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Impact of regular perturbations in input constrained optimal control problems
Author(s) -
Maamria D.,
Chaplais F.,
Sciarretta A.,
Petit N.
Publication year - 2020
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2605
Subject(s) - perturbation (astronomy) , nonlinear system , sequence (biology) , optimal control , magnitude (astronomy) , mathematical optimization , mathematics , function (biology) , control theory (sociology) , computer science , control (management) , physics , genetics , quantum mechanics , astronomy , artificial intelligence , biology , evolutionary biology
Summary This article explores the impact of regular perturbations (ie, small terms) in input constrained optimal control problems for nonlinear systems. In detail, it is shown that perturbation terms of magnitude ε appearing in the dynamics or the cost function lead to a variation of magnitude Kε 2 in the optimal cost. The scale factor K can be estimated from the nominal ( ε =0) solution and the analytic expressions of the perturbations. This result extends existing results that have been established in the absence of input constraints. Technically, the result is proven by means of interior penalties which allow constructing a sequence of suboptimal feasible solutions. Two numerical examples serve as illustration.