TY - GEN
T1 - Stability of adaptive delta modulators with a forgetting factor and constant inputs
AU - Dandach, Sandra Hala
AU - Dasgupta, Soura
AU - Anderson, Brian D.O.
PY - 2005
Y1 - 2005
N2 - Motivated by applications to feedback control over communication networks where the actuation and feedback signals are transmitted over communication channels, we study the stability of Adaptive Delta Modulators (ADM) when the coded signal is a constant. The importance of such a setting arises because a common control task is to track a dc input. In an earlier paper we had shown that a standard accumulator based adaptive delta modulator has the following characteristic: that virtually all combinations of the algorithm parameters result in 4-cycles, that the avoidance of 4-cycles requires a nongeneric initialization, and that steady state oscillations that generically arise in the course of these cycles can have amplitudes that can be arbitrarily close to the initial error. Consequently, in this paper we study the use of a forgetting factor in the ADM loop, and provide a detailed stability analysis and design guidelines.
AB - Motivated by applications to feedback control over communication networks where the actuation and feedback signals are transmitted over communication channels, we study the stability of Adaptive Delta Modulators (ADM) when the coded signal is a constant. The importance of such a setting arises because a common control task is to track a dc input. In an earlier paper we had shown that a standard accumulator based adaptive delta modulator has the following characteristic: that virtually all combinations of the algorithm parameters result in 4-cycles, that the avoidance of 4-cycles requires a nongeneric initialization, and that steady state oscillations that generically arise in the course of these cycles can have amplitudes that can be arbitrarily close to the initial error. Consequently, in this paper we study the use of a forgetting factor in the ADM loop, and provide a detailed stability analysis and design guidelines.
UR - http://www.scopus.com/inward/record.url?scp=33847202191&partnerID=8YFLogxK
U2 - 10.1109/CDC.2005.1583089
DO - 10.1109/CDC.2005.1583089
M3 - Conference contribution
SN - 0780395689
SN - 9780780395688
T3 - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
SP - 5808
EP - 5813
BT - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
T2 - 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Y2 - 12 December 2005 through 15 December 2005
ER -