Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 55, Issue 2, Pages 367-377Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2009.2034937
Keywords
Gradient systems; lie groups; observers; synchrony
Funding
- Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems
- Australian Research Council [DP0987411]
- Australian Research Council [DP0987411] Funding Source: Australian Research Council
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This paper proposes a design methodology for nonlinear state observers for invariant kinematic systems posed on finite dimensional connected Lie groups, and studies the associated fundamental system structure. The concept of synchrony of two dynamical systems is specialized to systems on Lie groups. For invariant systems this leads to a general factorization theorem of a nonlinear observer into a synchronous (internal model) term and an innovation term. The synchronous term is fully specified by the system model. We propose a design methodology for the innovation term based on gradient-like terms derived from invariant or non-invariant cost functions. The resulting nonlinear observers have strong (almost) global convergence properties and examples are used to demonstrate the relevance of the proposed approach.
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