The scenario approach to robust control design

By Giuseppe Carlo Calafiore, Marco Claudio Campi. IEEE Transactions on Automatic Control, 2006

1,258 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/459c0c4069b1cbbd3c188cbdac00f5fdecab1d9f

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In Control and Systems Engineering

Citations in the corpus

Theory and Applications of Robust Optimization (2010, background): “Many approaches have been considered to address the computational challenges they pose ([121, 111]), including work using sampling to approximate the chance constraints [47, 45, 71].”
The Exact Feasibility of Randomized Solutions of Uncertain Convex Programs (2008, methodology): “:3) is the key result of [6]: (2) Moving a fundamental step forward with respect to [6], in this paper we establish the validity of relation (3) (note that (3) holds with “=”; that is, it is not a bound) for the prototype class of fully-supported problems according to Deﬁnition 3 in section 2.”
Data-driven chance constrained stochastic program (2015, background): “, Calafiore and Campi [5, 6], Nemirovski and Shapiro [23], Luedtke and Ahmed [20], and Pagnoncelli et al.”
Lectures on Stochastic Programming: Modeling and Theory (2009, result): “This result builds on a previous work of Calafiore and Campi [33], and from the considered point of view gives a tightest possible estimate of the required sample size.”
A Probabilistic Particle-Control Approximation of Chance-Constrained Stochastic Predictive Control (2010, methodology): “For these parameters, the analytic result of Calafiore and Campi [14] specifies that Ns = 1439 scenarios are sufficient to ensure that the chance constraints are satisfied with high probability.”
Optimization under uncertainty with applications to design of truss structures (2008, background): “Specifically, setting robustness level = 0.05 and confidence β = 10 −10 , the best bound in Calafiore and Campi (2006) requires N = 1, 651 samples.”
Chance-Constrained Optimal Path Planning With Obstacles (2011, methodology): “Non-Gaussian uncertainty was handle d by [16], [18], [33] using sampling approaches.”
From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization (2010, methodology): “Indeed, sampling approximation of the chance constrained problem has been studied theoretically in Calaflore and Campi [11, 12 ], Ergodan and Iyengar [17] and Luedtke and Ahmed [22].”
Convex Approximations of Chance Constrained Programs (2006, background): “To some extent this question was resolved in recent papers of Calafiore and Campi [6] [7] and de Farias and Van Roy [10].”
Distributionally robust joint chance constraints with second-order moment information (2011, background): “Recently, Calafiore and Campi [5] as well as Luedtke and Ahmed [17] have proposed to replace the chance constraint (2) by a pointwise constraint that must hold at a finite number of sample points drawn randomly from the distribution Q.”
Second Order Cone Programming Approaches for Handling Missing and Uncertain Data (2006, methodology): “An alternative is constraint sampling, as proposed by (de Farias and Roy, 2004; Calafiore and Campi, 2004).”
Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications (2009, background): “Figures 7 and 9 tells us that relatively small sample sizes (e.g, if compared to Campi-Garatti estimates) can yield good candidate solutions.”
A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality (2011, methodology): “The approach of the present paper builds on the so-called “scenario” approach of [43, 44, 45].”
Stochastic Model Predictive Control: An Overview and Perspectives for Future Research (2016, positive): “The number of scenarios is chosen according to the scheme given in [96], so that probabilistic guarantees on constraint satisfaction can be achieved.”
Control: A perspective (2014, methodology): “Many design problems can be captured by convex optimization and LMI’s, as was shown by Boyd and others [105,237,519,583,468,370,129].”