Sequential predictors for delay compensation for discrete time systems with time-varying delays

Abstract

We study time-varying linear discrete time systems with uncertainties and time-varying measurement delays, whose outputs are perturbed by uncertainty. We build sequential predictors, which ensure input-to-state stability with respect to the uncertainties and which can be constructed using output values under arbitrarily long delays. The number of required sequential predictors is any upper bound for the delay in our feedback stabilized closed loop systems. We illustrate our work in a digital control problem for a continuous time system that is discretized through sampling.

Subpredictor approach for event-triggered control of discrete-time systems with input delays

“…for a = 3 to r, where the last equality is a consequence of the last equality in (19). We deduce that e a,k+1 = (A + R)e a,k + R 2 e a−1,k + ....…”

“…By providing a new design for event-triggered control for linear discrete-time systems with outputs and arbitrarily long constant input delays, we believe that this work is the first to use positive systems and interval observers to prove input-to-state stability (or ISS) for discrete-time systems with outputs whose delays are compensated by subpredictors. In particular, our work is novel relative to notable works on predictors that did not involve event triggering, such as [2], [3], [4], and [19]. For discrete-time systems, we do not have to rule out the possibility of Zeno's phenomenon.…”

“…Relative to previous methods, key novel features were our use of subpredictors, which made it possible to achieve an ISS-like result under an arbitrarily long constant input delay, and our event triggers that were based on matrices of absolute values instead of Euclidean norms. We hope to develop analogs for nonconstant delays, which could entail generalizing [19] (which did not allow event-triggering) to have the choice of the subpredictor in the control depend on the value of the delay, instead of choosing the last subpredictor in the control. Extensions to time-varying systems are also expected.…”

Predictor-based control of time-delay systems: a survey

“…discrete-time TDSs, sampled-data TDSs, NCSs. The discrete-time versions of (51) were analysed in (Mazenc & Malisoff, 2020b;Mazenc, Malisoff, & Bhogaraju, 2020) to compensate for the constant input delays and time-varying output delays, respectively. investigated the control of sampled-data linear systems with constant input delays: firstly dealt with perturbed LTI systems and (Mazenc & Malisoff, 2020a) proposed a control solution to perturbed LPV systems accompanying with experimental results on a DC motor.…”