for Controller Synthesis

Realization-Stability Lemma for Controller Synthesis

Robust AC Optimal Power Flow

A General Approach to Robust Controller Analysis and Synthesis

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