Optimal control for nonlinear systems driven by a known exogenous signal
Author(s)
Sassano, Mario
Mylvaganam, Thulasi
Astolfi, Alessandro
Type
Journal Article
Abstract
We consider optimal control problems for
continuous-time systems with time-dependent dynamics,
in which the time-dependence arises from the presence of a
known exogenous signal. The problem has been elegantly
solved in the case of linear input-affine systems, for which
it has been shown that the solution has a remarkable
structure: it is given by the sum of two contributions; a state
feedback, which coincides with the unperturbed optimal
control law, and a purely feedforward term in charge of
compensating the effect of the exogenous signal. The objective of this note is to extend the above result to nonlinear
input-affine systems. It is shown that, while some of the
relevant features of the linear case indeed rely heavily on
linearity and are not preserved in the nonlinear setting, several structural claims can be proved also in the nonlinear
case.
continuous-time systems with time-dependent dynamics,
in which the time-dependence arises from the presence of a
known exogenous signal. The problem has been elegantly
solved in the case of linear input-affine systems, for which
it has been shown that the solution has a remarkable
structure: it is given by the sum of two contributions; a state
feedback, which coincides with the unperturbed optimal
control law, and a purely feedforward term in charge of
compensating the effect of the exogenous signal. The objective of this note is to extend the above result to nonlinear
input-affine systems. It is shown that, while some of the
relevant features of the linear case indeed rely heavily on
linearity and are not preserved in the nonlinear setting, several structural claims can be proved also in the nonlinear
case.
Date Issued
2021-09-24
Date Acceptance
2021-08-11
Citation
IEEE Transactions on Automatic Control, 2021, 67 (6), pp.3678-3684
ISSN
0018-9286
Publisher
Institute of Electrical and Electronics Engineers
Start Page
3678
End Page
3684
Journal / Book Title
IEEE Transactions on Automatic Control
Volume
67
Issue
6
Copyright Statement
© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Sponsor
Commission of the European Communities
Identifier
https://ieeexplore.ieee.org/document/9547748
Grant Number
664639
Subjects
Industrial Engineering & Automation
0102 Applied Mathematics
0906 Electrical and Electronic Engineering
0913 Mechanical Engineering
Publication Status
Published
Date Publish Online
2021-09-24