Two‐stage stability control for strict‐feedback systems with input delays and input nonlinear uncertainties

Abstract

Summary In this paper, a two‐stage control procedure is proposed for stabilization of a class of strict‐feedback systems with unknown constant time delays and nonlinear uncertainties in the input. A nominal controller is first designed to compensate input time delays without considering input nonlinear uncertainties. Extended from backstepping algorithm, input delay compensation is realized by means of predicted states that are computed through integration of cascaded system dynamics, making the nominal closed‐loop system asymptotically stable. Based on the nominal controller presented for the input delay system, a multi‐timescale system is subsequently developed to estimate the unknown input nonlinearity and make the estimate approach the nominal control input as fast as possible. It is proved that the proposed control scheme can make states of the strict‐feedback systems converge to zero and all the signals of the closed‐loop systems are guaranteed to be bounded in the presence of input time delays and nonlinear uncertainties. Simulation verification is carried out to illuminate the effectiveness of the proposed control approach.

Adaptive compensation control for special actuator circumstances with input quantization

“…In practical control systems, it is necessary to take into consideration special circumstances of actuators to achieve satisfactory performance 11‐13 . One potential issue is input saturation constraint which is ubiquitous for the power provided by actual actuators is limited, and in some cases, a saturated input signal may lead to adverse effects such as performance degradation and system instability.…”