Asymptotic Hyperstability Research Articles

A series-parallel (SP) identifier with variable relaxation gains

Variable relaxation gains are introduced into the series-parallel (SP) identifier [1]-[5]. These gains are positive functions of the tracking error between the process and identifier outputs. The asymptotic hyperstability of the SP identifier with variable relaxation gains is proved theoretically and demonstrated experimentally. On-line computational requirements and minicomputer experiments of the SP identifier with constant and variable relaxation gains are summarized and compared.

A Series-Parallel Identifier With Auxiliary Signals

Auxiliary signals which are proportional to the tracking error between the process and identifier outputs are introduced into the series-parallel (SP) identifier [1-2]. The coefficients of these auxiliary signals are updated at each computational cycle. The asymptotic hyperstability of the resulting SP identifier with variable relaxation gains is proved theoretically and demonstrated experimentally. Computational considerations for implementing SP identifiers are noted and the on-line computational requirements of the two SP identifiers are then compared.

An extension of hyperstable adaptive control to non-minimum phase systems

In this paper the model reference adaptive control design of Suzuki and Takashima (1978) is extended to permit application to non-minimum phase systems. It is shown that the control system of Suzuki and Takashima does not explicitly include an a priori bounded plant input-output assumption necessary for their proof of asymptotic hyperstability. Although not stated explicitly, the same assumption of bounded input to the linear block is also a necessary condition for Landau' s theorems on hyperstability which have been used as the basis for many adaptive control investigations.