Impact of regular perturbations in input constrained optimal control problems. (28th April 2020)

• Record Type: Journal Article
• Authors: Maamria, D.; Chaplais, F.; Sciarretta, A.; Petit, N.
• Is Part Of: Optimal control applications and methods. Volume 41:Number 4(2020)
• Page Start: 1321
• Page End: 1351
• Publication Date: 2020-04-28
• Subjects: input constraints -- interior methods -- optimal control -- regular perturbations; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2605
• Languages: English
• ISSNs: 0143-2087

Abstract

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.