A Semidefinite Programming Approach to Control Synthesis for Stochastic Reach-Avoid Problems

Dalibor Drzajic; Nikolaos Kariotoglou; Maryam Kamgarpour; John Lygeros

doi:10.29007/fqg6

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A Semidefinite Programming Approach to Control Synthesis for Stochastic Reach-Avoid Problems

10 pages•Published: February 1, 2017

Dalibor Drzajic, Nikolaos Kariotoglou, Maryam Kamgarpour and John Lygeros

Abstract

We propose a computational approach to approximate the value function and control policies for a finite horizon stochastic reach-avoid problem as follows. First, we formulate an infinite dimensional linear program whose solution characterizes the optimal value function of the stochastic reach-avoid. Next, we introduce sum-of-squares polynomials to approximate the solution of this linear program through a semidefinite program. We compare our proposed tool to alternative numerical approaches via several case studies.

Keyphrases: approximated dynamic programming, control, gridding techniques, Markov Decision Processes, polynomial optimization, radial basis functions, reachability, semidefinite programming, stochastic control, sum of squares, synthesis, value function bounds

In: Goran Frehse and Matthias Althoff (editors). ARCH16. 3rd International Workshop on Applied Verification for Continuous and Hybrid Systems, vol 43, pages 134--143

Links:	https://easychair.org/publications/paper/MTm
	https://doi.org/10.29007/fqg6

BibTeX entry

@inproceedings{ARCH16:Semidefinite_Programming_Approach_to,
  author    = {Dalibor Drzajic and Nikolaos Kariotoglou and Maryam Kamgarpour and John Lygeros},
  title     = {A Semidefinite Programming Approach to Control Synthesis for Stochastic Reach-Avoid Problems},
  booktitle = {ARCH16. 3rd International Workshop on Applied Verification for Continuous and Hybrid Systems},
  editor    = {Goran Frehse and Matthias Althoff},
  series    = {EPiC Series in Computing},
  volume    = {43},
  pages     = {134--143},
  year      = {2017},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/MTm},
  doi       = {10.29007/fqg6}}

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