New prediction approach for stabilizing time-varying systems under time-varying input delay

Abstract

We provide a new sequential predictors approach for the exponential stabilization of linear time-varying systems with pointwise time-varying input delays. Our method circumvents the problem of constructing and estimating distributed terms in the stabilizing control laws, and allows arbitrarily large input delay bounds. We illustrate our method using a pendulum dynamics.

Sequential predictors under time-varying delays: Effects of delayed state observations in dynamic controller

“…whose state x and control u are valued in R n and R , respectively, for any dimensions n and , where h : R → [0, +∞) is a known time-varying delay. The dynamics (1) will be interconnected with a dynamic controller whose right side uses delayed values x(t − τ (t)) of the state, where the delay τ : R → [0, +∞) may differ from h. We make these assumptions, which agree with those of [12] when τ = 0: Assumption 1: The nonnegative valued functions h and τ are C 1 and bounded from above by constants c h > 0 and c τ ≥ 0 respectively, their first derivativesḣ andτ have finite lower bounds,ḣ andτ are bounded from above by constants l h ∈ (0, 1) and l τ ∈ (0, 1) respectively, andḣ has a global Lipschitz constant n h > 0.…”

“…Therefore, this work studies the combined effects of (i) feedback delays h(t) in the original system and (ii) measurement delays τ (t) in the sequential predictors. As in our team's paper [12], the new method in this work can allow arbitrarily long feedback delays h(t) in the original system, but [12] did not allow delays τ (t) in the state values in the sequential predictors, and in addition, we illustrate below how our new method can lead to a smaller number of required sequential predictors than were required by [12]. Hence, this work can benefit engineering systems that contain measurement delays, and reduce the computational burden relative to [12].…”

“…Malisoff and Weston were supported by NSF Grant 1408295. [12] require that the current state x(t) of the original systems be available to use in the predictors when the control is computed. This can be a limitation when the sequential predictor must be computed on a computer that is far from the physical system, which can cause delays in the transmission of the state measurements from the physical system to the dynamic controller.…”

Super-Twisting Algorithm-Based Time-Varying Delay Estimation With External Signal

“…Several control techniques are proposed to compensate TDS with known constant or time-varying delay (e.g. Smith predictor [2], prediction-based controller [3]- [5]). Therefore, time-delay estimation (TDE) is an effective way to achieve the stabilization of TDS with unknown time-delay.…”

State feedback control and delay estimation for LTI system with unknown input-delay

“…The Smith predictor is extended to the state-space method by finite spectrum assignment (FSA) (Manitius & Olbrot, 1979) and reduction method (Artstein, 1982). The predictorbased controller (Karafyllis & Krstic, 2017;Cacace, Conte, Germani, & Pepe, 2016;Mazenc & Malisoff, 2016) is a new extension of the Smith predictor that stabilizes linear and nonlinear systems with constant or time-varying delays. Another advantage of the predictor-based controller is the robustness with respect to the slight delay mismatch (Bresch-Pietri & Petit, 2014).…”