Adaptive Neural Dynamic Surface Control of Pure-Feedback Nonlinear Systems With Full State Constraints and Dynamic Uncertainties

Adaptive control of pure‐feedback nonlinear systems with full‐state time‐varying constraints and unmodeled dynamics

“…However, it was assumed that the lower and upper bounds of control gains were known in the considered system. In other works, the constrained nonlinear system was transformed into the unconstrained nonlinear systems by designing nonlinear mapping; furthermore, based on the transformed system, adaptive control scheme was developed and output constraints were carried out. However, the obtained results only discussed the constant constraint problem in other works …”

“…"> ii.Compared with the results of adaptive controller design based on integral or logarithmic BLF, adaptive control design scheme is simpler by using hyperbolic tangent function as nonlinear mapping in this paper. In addition, the considered constraints are time‐varying functions in this paper, whereas they are constants in other works …”

“…However, the obtained results only discussed the constant constraint problem in other works. [26][27][28][29][30][31] Inspired by the aforementioned works, 18,19,22 this paper proposes a new adaptive control scheme for a class of pure-feedback systems with input and state unmodeled dynamics as well as full-state time-varying constraints. This paper has the following major contributions.…”

“…In addition, the considered constraints are time-varying functions in this paper, whereas they are constants in other works. [21][22][23][24][25][26][27][28][29][30][31] iii. By introducing an adaptive adjustable parameter in the design final step and adding nonnegative normalization signal into the whole Lyapunov function and using the defined compact set in the stability analysis, all signals in the whole system are proved to be semiglobally uniformly ultimately bounded (SGUUB), and all states can obey the full-state time-varying constraint conditions.…”

An improved adaptive dynamic surface control approach for uncertain nonlinear systems

“…Nevertheless, the backstepping design procedure suffers from the widely recognized "explosion of complexity" problem arising from the repeated derivations of the virtual controls. [27][28][29][30] Very recently, to deal with the unmodeled dynamics and state constraints, a neural network (NN) DSC approach was proposed for a class of strict-feedback systems in the work of Zhang et al, 31 and later, this method was extended to pure-feedback systems in other work of Zhang et al 32 Xia et al 33 proposed adaptive DSC (ADSC) scheme for stochastic pure-feedback nonlinear systems with state and input unmodeled dynamics. 3 After more than 10 years of development, the DSC design framework has enjoyed widespread applications in various types of dynamical systems, ranging from linear systems, [4][5][6] to strict-/semi-strict feedback uncertain systems, 7-13 to pure-feedback or nonaffine systems, [14][15][16][17][18] to constrained systems, [19][20][21][22] and to many more complex systems such as fault-tolerant systems, 23,24 stochastic systems, 25,26 and large-scale interconnected systems.…”