FAST: an algorithm for the scenario approach with reduced sample complexity

Carè, Algo; Garatti, Simone; Campi, Marco C.

doi:10.3182/20110828-6-it-1002.02457

Cited by 5 publications

(5 citation statements)

References 29 publications

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“…The problem can be also written in the form (4), with non-convex cost J(x, y) := − x 2 + y 2 and non-convex constraints − x 2 + y 2 ≥ cos(δ (i) )x + sin(δ (i) )y − 1. We use the form in (36) to visualize the optimizing direction −z, as shown in Figure 2.…”

Section: Sp Ex [ω]mentioning

confidence: 99%

“…and non-convex constraints − x 2 + y 2 ≥ cos( δ(i) )x + sin( δ(i) )y − 1. We use the form in (36) to visualize the optimizing direction −z, as shown in Figure 2.…”

Section: Appendix a Counterexample With Unbounded Number Of Support C...mentioning

confidence: 99%

“…We first compute the optimal value J ex [ω] of SP ex [ω] in (36). By symmetry and regularity arguments (i.e.…”

Section: Appendix a Counterexample With Unbounded Number Of Support C...mentioning

confidence: 99%

See 2 more Smart Citations

A Scenario Approach for Non-Convex Control Design

Grammatico

Zhang

Margellos

et al. 2015

IEEE Trans. Automat. Contr.

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Randomized optimization is an established tool for control design with modulated robustness. While for uncertain convex programs there exist efficient randomized approaches, this is not the case for non-convex problems. Methods based on statistical learning theory are applicable to non-convex problems, but they usually are conservative in achieving the desired probabilistic guarantees. In this paper, we derive a novel scenario approach for a wide class of random non-convex programs, with a sample complexity similar to that of uncertain convex programs and with probabilistic guarantees that hold not only for the optimal solution of the scenario program, but for all feasible solutions inside a set of a-priori chosen complexity. We also address measure-theoretic issues for uncertain convex and non-convex programs. Among the family of non-convex control-design problems that can be addressed via randomization, we apply our scenario approach to stochastic model predictive control for chance constrained nonlinear control-affine systems

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Section: Sp Ex [ω]mentioning

confidence: 99%

“…and non-convex constraints − x 2 + y 2 ≥ cos( δ(i) )x + sin( δ(i) )y − 1. We use the form in (36) to visualize the optimizing direction −z, as shown in Figure 2.…”

Section: Appendix a Counterexample With Unbounded Number Of Support C...mentioning

confidence: 99%

See 1 more Smart Citation

A Scenario Approach for Non-Convex Control Design

Grammatico

Zhang

Margellos

et al. 2015

IEEE Trans. Automat. Contr.

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“…This may, however, cause an excessive computational effort. To cope with this issue, one can adopt a two-step procedure similar to that discussed in [18,17], where first α = 0.10 is used to optimize both Note that the histograms in Figure 2 reveal a larger variability compared to those in Figure 3. This is due to the fact that the latter results are associated to a value of α that is closer to the desired ε value for the violation probability.…”

Section: Jump Linear Stochastic Systems: a Numerical Examplementioning

confidence: 99%

“…This may, however, cause an excessive computational effort. To cope with this issue, one can adopt a two-step procedure similar to that discussed in [18,17], where first α = 0.10 is used to optimize both x M 1 0 and h, and then for α = 0.22 only h is optimized setting x M 1 0 equal to the value x M 1 , 0 obtained when α = 0.10. The guarantees provided by Theorem 1 on the re-optimized h still hold for model M 1 initialized with x M 1 , 0 .…”

Section: Jump Linear Stochastic Systems: a Numerical Examplementioning

confidence: 99%

Performance assessment and design of abstracted models for stochastic hybrid systems through a randomized approach

2014

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In this paper, a simulation-based method for the analysis and design of abstracted models for a stochastic hybrid system is proposed. The accuracy of a model is evaluated in terms of its capability to reproduce the system output for all the realizations of the stochastic input except for a set of (small) probability ε (ε-abstraction). This naturally leads to chance-constrained optimization problems, which are here tackled by means of a recently developed randomized approach. The main thrust of this paper is that, by testing how close the model and system outputs are over a finite number N of input realizations only, conclusions can be drawn about the model capability as an ε-abstraction. The key feature of the proposed method is its high versatility since it does not require specific assumptions on the system to be approximated. The only requirement is that of being able to run multiple simulations of the system behavior for different input realizations.

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