Thomas decompositions of parametric nonlinear control systems
Markus Lange-Hegermann, Daniel Robertz
TL;DR
This paper introduces a symbolic algorithm using Thomas decomposition to analyze how parameter variations affect the structural properties of nonlinear control systems, such as observability and flatness.
Contribution
It presents a novel algorithmic approach employing differential Thomas decomposition to classify parameter configurations impacting control-theoretic properties.
Findings
Identifies parameter sets influencing system behavior
Provides a symbolic method for structural analysis
Enables systematic study of nonlinear control systems
Abstract
This paper presents an algorithmic method to study structural properties of nonlinear control systems in dependence of parameters. The result consists of a description of parameter configurations which cause different control-theoretic behaviour of the system (in terms of observability, flatness, etc.). The constructive symbolic method is based on the differential Thomas decomposition into disjoint simple systems, in particular its elimination properties.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Control and Dynamics of Mobile Robots · Adaptive Control of Nonlinear Systems