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Lyapunov based analysis and controller synthesis for polynomial systems using sum-of-squares optimization

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lyapunov based analysis and controller synthesis for polynomial systems using sum-of-squares optimization
Author:	Jarvis-Wloszek, Zachary William.
Description:	141 p.
Notes:	Chair: Andrew K. Packard.
Notes:	Source: Dissertation Abstracts International, Volume: 65-02, Section: B, page: 0989.
Contained By:	Dissertation Abstracts International65-02B.
Subject:	Engineering, Mechanical.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3121531
ISBN:	0496688820

Lyapunov based analysis and controller synthesis for polynomial systems using sum-of-squares optimization
Jarvis-Wloszek, Zachary William.

Lyapunov based analysis and controller synthesis for polynomial systems using sum-of-squares optimization [electronic resource] - 141 p.

Chair: Andrew K. Packard.

Thesis (Ph.D.)--University of California, Berkeley, 2003.

Additionally, we extend the two local asymptotic stability algorithms to discrete time polynomial systems. Unfortunately, the structure of the local asymptotic stability Lyapunov theorem in discrete time does not allow for controller design using our iterative approach.

ISBN: 0496688820Subjects--Topical Terms:

212470
Engineering, Mechanical.

Lyapunov based analysis and controller synthesis for polynomial systems using sum-of-squares optimization
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245 1 0 $a Lyapunov based analysis and controller synthesis for polynomial systems using sum-of-squares optimization $h [electronic resource]
300 $a 141 p.
500 $a Chair: Andrew K. Packard.
500 $a Source: Dissertation Abstracts International, Volume: 65-02, Section: B, page: 0989.
502 $a Thesis (Ph.D.)--University of California, Berkeley, 2003.
520 # $a Additionally, we extend the two local asymptotic stability algorithms to discrete time polynomial systems. Unfortunately, the structure of the local asymptotic stability Lyapunov theorem in discrete time does not allow for controller design using our iterative approach.
520 # $a Since we do not always desire global results, we provide two algorithmic approaches to prove local stability. These approaches are coordinatewise convex and estimate the size of the system's region of attraction by finding the largest level set of a Lyapunov function on which the stability theorem's conditions hold. An example provides a graphical comparison of the two approaches. As with the global case, we then extend these algorithms to allow for state and output feedback controller design. Also, we derive bounds for the largest peak disturbance under which an invariant set remains invariant, and bounds for the local induced gain from disturbances to outputs on the set.
520 # $a This thesis considers a Lyapunov based approach to analysis and controller synthesis for systems whose dynamics are described by polynomials. We restrict the candidate Lyapunov functions as well as the controllers to be polynomials, so that the conditions in the Lyapunov theorem involve only polynomials. The Positivstellensatz delineates the exact manner to ascertain (i.e. "certify") if the theorem's conditions hold. For computational reasons we further restrict the choice of certificates to those, which, with fixed Lyapunov functions and controllers, can be checked using sum-of-squares optimization. Following these steps, we pose convex or coordinatewise convex (convex in one variable when the others are held fixed) iterative algorithms to search for Lyapunov functions and controllers.
520 # $a We provide a basic review of polynomials, the Positivstellensatz and the sum-of-squares optimization results, which gives the necessary background to follow the subsequent developments that lead to our proposed algorithms. First, we consider global stability by constructing convex algorithms to search for Lyapunov functions that demonstrate semi-global exponential stability. We then extend these algorithms in a coordinatewise convex form for both state and output feedback controller design. Additionally, we include a convex procedure to quantify a system's performance by bounding the induced norm from disturbances to outputs. Examples are included for illustration.
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790 1 0 $a Packard, Andrew K., $e advisor
791 $a Ph.D.
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