Svetlana Polenkova

Control and Analysis for the Stability of Hybrid and Embedded Systems

Description of research

The aim of the project is to develop a theory for stability and control of switched linear systems. A switched linear system is a dynamical system consisting of a finite number of different continuous time linear systems among which the overall system switches. With each continuous time system we associate a discrete state or location. The dynamics of the system has a discrete component that describes the switches from one discrete state to the other and a continuous component corresponding to the dynamics within each discrete state. For that reason switched systems are also referred to as hybrid systems. Hybrid systems arise naturally in the area of embedded systems design, where continuous dynamics of both physical components and the environment interact with logical and discrete processes implemented in software or hardware. In such cases stability is a crucial property for guaranteeing the system to be correct, dependable, and safe. Stability of switched systems is defined analogously to stability of systems described by ordinary differential equations. Whereas the stability theory for non-switched linear systems is elementary and well-understood, the stability of switched systems is, due to the interaction between the continuous and discrete dynamics, much more involved. In this project we will develop a stability theory for switched linear systems with two branches: one based on transition gain analysis and one based on delayed switching. In both approaches optimization of local Lyapunov functions is used to reduce conservatism. One of the main innovations is that the discrete dynamics and the corresponding interaction between the dynamics in the discrete states will be analyzed using methods from automata theory. Subsequently the stability results will be used for controller synthesis for the case that the continuous time systems in the discrete states are models of linear control systems. Finally, the project aims at the development of a more general and fundamental notion of hybrid Lyapunov function.

Advisor(s)

Dr Jan Willem Polderman (j.w.polderman@math.utwente.nl) and Dr Rom Langerak (langerak@cs.utwente.nl).

Duration

2008-2012

Project

CLASHES

Sponsor

NWO

Strategic Research Orientation

DSN - Dependable Systems and Networks

Links to relevant web pages:

http://www.math.utwente.nl/wsb/polenkova.html

Svetlana Polenkova

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Home CTIT symposium 2013 About CTIT News NIRICT Research Meet the PhDs Working at CTIT Internal Information Conferences Open Calls (updated May 3, 2013) Library and Videos Knowledge Transfer Links Sitemap Search	Svetlana Polenkova Control and Analysis for the Stability of Hybrid and Embedded Systems Description of research The aim of the project is to develop a theory for stability and control of switched linear systems. A switched linear system is a dynamical system consisting of a finite number of different continuous time linear systems among which the overall system switches. With each continuous time system we associate a discrete state or location. The dynamics of the system has a discrete component that describes the switches from one discrete state to the other and a continuous component corresponding to the dynamics within each discrete state. For that reason switched systems are also referred to as hybrid systems. Hybrid systems arise naturally in the area of embedded systems design, where continuous dynamics of both physical components and the environment interact with logical and discrete processes implemented in software or hardware. In such cases stability is a crucial property for guaranteeing the system to be correct, dependable, and safe. Stability of switched systems is defined analogously to stability of systems described by ordinary differential equations. Whereas the stability theory for non-switched linear systems is elementary and well-understood, the stability of switched systems is, due to the interaction between the continuous and discrete dynamics, much more involved. In this project we will develop a stability theory for switched linear systems with two branches: one based on transition gain analysis and one based on delayed switching. In both approaches optimization of local Lyapunov functions is used to reduce conservatism. One of the main innovations is that the discrete dynamics and the corresponding interaction between the dynamics in the discrete states will be analyzed using methods from automata theory. Subsequently the stability results will be used for controller synthesis for the case that the continuous time systems in the discrete states are models of linear control systems. Finally, the project aims at the development of a more general and fundamental notion of hybrid Lyapunov function. Advisor(s) Dr Jan Willem Polderman (j.w.polderman@math.utwente.nl) and Dr Rom Langerak (langerak@cs.utwente.nl). Duration 2008-2012 Project CLASHES Sponsor NWO Strategic Research Orientation DSN - Dependable Systems and Networks Links to relevant web pages: http://www.math.utwente.nl/wsb/polenkova.html