Optimality and passivity of input-quadratic nonlinear systems
File(s)
Accepted version
Author(s)
Sassano, mario
Astolfi, Alessandro
Type
Journal Article
Abstract
The infinite-horizon optimal control problem with stability in the presence of single-input, inputquadratic nonlinear systems is addressed and tackled in
this paper. In addition, it is shown that similar ideas can
be extended to study the property of passivity of the underlying input-quadratic system from a given output. The
constructive design of the optimal solution revolves around
the interesting fact that the property of optimality of the
closed-loop underlying system is shown to be locally equivalent to the property that an input-affine system possesses
an L2-gain less than one from a virtual disturbance signal.
The global version of the statement requires a technical
condition on the graph of the storage function of the latter
auxiliary plant, hence leads to the new notion of graphical
storage function. Finally, the theory is corroborated by the
application to the optimal control of the movable plane positioning in micro-mechanical systems (MEMS) actuators.
this paper. In addition, it is shown that similar ideas can
be extended to study the property of passivity of the underlying input-quadratic system from a given output. The
constructive design of the optimal solution revolves around
the interesting fact that the property of optimality of the
closed-loop underlying system is shown to be locally equivalent to the property that an input-affine system possesses
an L2-gain less than one from a virtual disturbance signal.
The global version of the statement requires a technical
condition on the graph of the storage function of the latter
auxiliary plant, hence leads to the new notion of graphical
storage function. Finally, the theory is corroborated by the
application to the optimal control of the movable plane positioning in micro-mechanical systems (MEMS) actuators.
Date Issued
2020-08-01
Date Acceptance
2019-09-09
Citation
IEEE Transactions on Automatic Control, 2020, 65 (8), pp.3229-3240
ISSN
0018-9286
Publisher
Institute of Electrical and Electronics Engineers
Start Page
3229
End Page
3240
Journal / Book Title
IEEE Transactions on Automatic Control
Volume
65
Issue
8
Copyright Statement
© 2019 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
Grant Number
664639
Subjects
0102 Applied Mathematics
0906 Electrical and Electronic Engineering
0913 Mechanical Engineering
Industrial Engineering & Automation
Publication Status
Published
Date Publish Online
2020-09-11