A Min-plus-SDDP Algorithm for Deterministic Multistage Convex Programming

We consider discrete time optimal control problems with finite horizon involving continuous states and possibly both continuous and discrete controls, subject to non-stationary linear dynamics and convex costs. In this general framework, we present a stochastic algorithm which generates monotone app...

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Published in:Proceedings of the IEEE Conference on Decision & Control pp. 3334 - 3339
Main Authors: Akian, Marianne, Chancelier, Jean-Philippe, Tran, Benoit
Format: Conference Proceeding
Language:English
Published: IEEE 01.12.2019
Subjects:
Approximation algorithms
Cost function
Deterministic multistage optimization problems
Dynamic programming
Heuristic algorithms
min-plus algebra
Optimal control
Optimized production technology
Stochastic Dual Dynamic Programming
tropical algebra
ISSN:2576-2370
Online Access:Get full text
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Abstract We consider discrete time optimal control problems with finite horizon involving continuous states and possibly both continuous and discrete controls, subject to non-stationary linear dynamics and convex costs. In this general framework, we present a stochastic algorithm which generates monotone approximations of the value functions as a pointwise supremum or infimum of basic functions (for example affine or quadratic) which are randomly selected. We give sufficient conditions on the way basic functions are selected in order to ensure almost sure convergence of the approximations to the value function on a set of interest. Then we study a linear-quadratic optimal control problem with one control constraint. On this toy example we show how to use our algorithm in order to build lower approximations, like the SDDP algorithm, as supremum of affine cuts and upper approximations, by min-plus techniques, as infimum of quadratic fonctions.
AbstractList We consider discrete time optimal control problems with finite horizon involving continuous states and possibly both continuous and discrete controls, subject to non-stationary linear dynamics and convex costs. In this general framework, we present a stochastic algorithm which generates monotone approximations of the value functions as a pointwise supremum or infimum of basic functions (for example affine or quadratic) which are randomly selected. We give sufficient conditions on the way basic functions are selected in order to ensure almost sure convergence of the approximations to the value function on a set of interest. Then we study a linear-quadratic optimal control problem with one control constraint. On this toy example we show how to use our algorithm in order to build lower approximations, like the SDDP algorithm, as supremum of affine cuts and upper approximations, by min-plus techniques, as infimum of quadratic fonctions.
Author Chancelier, Jean-Philippe
Tran, Benoit
Akian, Marianne
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  givenname: Marianne
  surname: Akian
  fullname: Akian, Marianne
  organization: INRIA and CMAP, École polytechnique,Palaiseau Cedex,France,91128
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  givenname: Jean-Philippe
  surname: Chancelier
  fullname: Chancelier, Jean-Philippe
  organization: CERMICS, École des Ponts ParisTech,Marne-la-Vallée,France,77455
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  givenname: Benoit
  surname: Tran
  fullname: Tran, Benoit
  organization: CERMICS, École des Ponts ParisTech, INRIA and CMAP, École polytechnique,Marne-la-Vallée,France,77455
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Snippet We consider discrete time optimal control problems with finite horizon involving continuous states and possibly both continuous and discrete controls, subject...
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StartPage 3334
SubjectTerms Approximation algorithms
Cost function
Deterministic multistage optimization problems
Dynamic programming
Heuristic algorithms
min-plus algebra
Optimal control
Optimized production technology
Stochastic Dual Dynamic Programming
tropical algebra
Title A Min-plus-SDDP Algorithm for Deterministic Multistage Convex Programming
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