Zero-error tracking control with pre-assignable convergence mode for nonlinear systems under nonvanishing uncertainties and unknown control direction

Tracking control of nonlinear systems with improved performance via transformational approach

“…Remark 8. When the error-dependent function transformation (9) and the time-varying scaling function transformation (33) are not applied into the control design, the proposed control scheme reduces to…”

“…12,[27][28][29][30][31] However, the corresponding lemma of Nussbaum function just prove the forward completeness property (namely, boundedness up to finite time), it is not clear that whether such lemma can guarantee the boundedness of all signals in the closed-loop systems over [0, ∞). Although the works of Zhao et al, 17 Zhang et al, 32 and Zhao et al 33 attempted to achieve asymptotic tracking for nonlinear systems in normal form under unknown control directions, the signals in the closed-loop systems are still bounded on a finite-time interval. Recently, a novel Nussbaum function-based adaptive control scheme is proposed in the work of Huang et al 34 for a class of strict-feedback nonlinear systems with external disturbances so that the asymptotic stabilization of system output is ensured, whereas the introduced integral function (t) is not considered explicitly in stability analysis and the transient tracking performance is not included in controller design.…”

“…= (t)z 1(33) with being defined in(30). † It should be stressed that although (t) is defined piecewise, it is continuous everywhere for ∀t ≥ 0 including t = T. ‡ The scaling function and its derivatives (i) , i = 1, … , n, are computable for control design but (n + 1) is only utilized for establishing the boundedness of control rateu.…”

Robust adaptive fault‐tolerant quantized control of nonlinear systems with constraints on system behaviors and states

“…Furthermore, it is highly desirable to achieve prescribed tracking performance specifications in many engineering systems, namely, the tracking error always preserves within a prescribed performance region. Up to now, there are some effective control methods on improving tracking performance, see for example, prescribed performance bound control, funnel control, and accelerated control . But it is noted that, thus far, there are no previous works of prescribed performance specifications that address the issue of quantized control for nonlinear systems under state constraints without involving feasibility conditions.…”

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

“…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.…”