Dynamic feedback linearization of control systems with symmetry
type: Item
instance of: scholarly article
title: Dynamic feedback linearization of control systems with symmetry
author: Jeanne N. Clelland
author: Taylor J. Klotz
author: Peter J. Vassiliou
published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
publication date: 2024-08-15T00:00:00Z
review text: Control systems of interest are usually invariant under Lie groups of transformations. This paper formulates the geometric framework based on Lie symmetry for such control systems, and obtains from this a sufficient condition for dynamical feedback linearizability. Furthermore, a systematic procedure for obtaining all the smooth, generic system trajectories is shown to follow from the theory. Besides smoothness and the existence of symmetry, no further assumption is made on the local form of the control system, which is therefore permitted to be fully nonlinear and time varying. Likewise, no constraints are imposed on the local form of the dynamic compensator. Particular attention is given to the consideration of geometric (coordinate independent) structures associated to control systems with symmetry. To show how the theory is applied in practice, the authors work through illustrative examples of control systems, including the vertical take-off and landing system, demonstrating the significant role that Lie symmetry plays in dynamic feedback linearization. Besides these, a number of more elementary pedagogical examples are discussed as an aid to reading the paper. The constructions have been automated in the Maple package \textit{DifferentialGeometry}.
reviewed by: Yong Kui Chang
Mathematics Subject Classification ID: 37N35
Mathematics Subject Classification ID: 70Q05
Mathematics Subject Classification ID: 70H06
Mathematics Subject Classification ID: 70G45
Mathematics Subject Classification ID: 93B27
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 7897509
zbMATH Keywords: Lie symmetry reduction
zbMATH Keywords: contact structures
zbMATH Keywords: static feedback linearization
zbMATH Keywords: explicit integrability
zbMATH Keywords: flat outputs
zbMATH Keywords: principal bundle
MaRDI profile type: Publication
cites work: Exterior differential systems with symmetry
cites work: A linear algebraic framework for dynamic feedback linearization
cites work: Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states
cites work: A Geometric Approach to Dynamic Feedback Linearization
cites work: Q5597890
cites work: Sufficient Conditions for Dynamic State Feedback Linearization
cites work: Flatness of dynamically linearizable systems
cites work: On absolute equivalence and linearization I
cites work: Symmetry Reduction, Contact Geometry, and Partial Feedback Linearization
cites work: An Algorithm for Local Transverse Feedback Linearization
cites work: Q4240118
cites work: Flatness and defect of non-linear systems: introductory theory and examples
cites work: A Lie-Backlund approach to equivalence and flatness of nonlinear systems
cites work: Linearization by prolongations: new bounds on the number of integrators
cites work: An algorithm for feedback linearization
cites work: The GS algorithm for exact linearization to Brunovsky normal form
cites work: The structure of nonlinear control systems possessing symmetries
cites work: A structurally flat triangular form based on the extended chained form
cites work: Necessary and sufficient conditions for the linearisability of two-input systems by a two-dimensional endogenous dynamic feedback
cites work: A condition for dynamic feedback linearization of control-affine nonlinear systems
cites work: Nonlinear control design for slightly non-minimum phase systems: Application to V/STOL aircraft
cites work: Q3332867
cites work: Q3951974
cites work: Geometry of cascade feedback linearizable control systems
cites work: Q5731354
cites work: Analysis and control of nonlinear systems. A flatness-based approach
cites work: Multi-input control-affine systems static feedback equivalent to a triangular form and their flatness
cites work: On the largest feedback linearizable subsystem
cites work: Geometric properties of linearizable control systems
cites work: A different look at output tracking: Control of a VTOL aircraft
cites work: Geometric approach to Goursat flags
cites work: Flatness of Multi-Input Control-Affine Systems Linearizable via One-Fold Prolongation
cites work: Q4273954
cites work: Q4849745
cites work: A global formulation of the Lie theory of transformation groups
cites work: Some remarks on static-feedback linearization for time-varying systems
cites work: Q4856512
cites work: On dynamic feedback linearization of four-dimensional affine control systems with two inputs
cites work: Q3069276
cites work: Absolute equivalence and dynamic feedback linearization
cites work: A flat triangular form for nonlinear systems with two inputs: necessary and sufficient conditions
cites work: Linearization and input-output decoupling for general nonlinear systems
cites work: Differential Flatness and Absolute Equivalence of Nonlinear Control Systems
cites work: A constructive generalised Goursat normal form
cites work: Efficient construction of contact coordinates for partial prolongations
cites work: Cascade linearization of invariant control systems
DOI: 10.3842/SIGMA.2024.058
description: scientific article; zbMATH DE number 7897509