Regularity and directional differentiability with respect to parameters of solutions to nonlinear switching systems
Many physical systems and processes encompass several modes of operation with a different dynamical behavior in each mode. Switching systems provide a suitable mathematical model for such processes. It is well known that the continuous states of switching systems are often non-differentiable with re...
| Main Authors: | , |
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| Format: | Conference Paper |
| Published: |
Institute of Electrical and Electronics Engineers Inc.
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/9235 |
| _version_ | 1848745891126575104 |
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| author | Ye, J. Xu, Honglei |
| author_facet | Ye, J. Xu, Honglei |
| author_sort | Ye, J. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Many physical systems and processes encompass several modes of operation with a different dynamical behavior in each mode. Switching systems provide a suitable mathematical model for such processes. It is well known that the continuous states of switching systems are often non-differentiable with respect to parameters at the switching instants. However, states at these instants are often involved in optimal control of switching systems, resulting in nonsmooth dynamic programming problems. Directional derivative plays an important role in optimization and control theory. In this paper, we explore the directional differentiability of solutions to a class of switching systems with respect to parameters. We present some basic properties for the switching systems, including non-Zenoness, existence and uniqueness of solution, and local Lipschitzean of solution with respect to parameters. On this basis, we assert the directional differentiability of the solution with respect to parameters and give the formula of the directional derivative. |
| first_indexed | 2025-11-14T06:24:33Z |
| format | Conference Paper |
| id | curtin-20.500.11937-9235 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T06:24:33Z |
| publishDate | 2015 |
| publisher | Institute of Electrical and Electronics Engineers Inc. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-92352017-09-13T14:48:44Z Regularity and directional differentiability with respect to parameters of solutions to nonlinear switching systems Ye, J. Xu, Honglei Many physical systems and processes encompass several modes of operation with a different dynamical behavior in each mode. Switching systems provide a suitable mathematical model for such processes. It is well known that the continuous states of switching systems are often non-differentiable with respect to parameters at the switching instants. However, states at these instants are often involved in optimal control of switching systems, resulting in nonsmooth dynamic programming problems. Directional derivative plays an important role in optimization and control theory. In this paper, we explore the directional differentiability of solutions to a class of switching systems with respect to parameters. We present some basic properties for the switching systems, including non-Zenoness, existence and uniqueness of solution, and local Lipschitzean of solution with respect to parameters. On this basis, we assert the directional differentiability of the solution with respect to parameters and give the formula of the directional derivative. 2015 Conference Paper http://hdl.handle.net/20.500.11937/9235 10.1109/WCICA.2014.7052902 Institute of Electrical and Electronics Engineers Inc. restricted |
| spellingShingle | Ye, J. Xu, Honglei Regularity and directional differentiability with respect to parameters of solutions to nonlinear switching systems |
| title | Regularity and directional differentiability with respect to parameters of solutions to nonlinear switching systems |
| title_full | Regularity and directional differentiability with respect to parameters of solutions to nonlinear switching systems |
| title_fullStr | Regularity and directional differentiability with respect to parameters of solutions to nonlinear switching systems |
| title_full_unstemmed | Regularity and directional differentiability with respect to parameters of solutions to nonlinear switching systems |
| title_short | Regularity and directional differentiability with respect to parameters of solutions to nonlinear switching systems |
| title_sort | regularity and directional differentiability with respect to parameters of solutions to nonlinear switching systems |
| url | http://hdl.handle.net/20.500.11937/9235 |