Solving Stochastic LQR Problems by Polynomial Chaos

Levajković, Tijana; Mena, Hermann; Pfurtscheller, Lena-Maria

doi:10.1109/lcsys.2018.2844730

Cited by 5 publications

(3 citation statements)

References 22 publications

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“…Efficient algorithmic frameworks have been devised to numerically solve LCPs, ranging from local search [5] and dual representations [6,7], to deterministic-equivalent reformulations [8,9], among others. In the special case of LQPs, those techniques may be further improved by combining SRE theory with semidefinite programming [10,11], finite-dimensional approximation [12,13], or chaos expansion [14].…”

Section: Introductionmentioning

confidence: 99%

Sequential convex programming for non-linear stochastic optimal control

2022

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This work introduces a sequential convex programming framework for non-linear, finite-dimensional stochastic optimal control, where uncertainties are modeled by a multidimensional Wiener process. We prove that any accumulation point of the sequence of iterates generated by sequential convex programming is a candidate locally-optimal solution for the original problem in the sense of the stochastic Pontryagin Maximum Principle. Moreover, we provide sufficient conditions for the existence of at least one such accumulation point. We then leverage these properties to design a practical numerical method for solving non-linear stochastic optimal control problems based on a deterministic transcription of stochastic sequential convex programming.

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Section: Introductionmentioning

confidence: 99%

Sequential convex programming for non-linear stochastic optimal control

2022

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“…The list of references is long, here we mention just a few [20], [28], [32], [33]. In [25], [26], [27] this approach has been recently applied to the stochastic optimal regulator control problem [13]. Practical application of the Wiener polynomial chaos involves two truncations, truncation with respect to the number of the random variables and truncation with respect to the order of the orthogonal Askey polynomials used (in the particular case considered, the Legendre polynomials), see e.g.…”

Section: Introductionmentioning

confidence: 99%

A splitting/polynomial chaos expansion approach for stochastic evolution equations

Kofler,

Levajković,

Mena

et al. 2019

Preprint

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In this paper we combine deterministic splitting methods with a polynomial chaos expansion method for solving stochastic parabolic evolution problems. The stochastic differential equation is reduced to a system of deterministic equations that we solve explicitly by splitting methods. The method can be applied to a wide class of problems where the related stochastic processes are given uniquely in terms of stochastic polynomials. A comprehensive convergence analysis is provided and numerical experiments validate our approach.

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“…Quite efficient algorithmic frameworks have been conceived to numerically solve LCPs, that range from local search [17] and duality [33,18], to deterministic-equivalent reformulation [6,4], to name a few. In the special case of LQPs, those techniques may be further improved by thoroughly combining SRE theory with semidefinite programming [32,38], finite-dimensional approximation [5,14] or chaos expansion [23].…”

mentioning

confidence: 99%

Sequential Convex Programming For Non-Linear Stochastic Optimal Control

Bonalli¹,

Lew²,

Pavone³

2020

Preprint

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We introduce a sequential convex programming framework to solve general nonlinear stochastic optimal control problems in finite dimension, where uncertainties are modeled by a multidimensional Wiener process. We provide sufficient conditions for the convergence of the method. Moreover, we prove that, when convergence is achieved, sequential convex programming finds a candidate locally optimal solution for the original problem in the sense of the stochastic Pontryagin Maximum Principle. We leverage those properties to design a practical numerical method to solve non-linear stochastic optimal control problems that is based on a deterministic transcription of stochastic sequential convex programming.

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Solving Stochastic LQR Problems by Polynomial Chaos

Cited by 5 publications

References 22 publications

Sequential convex programming for non-linear stochastic optimal control

Sequential convex programming for non-linear stochastic optimal control

A splitting/polynomial chaos expansion approach for stochastic evolution equations

Sequential Convex Programming For Non-Linear Stochastic Optimal Control

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