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Operational models of piecewise-smooth systems

Operational models of piecewise-smooth systems
Operational models of piecewise-smooth systems
In this article we study ways of constructing meaningful operational models of piecewise-smooth systems (PWS). The systems we consider are described by polynomial vector fields defined on non-overlapping semi-algebraic sets, which form a partition of the state space. Our approach is to give meaning to motion in systems of this type by automatically synthesizing operational models in the form of hybrid automata (HA). Despite appearances, it is in practice often difficult to arrive at satisfactory HA models of PWS. The different ways of building operational models that we explore in our approach can be thought of as defining different semantics for the underlying PWS. These differences have a number of interesting nuances related to phenomena such as chattering, non-determinism, so-called mythical modes and sliding behaviour.
piecewise-smooth systems, hybrid automata, discontinuous differential equations, polynomial vector fields, semantics of hybrid systems
1539-9087
1-19
Sogokon, Andrew
2600b17f-45e5-4e54-9a99-44baaf8eaf18
Ghorbal, Khalil
78ea6702-dcc4-41a9-b197-b850ff086df2
Johnson, Taylor
204159bb-e1e9-4eaa-a089-7aa02e55e46b
Sogokon, Andrew
2600b17f-45e5-4e54-9a99-44baaf8eaf18
Ghorbal, Khalil
78ea6702-dcc4-41a9-b197-b850ff086df2
Johnson, Taylor
204159bb-e1e9-4eaa-a089-7aa02e55e46b

Sogokon, Andrew, Ghorbal, Khalil and Johnson, Taylor (2017) Operational models of piecewise-smooth systems. ACM Transactions on Embedded Computing Systems, 16 (5), 1-19, [185]. (doi:10.1145/3126506).

Record type: Article

Abstract

In this article we study ways of constructing meaningful operational models of piecewise-smooth systems (PWS). The systems we consider are described by polynomial vector fields defined on non-overlapping semi-algebraic sets, which form a partition of the state space. Our approach is to give meaning to motion in systems of this type by automatically synthesizing operational models in the form of hybrid automata (HA). Despite appearances, it is in practice often difficult to arrive at satisfactory HA models of PWS. The different ways of building operational models that we explore in our approach can be thought of as defining different semantics for the underlying PWS. These differences have a number of interesting nuances related to phenomena such as chattering, non-determinism, so-called mythical modes and sliding behaviour.

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More information

Published date: October 2017
Keywords: piecewise-smooth systems, hybrid automata, discontinuous differential equations, polynomial vector fields, semantics of hybrid systems

Identifiers

Local EPrints ID: 434325
URI: http://eprints.soton.ac.uk/id/eprint/434325
ISSN: 1539-9087
PURE UUID: a9801a48-98c6-4b27-a822-1083127ab093

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Date deposited: 19 Sep 2019 16:30
Last modified: 18 Nov 2019 17:31

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