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http://hdl.handle.net/2108/1251
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| DC Field | Value | Language |
|---|
| contributor.advisor | Pettorossi, Alberto | - |
| contributor.advisor | Zaccarian, Luca | - |
| contributor.author | Forni, Fulvio | - |
| date.accessioned | 2010-04-29T09:48:28Z | - |
| date.available | 2010-04-29T09:48:28Z | - |
| date.issued | 2010-04-29T09:48:28Z | - |
| identifier.uri | http://hdl.handle.net/2108/1251 | - |
| description | 22. ciclo | en |
| description.abstract | I sistemi ibridi possono essere utilizzati per modellare processi continui, come quelli descritti da equazioni differenziali, e processi discreti, come quelli descritti da relazioni di transizione. Circuiti elettrici composti da parti analogiche e digitali, sistemi con impatti, computer operanti con vincoli di real-time sono esempi di sistemi definibili mediante la modellazione come sistema ibrido delle loro parti continue e discrete e della relativa interazione.
Molte definizioni di sistema ibrido possono essere trovate in letteratura. In generale, la modellazione del comportamento di un sistema ibrido e l'interazione delle parti discrete e continue è basata sulla nozione centrale di stato. In questa tesi si considera una definizione di sistema ibrido molto generale, che sussume le altre definizioni presenti in letteratura. Utilizzando questa definizione generale, nella tesi vengono studiati due problemi classici per la teoria del controllo e per l'informatica: problemi di stabilità e problemi di verifica formale, entrambi generalizzati su sistemi ibridi.
Il problema della stabilità di sistemi ibridi è studiato per una particolare classe di sistemi ibridi detti homogenei. Si segue un approccio prossimo alla teoria di Lyapunov e sono proposti degli algoritmi basati sulla decomposizione di polinomi in somme dei quadrati (sum of squares problems). Il problema della verifica formale di sistemi ibridi è studiato attraverso la generalizzazione della semantica della logica temporale TCTL su sistemi ibridi. Si propone poi un metodo per ridurre formule TCTL a espressioni di punto fisso.
Nella tesi sono trattati anche problemi di sintesi di controllori, nell'ambito classico della teoria del controllo. Sono proposti controllori continui per sistemi con saturazioni in input. Sono poi proposti controllori ibridi per problemi di passività di sistemi e di definizione di politiche di trasmissione dati su modelli semplificati di reti. | en |
| description.abstract | Hybrid systems define a common mathematical framework for
combining continuous and discrete processes, like the
case of processes defined by differential equations and by
transition relations, respectively.
Electrical circuits with both analog and
digital components, models of impacts, computing devices running real-time
applications, are all examples of processes defined by a combination
of differential equations and transition relations. Thus,
they can be modeled and studied as hybrid systems.
Hybrid systems have been studied in the last twenty years both by the
computer science community and by the control community, and
a lot of different definitions and results have been developed.
Common to all of these definitions is the mathematical
characterization of the evolution and of the interaction
of continuous and discrete processes by way of the crucial notion of
state. In this thesis, we consider a quite general definition
of hybrid systems that, to the best of the knowledge of the candidate,
subsumes classical definitions of a hybrid system in both computer
science and control theory. Based on this general definition
of a hybrid system, we study two classical problems:
stability problems of control theory and
verification problems of computer science, both generalized
to hybrid systems. Indeed, in the first part of the thesis,
we propose Lyapunov-like tools for the stability problem of a
peculiar class of hybrid systems, and we propose a
specific temporal logic, and a method for rewriting the formulas of
this logic as fixpoint expressions, for the verification problem of
hybrid systems.
The synthesis problem on hybrid systems, namely the problem
of synthesizing a hybrid system for achieving some
predetermined goal, is a forward consequence of
the studies on analysis of hybrid systems.
In the second part of the thesis,
we consider the framework of dynamical control systems,
proposing non-hybrid controllers
on continuous systems with bounds on the inputs, and hybrid controllers that,
by virtue of their discrete dynamics, guarantee suitable properties of the
closed loop. Is worth mentioning that the combination of a classical
continuous process and of a hybrid controller results in a hybrid system
that can be studied with the analysis tools developed in the first part of
the thesis. | en |
| description.tableofcontents | 1 The Hybrid Systems Framework
1.1 Hybrid Systems: Models and Solutions
1.2 Relations to Other Models
1.3 Basic Conditions
1.4 Stability
2 Stability of Homogeneous Systems
2.1 The Class of Hybrid Systems
2.2 Stability
2.2.1 Main Results
2.2.2 Sum of Squares Algorithm
2.2.3 Example
2.3 Overshoots and Instability
2.3.1 Main Results
2.3.2 Sum of Squares Algorithms
2.3.3 Example
2.4 Notes on Sum of Squares Implementation
3 Formal Verification of Hybrid Systems
3.1 A Model for Hybrid Systems
3.2 HTCTL
3.2.1 HTCTL and CTL
3.3 Abstractions
3.4 From HTCTL Formulas to Fixpoints
3.4.1 The Extended Hybrid System
3.4.2 From Time Intervals rop (ct, cj) to Time Intervals ≥(0,0)
3.4.3 From ∃ϕ1Uϕ2 and ∀ϕ1Uϕ2 to Fixpoints
3.5 The Verification Procedure
4 Control of Constrained Systems
4.1 Globally Stabilizing Quasi-Optimal Control of Planar Saturated Linear Systems
4.1.1 A Family of State Feedback Stabilizers
4.1.2 Parameter Selections for Quasi Time-Optimal Responses
4.1.3 Parameter Selections for Quasi Fuel-Optimal Responses
4.1.4 Simulation Examples
4.2 Model Recovery Anti-Windup for Rate and Magnitude Saturated Plants
4.2.1 Problem Definition
4.2.2 Plant-Order Anti-Windup Solution
4.2.3 Extended Anti-Windup Solution
4.2.4 Simulation Example
5 Case Studies of Hybrid Control Systems
5.1 Passification of Controllers via Time-Regular Reset Map
5.1.1 A Class of Nonlinear Reset Controllers
5.1.2 Passivity of the Reset Controller
5.1.3 Application to Feedback Systems
5.1.4 Simulation Example
5.2 Control over Network: Lazy Sensors
5.2.1 Problem statement
5.2.2 State feedback: synchronous approach
5.2.3 State feedback, asynchronous approach
5.2.4 Output feedback approach
5.2.5 Simulation example
6 Proofs | en |
| format.extent | 33892 bytes | - |
| format.extent | 3467143 bytes | - |
| format.mimetype | application/pdf | - |
| format.mimetype | application/pdf | - |
| language.iso | en | en |
| subject | hybrid systems | en |
| subject | stability | en |
| subject | verification | en |
| subject | formal methods | en |
| subject | reset | en |
| subject | nonlinear | en |
| subject | passivity | en |
| subject | Lyapunov | en |
| subject | temporal logic | en |
| subject.classification | ING-INF/05 Sistemi di elaborazione delle informazioni | en |
| title | Analisi di sistemi ibridi e progetto di controllori ibridi | en |
| title.alternative | Analysis of hybrid systems and design of hybrid controllers | en |
| type | Doctoral thesis | en |
| degree.name | Informatica e ingegneria dell'automazione | en |
| degree.level | Dottorato | en |
| degree.discipline | Facoltà di ingegneria | en |
| degree.grantor | Università degli studi di Roma Tor Vergata | en |
| date.dateofdefense | A.A. 2009/2010 | en |
| Appears in Collections: | Tesi di dottorato in ingegneria
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| thesis.pdf | | 3385Kb | Adobe PDF | View/Open |
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