Decentralized Discrete Model Reference Adaptive Control

Abstract

In this paper some results of direct decentralized adaptive control based on input/output methods are presented. The plant is assumed to have several local adaptive controllers, of which each local controller can observe only local systems outputs and control only local inputs. Conditions for the stability of the decentralized control scheme are derived using the I/O sector stability theorem of Safonov (1980). The associated error model of the adaptive scheme can be represented under the form of an equivalent feedback configuration formed by a non-linear, time-varying feedforward block describing the adaptation law and a linear, time-invariant feedback block, which depends on the interactions of the different control loops. Stability is obtained, if the blocks verify certain sector conditions. It will be demonstrated that conventional adaptation algorithms have to be modified. The proposed RLS parameter adaptation law differs from standard algorithms by the introduction of signal normalization, σ-modification and a variable forgetting factor. The allowable class of interactions is restricted by the sector condition for the linear feedback block. It will be shown, that less conservative conditions can be found when a parallel filter, the so called correction network, is introduced. Such filters make direct adaptive control possible even for nonminimum phase systems. In addition the correction network makes the adaptive controller robust to uncertainties in the structure of the plant e.g. missmodelled deadtime.