Discrete-time Adaptive Regulation of Systems with Uncertain Upper-bounded Input Delay: A State Substitution Approach

Abstract

This paper proposes a discrete-time adaptive regulation approach for scalar linear time-invariant systems with unknown, constant input time delay that has a known upper-bound, without explicitly estimating the time delay. To cope with the unknown time delay, a state substitution is made that results in a delay free system that simplifies the control law design. In addition, the proposed approach does not require that the system have stable open-loop zeros. A stability analysis shows that the proposed regulator drives the system state to zero asymptotically and simulation results are shown to verify the approach.

Discrete‐time adaptive control of uncertain sampled‐data systems with uncertain input delay: a reduction

“…The approach taken here may be considered an application of Artstein's model reduction to the discrete‐time case, with the modifications needed to support stable adaptive laws. [An earlier version of this work which also applied only to scalar systems was presented in [22]. For a different approach, see also [23]. ]…”

Disturbance Compensating Adaptive Regulator for MIMO Time-Delayed Discrete-Time Systems

“…This paper proposes a discrete-time adaptive regulator for uncertain LTI plants with input time delays, subject to unmeasurable disturbances. It is based on previous work by the authors, where Artstein's reduction was applied as part of an adaptive controller for an uncertain scalar LTI plant [7]. This was later extended to the n th order SISO case with disturbance in [8] (in press).…”