Close tracking of equilibrium paths

Summary A method to control a generic system of nonlinear ordinary differential equations between equilibrium states is analyzed. The objective is to ensure that the system's state space trajectory closely tracks an equilibrium path. The control law is obtained via time parameterization of the...

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Bibliographic Details
Published inInternational journal of robust and nonlinear control Vol. 28; no. 6; pp. 2209 - 2230
Main Author Sultan, Cornel
Format Journal Article
LanguageEnglish
Published Bognor Regis Wiley Subscription Services, Inc 01.04.2018
Subjects
Computation
Economic models
equilibrium path
Nonlinear differential equations
Nonlinear equations
nonlinear systems
Ordinary differential equations
Parameterization
System theory
Systems theory
Tracking
tracking control
tracking error bounds
Tracks (paths)
Trajectories
Upper bounds
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Summary:Summary A method to control a generic system of nonlinear ordinary differential equations between equilibrium states is analyzed. The objective is to ensure that the system's state space trajectory closely tracks an equilibrium path. The control law is obtained via time parameterization of the corresponding equilibrium control path. Conditions which guarantee that the system's state space trajectory closely tracks the equilibrium path are proved using two approaches. One approach uses the mean value theorem, and the other uses the slowly time‐varying systems theory. Importantly, both methods provide relationships between the control rate norm and the tracking error norm. These allow computation of upper bounds on the control rate norm which guarantee a desired upper bound on the tracking error norm. They also enable computation of upper bounds on the tracking error norm for a given upper bound on the control rate norm. Examples illustrate the theoretical results.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.4012