Consensus algorithms constitute a powerful tool for computing average values or coordinating agents in many distributed applications. Unfortunately, the same property that allows this computation (i.e., the nontrivial nullspace of the state matrix) leads to unbounded state variance in the presence of measurement errors. In this work, we explore the trade-off between relative and absolute communication (feedback) in the presence of measurement errors. We evaluate the robustness of first and second-order integrator systems under a parameterized family of controllers (homotopy), that continuously trade between relative and absolute feedback interconnections, in terms of the H 2 norm of an appropriately defined input-output system. Our approach extends the previous H 2 norm-based analysis to systems with directed feedback interconnections whose underlying weighted graph Laplacians are diagonalizable. Our results indicate that any level of absolute communication is sufficient to achieve a finite H 2 norm, but purely relative feedback can only achieve finite norms when the measurement error is not exciting the subspace associated with the consensus state. Numerical examples demonstrate that smoothly reducing the proportion of absolute feedback in double integrator systems smoothly decreases the system performance (increases the H 2 norm) and that this performance degradation is more rapid in systems with relative feedback in only the first state (position).
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Disorder in large-scale networks with uni-directional feedback
This work investigates local and global measures
of disorder in large-scale directed networks of double-integrator
systems connected over a multi-dimensional torus. We quantify
these performance measures in systems subjected to distributed
disturbances using an H2 norm with outputs corresponding
to local state errors or deviations from the global average.
We consider two directed uni-directional state feedback inter-
connections that correspond to relative position and relative
velocity feedback in vehicle network applications. Our main
result reveals that absolute state feedback plays a critical role
in system robustness when local state measurements are uni-
directional. Specifically, if absolute measurements of either state
variable are available, then systems with uni-directional relative
feedback perform as well as their symmetric bi-directional
counterparts but have the advantage of reduced communication
requirements. However in the absence of absolute feedback
their performance is worse; in fact, it is impossible to maintain
stability (i.e. a finite H2 norm) with uni-directional state mea-
surements for arbitrarily large networks. Numerical examples
illustrate the theory.
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- Award ID(s):
- 1544771
- NSF-PAR ID:
- 10109816
- Date Published:
- Journal Name:
- American Control Conference
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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