Prediction‐Based Control for Nonlinear Systems with Input Delay

Abstract

This work has two primary objectives. First, it presents a state prediction strategy for a class of nonlinear Lipschitz systems subject to constant time delay in the input signal. As a result of a suitable change of variable, the state predictor asymptotically provides the value of the state units of time ahead. Second, it proposes a solution to the stabilization and trajectory tracking problems for the considered class of systems using predicted states. The predictor-controller convergence is proved by considering a complete Lyapunov functional. The proposed predictor-based controller strategy is evaluated using numerical simulations.

Observer‐based predictor for a susceptible‐infectious‐recovered model with delays: An optimal‐control case study

“…There are two main difficulties in establishing the stability of ( 17): The time-varying nature of B 0 , and the presence of the delayed state. The former difficulty will be addressed by formulating (17) in the framework of polytopic differential inclusions (Reference 22, chapter 5). In order to do so, we will focus on the state-space rectangle [0, 1] × [0,Ī], where I max ≤Ī ≤ 1.…”

“…An obvious necessary condition for the stability of the polytopic model (17,18,19) is the stability of its linearized vertices,…”

“…Figure 6 shows the boundaries of the stability regions for a larger delay, = 2.5, but a smaller incidence,Ī = 0.03. Since stability of the three vertices is a necessary condition for the stability of (17,18,19), we require to be placed at the intersection of the three regions (boundaries drawn in black), for example, at an approximate centroid of the intersection (marked with ⋆).…”

“…Also, it is readily applicable to the case of partial state information in observable systems, especially when observers are readily available. Systems with state delays 16 or nonlinear systems 17 can be modified easily to successfully compensate for input or output delays.…”

Consensus Problem for Linear Time‐Invariant Systems with Time‐Delay

“…It should be pointed out that a predictor of the form (23) with = 1 designed for a system with time delay at the output was considered in [25]; also, for the case = 1, in [44] a predictor for a nonlinear input delay system is designed. As mentioned before, the partitioned predictor presented in [31] is similar to the one presented in this section, considering = .…”