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

Abstract

For a class of non-strict-feedback nonlinear systems with input delay and saturation, the tracking control problem is addressed in this paper. An auxiliary system is constructed to handle the difficulty in control design caused by input delay. Moreover, hyperbolic tangent function is used to approximate the non-smooth saturation function to achieve controller design. The unknown nonlinear functions generated in backstepping control design are approximated by radial basis function neural networks. And then, with the help of backstepping approach, an adaptive neural control scheme is proposed. It is proved by Lyapunov stability theory that the tracking errors converge to a small neighbourhood of the origin and the other closed-loop signals are bounded. At last, a simulation example is able to verify the validity of this tracking control scheme.

Robust adaptive control design of nonlinear systems with input delay

“…A lot of work is done for the nonlinear systems with known delays. [15][16][17][18][19][20] State prediction based control law for the nonlinear systems with known delays is developed by Georges et al 15 Proof of global stability is given by Krstic 16 for the system with arbitrary length of delay, however it is applicable only to those systems which are stable without delay. Bekiaris et al 17 guaranteed closed-loop stability for the linear as well as nonlinear systems with the input delays which are functions of states.…”

“…All the above mentioned results obtained for linear systems can not be exactly applied to the class of nonlinear systems, hence, it becomes vital to determine the solutions for the delayed nonlinear systems, separately. A lot of work is done for the nonlinear systems with known delays 15‐20 . State prediction based control law for the nonlinear systems with known delays is developed by Georges et al 15 Proof of global stability is given by Krstic 16 for the system with arbitrary length of delay, however it is applicable only to those systems which are stable without delay.…”

“…Uniformly ultimate boundedness of nonlinear systems with unknown constant delay is proved by designing an adaptive fuzzy sliding mode controller by Khazaee et al 18 In Reference 19, the authors Deng et al proposed tracking control of input delayed nonlinear systems with time‐varying output constraints, parametric uncertainties and additive disturbances, which requires the exact knowledge of input delay and it's first and second derivatives to be bounded by known positive constants. An adaptive neural control scheme based backstepping control design is used to solve tracking problem for the nonlinear systems with input delay and saturation by Li et al 20 Some more results based on robust control design are available for the nonlinear systems that is, Euler‐Lagrange system with known input delays 21 . Despite above mentioned results, the challenge of solving the problem of nonlinear systems with unknown input delay, uncertainty in dynamical parameters and disturbances, is still an open problem.…”

Fixed‐time adaptive tracking control for MIMO nonlinear system with input delay saturation based on echo state network

“…In recent years, many studies on input delay compensation for nonlinear systems have been published in refs. [15][16][17]. In ref.…”

“…In addition, input delays and saturation of nonlinear systems were addressed in ref. [16]. Meanwhile, system control involving saturation is a challenging topic.…”