Piecewise-Affine Approximation-Based Stochastic Optimal Control with Gaussian Joint Chance Constraints

Vinod, Abraham P.; Sivaramakrishnan, Vignesh; Oishi, Meeko

doi:10.23919/acc.2019.8814977

Cited by 16 publications

(14 citation statements)

References 21 publications

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“…We first consider a Gaussian noise with zero mean and covariance Σ = diag(10 −4 •I 3 , 5×10 −8 •I 3 ). Once reformulated, the target set constraint has a Gaussian distribution, but the collision avoidance has a Chi distribution with three degrees of freedom, which does not have an analytical expression for the quantile function, and precludes use of standard tools or methods [14], [16] for Gaussian distributions.…”

Section: A 6d Cwh With a Gaussian Disturbancementioning

confidence: 99%

“…Approaches that rely upon moments [7], [8], [9] may create excessive conservativism, and typically require an iterative approach to controller synthesis and risk allocation, to circumvent non-convexity that arises in the process of separating joint chance constraints into individual chance constraints via Boole's inequality [10], [11], [12]. Recent work has employed Fourier transforms in combination with piecewise affine approximations [13], [14], to evaluate chance constraints without quadrature for linear time-invariant (LTI) systems with disturbance processes that have log-concave probability distribution functions.…”

Section: Introductionmentioning

confidence: 99%

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Approximate Quantiles for Stochastic Optimal Control of LTI Systems with Arbitrary Disturbances

Priore¹,

Petersen²,

Oishi³

2021

Preprint

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We propose a method for open-loop stochastic optimal control of LTI systems based in approximations of a quantile function. This approach enables efficient computation of quantile functions that arise in chance constraints. We are motivated by multi-vehicle planning problems in LTI systems, with norm-based collision avoidance constraints and polytopic feasibility constraints. These constraints can be posed as reverseconvex and convex chance constraints, respectively, that are affine in the control and in the disturbance. We show that for constraints of this form, piecewise affine approximations of the quantile function can be embedded in a difference-of-convex program that enables use of conic solvers. We demonstrate our method on multi-satellite coordination with Gaussian and Cauchy disturbances, and provide a comparison with particle control.

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Section: A 6d Cwh With a Gaussian Disturbancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approximate Quantiles for Stochastic Optimal Control of LTI Systems with Arbitrary Disturbances

Priore¹,

Petersen²,

Oishi³

2021

Preprint

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show abstract

“…The accuracy of the fuzzy formulation proposed in this work could be further improved by ac-counting for monthly/weekly uctuations; by reformulating the MO biofuel supply chain problem by utilizing a type-2 fuzzy framework. This work can also be extended by exploring other approaches for handling uncertainty such as: robust optimization, (Bairamzadeh et al [7]; Kara et al [31]), stochastic optimal control (Vinod et al [63]) and chance constraint optimization (Cheng et al [17]). This extension could include emerging areas of applications such as complex networks in alternative energy systems (Syahputra et al [60]; Lot et al [39]), social networks, gene networks (Youseph et al [67]) and pharmaceutical supply chain networks (Zahiri et al [68]…”

Section: Conclusion and Recommendationsmentioning

confidence: 99%

Random Matrix Generators for Optimizing a Fuzzy Biofuel Supply Chain System

Ganesan¹,

Vasant

Sanghvi³

et al. 2020

J. ADV. ENG. COMPUT.

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Complex industrial systems often contain various uncertainties. Hence sophisticated fuzzy optimization (metaheuristics) techniques have become commonplace; and are currently indispensable for effective design, maintenance and operations of such systems. Unfortunately, such state-of-the-art techniques suffer several drawbacks when applied to largescale problems. In line of improving the performance of metaheuristics in those, this work proposes the fuzzy random matrix theory (RMT) as an add-on to the cuckoo search (CS) technique for solving the fuzzy large-scale multiobjective (MO) optimization problem; biofuel supply chain. The fuzzy biofuel supply chain problem accounts for uncertainties resulting from fluctuations in the annual electricity generation output of the biomass power plant [kWh/year]. The details of these investigations are presented and analyzed.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

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“…For a ψ w that is Gaussian, risk allocation is an established approach to conservatively assure (5c) [8], [9], [2], [10], [20]. By exploiting the properties of a Gaussian random variable, in conjunction with Boole's inequality, (5c) can be reformulated as a collection of linear or second order cone constraints.…”

Section: Problem Statementmentioning

confidence: 99%

“…The standard risk-allocation approach [2], [8], [9], [10], [20], transforms the joint chance constraints (5c) into a set of individual chance constraints via Boole's inequality,…”

Section: A Risk-allocation For Log-concave Sisturbancesmentioning

confidence: 99%

Convexified Open-Loop Stochastic Optimal Control for Linear Non-Gaussian Systems

Sivaramakrishnan¹,

Vinod²,

Oishi³

2020

Preprint

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We consider stochastic optimal control of linear dynamical systems with additive non-Gaussian disturbance. We propose a novel, sampling-free approach, based on Fourier transformations and convex optimization, to cast the stochastic optimal control problem as a difference-of-convex program. In contrast to existing moment based approaches, our approach invokes higher moments, resulting in less conservatism. We employ piecewise affine approximations and the well-known convexconcave procedure, to efficiently solve the resulting optimization problem via standard conic solvers. We demonstrate that the proposed approach is computationally faster than existing particle based and moment based approaches, without compromising probabilistic safety constraints.

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Piecewise-Affine Approximation-Based Stochastic Optimal Control with Gaussian Joint Chance Constraints

Cited by 16 publications

References 21 publications

Approximate Quantiles for Stochastic Optimal Control of LTI Systems with Arbitrary Disturbances

Approximate Quantiles for Stochastic Optimal Control of LTI Systems with Arbitrary Disturbances

Random Matrix Generators for Optimizing a Fuzzy Biofuel Supply Chain System

Convexified Open-Loop Stochastic Optimal Control for Linear Non-Gaussian Systems

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