Optimal Control Problems with Mixed and Pure State Constraints
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Optimal control problems.pdf
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273.39 KB
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Author(s)
de Pinho, M. D. R.
Vinter, R. B.
Boccia, Andrea
Date Issued
November 2016
Journal
SIAM Journal on Control and Optimization
Publisher
Society for Industrial and Applied Mathematics
Citation
Boccia, A.; de Pinho, M. D. R. and Vinter, R. B. “Optimal Control Problems with Mixed and Pure State Constraints.” SIAM Journal on Control and Optimization 54, no. 6 (January 2016): 3061–3083 © 2016, Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
This paper provides necessary conditions of optimality for optimal control problems, in which the pathwise constraints comprise both “pure” constraints on the state variable and “mixed” constraints on control and state variables. The proofs are along the lines of earlier analysis for mixed constraint problems, according to which Clarke's theory of “stratified” necessary conditions is applied to a modified optimal control problem resulting from absorbing the mixed constraint into the dynamics; the difference here is that necessary conditions which now take into account the presence of pure state constraints are applied to the modified problem. Necessary conditions are given for a rather general formulation of the problem containing both forms of the constraints, and then these are specialized to problems having special structure. While combined pure state and mixed control/state problems have been previously treated in the literature, the necessary conditions in this paper are proved under less restrictive hypotheses and for novel formulations of the constraints.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/15M1041845
