Adaptive dynamic surface asymptotic tracking for a class of uncertain nonlinear systems

Abstract

Summary This paper contributes to dynamic surface asymptotic tracking for a class of uncertain nonlinear systems in strict‐feedback form. By utilizing the nonlinear filters with a positive time‐varying integral function, an adaptive state feedback controller is explicitly designed via a dynamic surface approach, where the compensating term with the estimate of an unknown bound is introduced to eliminate the effect raised by the boundary layer error at each step. Compared with the existing results in the literature, the proposed control scheme not only avoids the issue of “explosion of complexity” inherent in the backstepping procedure but also holds the asymptotic output tracking. Finally, simulation results are presented to verify the effectiveness of the proposed methodology.

Adaptive asymptotic stabilization of a class of unknown nonlinear systems with specified convergence rate

“…Employing the presented adaptive control algorithm (5) to (8) obeying rule (4) of parameter selections guarantees the following.…”

“…In other works, [16][17][18][19]27,28,40 applying the state constraint scheme − guarantees the biased convergence of the constrained variables to zero, although the bounds of the steady-state errors are adjustable and known in advance. In this paper, the state constraint technique is newly introduced to the adaptive design (8) to generate an adaptive gainr, which is able to compensate for the unknown nonlinearities completely such that asymptotic stabilization can be achieved. Moreover, a technical lemma (Lemma 1) is provided for the subsequent stability analysis.…”

“…Remark 3. Careful inspections of the aforementioned design procedures (5) to (8) reveal that, despite the presence of unknown nonlinearities, no approximating structures such as NNs employed in related works [14][15][16][17][23][24][25] or fuzzy logic systems utilized in other works [25][26][27] are incorporated into the controller. As a result, no extra adaptive or learning parameters need to be updated online.…”

“…One of the powerful tools in coping with unmodeled dynamics is the adaptive technique. [1][2][3][4][5][6][7][8][9][10][11][12][13] An exponential Lyapunov stability for unknown linear time invariant systems was provided in the work of Miller and Davison. 4 Toward the system with parametric uncertainties, asymptotic stability was guaranteed by other works.…”

“…4 Toward the system with parametric uncertainties, asymptotic stability was guaranteed by other works. [5][6][7][8] In the presence of nonlinear function uncertainties or unmatched disturbances, uniformly ultimately bounded (UUB) stability was preserved in the works of Polycarpou and Ioannou 9 and Pan and Başar, 10 ie, the convergence of certain variables to a residual set was achieved, whose size is adjustable but unknown in advance. In the case of control direction uncertainties, zero-error tracking control with predefined convergence mode was accomplished in the work of Zhao et al 11 In the absence of persistent excitation, exponential regulation of system states and asymptotic constancy of parameter estimates were realized in the work of Song et al 12 To make the error decay rate as fast as exponential or even faster, an accelerated adaptive control strategy was proposed by Song and Zhao.…”