Predictor-Feedback Stabilization of Multi-Input Nonlinear Systems

Abstract

We develop a predictor-feedback control design for multi-input nonlinear systems with distinct input delays, of arbitrary length, in each individual input channel. Due to the fact that different input signals reach the plant at different time instants, the key design challenge, which we resolve, is the construction of the predictors of the plant's state over distinct prediction horizons such that the corresponding input delays are compensated. Global asymptotic stability of the closed-loop system is established by utilizing arguments based on Lyapunov functionals or estimates on solutions. We specialize our methodology to linear systems for which the predictor-feedback control laws are available explicitly and for which global exponential stability is achievable. A detailed example is provided dealing with the stabilization of the nonholonomic unicycle, subject to two different input delays affecting the speed and turning rate, for the illustration of our methodology.

Robustness to diffusion of prediction-based control for convection processes

“…In this paper, we proved that prediction-based controller for linear systems subject to a single input-delay are robust to diffusion in the actuation path. Future works should investigate the extension of this property to systems subject to multiple input-delays [3], [22].…”

Adaptive neural tracking control for a class of nonlinear systems with input delay and saturation

“…Krstic (2009) gives an approach to compensate input delay for strict-feedforward nonlinear systems. The predictor-based technique is used to offset the input delay for nonlinear systems in (Bekiaris-Liberis & Krstic, 2012Krstic, , 2016. Furthermore, Kamalapurkar et al (2015) and Obuz et al (2017) propose the proportional integral derivative control schemes that can solve the input delay problem of nonlinear systems.…”

Predictor-feedback synthesis in coordinate-free formation control under time-varying delays

“…Hence, time delays become a relevant issue in the stability analysis of formation control systems. Although the stability analysis in the presence of delays has been investigated in different problems involving cooperative control of multi-agent systems, such as consensus control [12,13], leader-following formation control [14][15][16] and coordinate-free formation control [9], little attention has been paid to investigate advanced control strategies based on delay compensation [17][18][19][20] in order to counteract their negative effects.…”