1.1. The origin of our work on symbolic computation for nonlinear control all-apr-2000.add:
3.1. The PDE leading to the nonlinear control law all-apr-2000.add:
3.2. Iterative calculation of the nonlinear state-feedback control law all-apr-2000.add:
5.2. Design of nonlinear extended filters all-apr-2000.add:
Appendix 1. Symbolic computation tools for nonlinear control all-apr-2000.add:design of nonlinear extension of linear series compensators, to the design of all-apr-2000.add:a nonlinear extension of a typical combination of linear series and parallel all-apr-2000.add:compensators for the n-th order nonlinear dynamical control systems. all-apr-2000.add:would allow to design nonlinear extensions of virtually any combination of all-line.add:=ADD==author=Bajer; Jiri + Lisonek; Petr=title=symbolic computation approach to nonlinear dynamics=year=1991=journal=Journal of Modern Optics=volume=38=pages=719-729=location=2=owner=2=source=3=reftype=0 all-line.add:=ADD==reftype=14=number=97-37=url=ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1997/97-37.ps.gz=note=PhD Thesis=sponsor=ACCLAIM project sponsored by the European Community Basic Research Action(ESPRIT 7195) and the Austrian Science Foundation (FWF Project No. P9374-PHY);CEI PACT project sponsored by the Austrian Ministry of Science and Research.=year=1997=author=Neubacher; Andreas=title=Parametric Robust Stability by Quantifier Elimination=month=11=abstract=Stability analysis is a central aspect of the theory of differentialequations, especially for parameterized problems; one application areawhere parametric stability plays an important rôle is control theory. Themain goals of this thesis are to apply a quantifier elimination frameworkconsistently to various stability problems and to develop specializedmethods that solve these problems either symbolically or numerically withmathematically guaranteed exactness more efficiently than generalquantifier elimination methods.As a first step, known parametric robust stability problems and knownmethods for solving parameter-free problems are formulated in a generalquantifier elimination framework. This approach extends work done by otherauthors on applying quantifier elimination theory to robust control andparametric design problems.A known stability test based on positiveness of the Hurwitz determinant isgeneralized and new proofs are given for this test as well as forKharitonov's theorem.In the case where parameters appear linearly and independently, a newmethod for exactly computing the stability margin is presented.In the case where parameters appear nonlinearly and depedently, new methodsfor computing a lower bound on the stability margin and for exactlycomputing the stability margin are developed.Finally, a framework and a general method for approximate quantifierelimination are presented.=location=2=owner=2=source=3 all-line.add:=ADD==reftype=14=number=99-24=url=ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1999/99-24.ps.gz=year=1999=month=08=author=Rodriguez-Millan; Jesus=title=Nonlinear Control by Extended Linearization: A Symbolic Computation Approach=abstract=Table of Contents:
1. Introduction
1.1. The origin of our work on symbolic computation for nonlinear control
2. Jacobian and extended linearization
2.1. General design strategy
2.2. Which systems might be stabilized by extended linearization?
3. Extended state-feedback control
3.1. The PDE leading to the nonlinear control law
3.2. Iterative calculation of the nonlinear state-feedback control law
3.3. NLFeedback and NLFeedback 2.0
4. Extended PID control
5. Control devices as filters
5.1. The two-blocks decomposition approach
5.2. Design of nonlinear extended filters
6. Extended Lag-Lead Control
6.1. Two-blocks decomposition of a linear lag-lead compensator
6.2. Symbolic algorithmic calculation of the linear gains
7. NLControl
8. Concluding remarks
References
Appendix 1. Symbolic computation tools for nonlinear control
Complementary references=keywords=control systems all-line.add:=ADD==reftype=14=number=99-25=url=ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1999/99-25.ps.gz=year=1999=month=08=author=Rodriguez-Millan; Jesus=title=Integrated Symbolic--Graphic--Numeric Computation Tools for Dynamical Nonlinear Control Systems=abstract=In this work we extend our previous two-blocks decomposition approach for thedesign of nonlinear extension of linear series compensators, to the design ofa nonlinear extension of a typical combination of linear series and parallelcompensators for the n-th order nonlinear dynamical control systems.This particular extension shows how the two-blocks decomposition approachwould allow to design nonlinear extensions of virtually any combination ofcompensators.We illustrate the results by applying them to a model of the centrifugalpendulum in Watt's governor.=keywords=control systems all-sorted.add:=ADD==author=Bajer; Jiri + Lisonek; Petr=title=symbolic computation approach to nonlinear dynamics=year=1991=journal=Journal of Modern Optics=volume=38=pages=719-729=location=2=owner=2=source=3=reftype=0 all-sorted.add:=ADD==reftype=14=number=97-37=url=ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1997/97-37.ps.gz=note=PhD Thesis=sponsor=ACCLAIM project sponsored by the European Community Basic Research Action(ESPRIT 7195) and the Austrian Science Foundation (FWF Project No. P9374-PHY);CEI PACT project sponsored by the Austrian Ministry of Science and Research.=year=1997=author=Neubacher; Andreas=title=Parametric Robust Stability by Quantifier Elimination=month=11=abstract=Stability analysis is a central aspect of the theory of differentialequations, especially for parameterized problems; one application areawhere parametric stability plays an important rôle is control theory. Themain goals of this thesis are to apply a quantifier elimination frameworkconsistently to various stability problems and to develop specializedmethods that solve these problems either symbolically or numerically withmathematically guaranteed exactness more efficiently than generalquantifier elimination methods.As a first step, known parametric robust stability problems and knownmethods for solving parameter-free problems are formulated in a generalquantifier elimination framework. This approach extends work done by otherauthors on applying quantifier elimination theory to robust control andparametric design problems.A known stability test based on positiveness of the Hurwitz determinant isgeneralized and new proofs are given for this test as well as forKharitonov's theorem.In the case where parameters appear linearly and independently, a newmethod for exactly computing the stability margin is presented.In the case where parameters appear nonlinearly and depedently, new methodsfor computing a lower bound on the stability margin and for exactlycomputing the stability margin are developed.Finally, a framework and a general method for approximate quantifierelimination are presented.=location=2=owner=2=source=3 all-sorted.add:=ADD==reftype=14=number=99-24=url=ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1999/99-24.ps.gz=year=1999=month=08=author=Rodriguez-Millan; Jesus=title=Nonlinear Control by Extended Linearization: A Symbolic Computation Approach=abstract=Table of Contents:
1. Introduction
1.1. The origin of our work on symbolic computation for nonlinear control
2. Jacobian and extended linearization
2.1. General design strategy
2.2. Which systems might be stabilized by extended linearization?
3. Extended state-feedback control
3.1. The PDE leading to the nonlinear control law
3.2. Iterative calculation of the nonlinear state-feedback control law
3.3. NLFeedback and NLFeedback 2.0
4. Extended PID control
5. Control devices as filters
5.1. The two-blocks decomposition approach
5.2. Design of nonlinear extended filters
6. Extended Lag-Lead Control
6.1. Two-blocks decomposition of a linear lag-lead compensator
6.2. Symbolic algorithmic calculation of the linear gains
7. NLControl
8. Concluding remarks
References
Appendix 1. Symbolic computation tools for nonlinear control
Complementary references=keywords=control systems all-sorted.add:=ADD==reftype=14=number=99-25=url=ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1999/99-25.ps.gz=year=1999=month=08=author=Rodriguez-Millan; Jesus=title=Integrated Symbolic--Graphic--Numeric Computation Tools for Dynamical Nonlinear Control Systems=abstract=In this work we extend our previous two-blocks decomposition approach for thedesign of nonlinear extension of linear series compensators, to the design ofa nonlinear extension of a typical combination of linear series and parallelcompensators for the n-th order nonlinear dynamical control systems.This particular extension shows how the two-blocks decomposition approachwould allow to design nonlinear extensions of virtually any combination ofcompensators.We illustrate the results by applying them to a model of the centrifugalpendulum in Watt's governor.=keywords=control systems