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Joint Chance-Constrained Dynamic ProgrammingThis paper presents a novel dynamic programming algorithm with a joint chance constraint, which explicitly bounds the risk of failure in order to maintain the state within a specified feasible region. A joint chance constraint cannot be handled by existing constrained dynamic programming approaches since their application is limited to constraints in the same form as the cost function, that is, an expectation over a sum of one-stage costs. We overcome this challenge by reformulating the joint chance constraint into a constraint on an expectation over a sum of indicator functions, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the primal variables can be optimized by a standard dynamic programming, while the dual variable is optimized by a root-finding algorithm that converges exponentially. Error bounds on the primal and dual objective values are rigorously derived. We demonstrate the algorithm on a path planning problem, as well as an optimal control problem for Mars entry, descent and landing. The simulations are conducted using a real terrain data of Mars, with four million discrete states at each time step.
Document ID
20150008714
Document Type
Conference Paper
External Source(s)
Authors
Ono, Masahiro
(Keio Univ. Kanagawa, Japan)
Kuwata, Yoshiaki
(Jet Propulsion Lab., California Inst. of Tech. Pasadena, CA, United States)
Balaram, J. Bob
(Jet Propulsion Lab., California Inst. of Tech. Pasadena, CA, United States)
Date Acquired
May 21, 2015
Publication Date
December 10, 2012
Subject Category
Systems Analysis And Operations Research
Lunar And Planetary Science And Exploration
Meeting Information
2012 IEEE Conference on Decision and Control(Maui, HI)
Distribution Limits
Public
Copyright
Other

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