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Quotient Methods for Approximate Linearization of Nonlinear Dynamical

English title Quotient Methods for Approximate Linearization of Nonlinear Dynamical
Applicant Müllhaupt Philippe
Number 117573
Funding scheme Project funding
Research institution Laboratoire d'automatique EPFL - STI - IGM - LA1
Institution of higher education EPF Lausanne - EPFL
Main discipline Information Technology
Start/End 01.10.2007 - 30.09.2009
Approved amount 94'605.00
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Keywords (4)

commande non linéaire; géométrie différentille; Quotient Methods Approximate Linearization; Nonlinear Dynamical Systems

Lay Summary (English)

Lead
Lay summary
This project deals with the design of efficient control laws for complex nonlinear dynamical systems. The control problem is addressed from the perspective of obtaining a suitable transformation of the original system to an hopefully more manageable one with new inputs. The equivalence, or near-equivalence, of the two problems is solved by finding a change of coordinates and an appropriate feedback law. This task is nontrivial due to the presence of a large number of states and intricate couplings between them. Hence, it would be very helpful to have a systematic method for solving a succession of smaller equivalence problems in some iterative way. In addition, the transformation and the resulting level of equivalence should be such that the synthesis of a controlled system for the transformed representation is simpler and sufficiently accurate to be applied safely to the original system. The project has a strong mathematical flavor. The contribution of the proposed research lies in the use of quotient subspace methods for solving a specific nonlinear control problem and proposing a useful type of equivalence. The result is an approximation of exact feedback linearization, where dimensionality reduction is obtained by the use of iterative quotient operations. These operations are performed algebraically and, at each stage, represent an equivalent class of problems. Quotient subspace methods are generalization of projections methods used in linear algebra. They provide an appropriate theoretical framework for dealing with more abstract mathematical objects such as differential algebraic modules and differential manifolds that are used to describe nonlinear systems In the present context, the mathematical objects are manifolds for which vector fields and differential forms can be defined. This way, equivalent classes between vector fields and differential forms result naturally, thereby leading to the appropriate notion of quotient after invoking suitable integrability conditions. The purpose of the proposed research is to elaborate an efficient approximate linearization methodology for nonlinear input-affine systems. This methodology considers the main nonlinearities and uses feedback with time-scale decomposition to overcome the effects that initially blocked the linearization process.
Direct link to Lay Summary Last update: 21.02.2013

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Associated projects

Number Title Start Funding scheme
126916 Iterative Methods for Nonlinear Control 01.10.2009 Project funding

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