Delay-Adaptive Predictor Feedback for Systems With Unknown Long Actuator Delay $ $

Abstract

Stabilization of an unstable system with an unknown actuator delay of substantial length is an important problem that has never been attempted. We present a Lyapunovbased adaptive control design, prove its stability and regulation properties for the plant and actuator states, and present a simulation example inspired by the problem of control of pitch and flight path rates in the unstable X-29 aircraft.

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

“…The existence of time delay may result in unexpected degradation in control performance and even instability. 1 Hence, how to effectively attenuate the effect of time delay has always been the research hotspot during the latest several decades, with numerous control schemes proposed, such as previous studies [2][3][4][5][6][7][8][9][10][11][12] for input delay and other studies [13][14][15][16][17][18] for state delay. Especially in Sun et al 17 and Sun and Liu, 18 stabilization of high-order uncertain nonlinear systems with state delays were investigated by using adaptive approach.…”

“…21 In addition, many predictive controllers have also been synthesized based on the fact that the input delayed systems can be modeled as hyperbolic differential equations, examples like in previous studies. [7][8][9][10][11]22 Especially in Krstic and Smyshlyaev, 11 by modeling the first-order time delayed system as an ordinary differential equation-partial differential equation cascade where the nondelayed input acts at the partial differential equation boundary, the backstepping method was used to develop an input delay compensation controller. Due to the difficulty of stability analysis, the abovementioned predictive approaches and their variations have been mainly used to solve the input delay problem for linear systems or linearizable nonlinear systems, which greatly limits their usage in practical nonlinear systems.…”

“…For instance, the backstepping approach in Mazenc and Bliman 23 was developed for nonlinear systems in feedback form with input delay by constructing an LK functional. Approaches in previous studies [7][8][9][10][11] were extended to nonlinear systems with arbitrary large input delay in Krstic. 24,25 The compensation problem of input delay for nonlinear systems with both input and state delays of arbitrary length was solved in Bekiaris-Liberis.…”

Control of thermodynamical system with input-dependent state delays

“…Krstic is with the Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411, USA krstic@ucsd.edu trajectories. Building on results developed in [3], [9] and [10] tackled a system that is superficially similar to the cooling system considered in this paper (mixing hot and cold water in a shower), but in their case the transport delay was treated as an input delay and some of the aforementioned complications could thus be avoided (although the design still turned out to be quite complex).…”

An adaptive control scheme for hyperbolic partial differential equation system (drilling system) with unknown coefficient

“…Particularly, we consider the wave equation describing the dynamics of the deformation denoted by z(x,t).The research activities in boundary control field were devoted to parabolic PDEs in the early 2000s [1]. In recent years, however, more attention has been given to the hyperbolic PDEs and in particular to the stabilization of such dynamics [2][3][4][5].Many physical systems can be described by first-order hyperbolic PDEs, such as traffic flow, heat exchangers [20].Subsequently, in [6] systems with unknown input delay, i.e., an important class of infinite dimensional systems with first-order hyperbolic PDE dynamics is tackled. In [18][19] sufficient condition for exponential stability for various class of nonlinear first-order hyperbolic PDE system is given.…”