Robust adaptive quantized DSC of uncertain pure‐feedback nonlinear systems with time‐varying output and state constraints

Abstract

In this paper, the problem of neural adaptive dynamic surface quantized control is studied the first time for a class of pure-feedback nonlinear systems in the presence of state and output constraint and unmodeled dynamics. The considered system is under the control of a hysteretic quantized input signal. Two types of one-to-one nonlinear mapping are adopted to transform the pure-feedback system with different output and state constraints into an equivalent unconstrained pure-feedback system. By designing a novel control law based on modified dynamic surface control technique, many assumptions of the quantized system in early literary works are removed. The unmodeled dynamics is estimated by a dynamic signal and approximated based on neural networks. The stability analysis indicates that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded, and the output and all the states remain in the prescribed time-varying or constant constraints. Two numerical examples with a coarse quantizer show that the proposed approach is effective for the considered system. KEYWORDSadaptive quantized control, output and state constraints, pure-feedback systems, robust adaptive DSC, unmodeled dynamics Int J Robust Nonlinear Control. 2018;28:3357-3375. wileyonlinelibrary.com/journal/rnc

A new approach to stabilization of high‐order nonlinear systems with an asymmetric output constraint

“…To be more specific, when the time‐varying parameters d i ( t )'s and nonlinearities ϕ ( t , x , u )'s involve uncertainties, with the aid of Assumptions and , a stabilizer given by can be explicitly constructed with the gain functions 's depending only on the upper/lower bounds of d i ( t )'s and ϕ ( t , x , u )'s. In the case when system suffers from bounded disturbances, robust adaptive schemes, which indeed play as efficient treatments of bounded disturbances, can be skillfully utilized to further develop a robust approach to the problem of stabilization for system with an asymmetric output constraint. Addressing this issue will be one of our future research directions.…”

Adaptive neural output feedback control for uncertain nonlinear systems with input quantization and output constraints

“…An output feedback control scheme based on dynamic surface method was presented for nonlinear system with input quantization, time‐varying output constraints, and unmodeled dynamics in the work of Xia and Zhang . Adaptive DSC was presented for a class of nonaffine nonlinear systems with input quantization and state and output constraints in the work of Xia and Zhang . An adaptive control strategy was developed for finite time input quantization in the other works .…”

“…18 Adaptive DSC was presented for a class of nonaffine nonlinear systems with input quantization and state and output constraints in the work of Xia and Zhang. 19 An adaptive control strategy was developed for finite time input quantization in the other works. 20,21 A fuzzy adaptive approach for stochastic strict-feedback nonlinear systems with quantized input signal was discussed in the work of Niu et al 22 Three adaptive control schemes with input or state quantization were investigated for uncertain systems with unknown control direction and guaranteed transient performance in the other works.…”

Adaptive dynamic surface control of stochastic nonstrict‐feedback constrained nonlinear systems with input and state unmodeled dynamics

“…5 Furthermore, a new adaptive DSC strategy was presented for a class of pure-feedback nonlinear systems with full state constraints and dynamic uncertainties in the work of Zhang et al 6 The adaptive control problem of uncertain pure-feedback nonlinear systems with quantized input and time-varying output constraints was discussed by using DSC in the work of Xia and Zhang. 7 Unmodeled dynamics caused by factors such as model simplification and external disturbances widely existed in practical nonlinear systems. Its existence degraded the performance of control system.…”

“…The requirements of dynamic uncertain terms for state unmodeled dynamics are relaxed without the lower triangle structure restriction about whole state vector in other works. [6][7][8][9][10][11]35,36 The normalization signal and a tuning parameter are used to deal with input unmodeled dynamics. Compared with integral or logarithmic BLF in other works, [14][15][16] the hyperbolic tangent function as nonlinear mapping is used to dispose of the output restrictions in probability in this paper.…”