A novel approach to chance constrained optimal control problems

Zhao, Zinan; Liu, Fengjin; Kumar, Mrinal; Rao, Anil V.

doi:10.1109/acc.2015.7172218

Cited by 5 publications

(3 citation statements)

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“…Require: Current sample for the random parameter: (3), or (6)) of this candidate. 3: Calculate the ratio between the proposed and the candidate sample evaluated at the target pdf, e.g.,…”

Section: Algorithmmentioning

confidence: 99%

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Rare Event Chance-Constrained Optimal Control Using Polynomial Chaos and Subset Simulation

2019

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This study develops a ccoc framework capable of handling rare event probabilities. Therefore, the framework uses the gpc method to calculate the probability of fulfilling rare event constraints under uncertainties. Here, the resulting cc evaluation is based on the efficient sampling provided by the gpc expansion. The subsim method is used to estimate the actual probability of the rare event. Additionally, the discontinuous cc is approximated by a differentiable function that is iteratively sharpened using a homotopy strategy. Furthermore, the subsim problem is also iteratively adapted using another homotopy strategy to improve the convergence of the Newton-type optimization algorithm. The applicability of the framework is shown in case studies regarding battery charging and discharging. The results show that the proposed method is indeed capable of incorporating very general cc within an ocp at a low computational cost to calculate optimal results with rare failure probability cc.

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“…Require: Current sample for the random parameter: (3), or (6)) of this candidate. 3: Calculate the ratio between the proposed and the candidate sample evaluated at the target pdf, e.g.,…”

Section: Algorithmmentioning

confidence: 99%

“…Additionally, feedback control is used to satisfy system constraints. In [3], a strategy to approximate a CC based on split Bernstein polynomials is introduced. Here, pseudo-spectral methods are applied and a single optimization run is used on the transformed CC-OC.…”

Section: Introductionmentioning

confidence: 99%

Rare Event Chance-Constrained Optimal Control Using Polynomial Chaos and Subset Simulation

2019

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“…The results in [4] introduce both analytical methods and sampling-based methods to handle chance constraints, and the feedback controller is incorporated into the optimization with a risk allocation. A strategy based on split Bernstein polynomials and Markov chain Monte Carlo (MCMC) is implemented to estimate chance constraints for optimal control problems in [5]. In [6], polynomial chaos expansion (PCE) and subset simulation (SuS) are employed to approximate rare-event probabilities within a chance-constrained open-loop optimal control framework.…”

Section: Introductionmentioning

confidence: 99%

Rare-Event Chance-Constrained Flight Control Optimization Using Surrogate-Based Subset Simulation

Shi,

Holzapfel

2020

Preprint

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A probabilistic performance-oriented control design optimization approach is introduced for flight systems. Aiming at estimating rare-event probabilities accurately and efficiently, subset simulation is combined with surrogate modeling techniques to improve efficiency. At each level of subset simulation, the samples that are close to the failure domain are employed to construct a surrogate model. The existing surrogate is then refined progressively. In return, seed and sample candidates are screened by the updated surrogate, thus saving a large number of calls to the true model and reducing the computational expense. Afterwards, control parameters are optimized under rare-event chance constraints to directly guarantee system performance. Simulations are conducted on an aircraft longitudinal model subject to parametric uncertainties to demonstrate the efficiency and accuracy of this method.

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