Further Results on the Use of Nussbaum Gains in Adaptive Neural Network Control

Tracking control of nonlinear systems with improved performance via transformational approach

“…However, a careful examination of the proof of reveals that the bounds of V and χ obtained are dependent on finite time t f , it is not clear that whether the finite time t f can be extended to infinity. As shown in the work of Psillakis, an explicit answer to such question is provided, which proves that the boundedness for all time cannot be obtained from (the interested readers can read the detailed analysis in the aforementioned work). In this paper, we use the integrable functions ε i ( t ), i = 1,…, n , to robustly handle the disturbances novelly, such that t f in Lemma could be extended to ∞ .…”

Unifying adaptive control with the nonlinear PI methodology: Designs for unknown strict‐feedback nonlinear systems with nonsmooth actuator nonlinearities

“…5 Moreover, actuation sign errors have been observed in attitude control of microsatellites. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] On the other hand, the nonlinear PI method provides an effective alternative strategy to the unknown control direction problem (see section 6 in the work of Ortega et al 1 ). 7 This approach has received increased popularity over the years as it provides a design tool for general classes of systems and can be combined successfully with parameter adaptation algorithms.…”

A new adaptive controller for bio-reactors with unknown kinetics and biomass concentration: Guarantees for the boundedness and convergence properties

“…Indeed, if the controller is properly devised, upper or lower bounds of plant parameters are not required to be known. The main drawbacks of the Nussbaum gain method are: (i) the upper bound of the transient behavior of the tracking error is significantly modified in comparison with that of the disturbance-free case, as the value of this bound depends on the time integral of terms that comprise the Nussbaum terms, (see [33,37,9,10,14,12,11,41,8]); (ii) upper or lower bounds of the plant coefficients are required to be known to achieve asymptotic convergence of the tracking error to a residual set of user-defined size, as in [33,10,14,12,13,6,39,21]; (iii) the control or update law involves signum type signals, as in [37,9,11,41,8,32]. In addition, several assumptions on the control gain are usually required: (iv) the control gain is assumed to be the product of an unknown constant and a known function, as in [39,21]; (v) the control gain is assumed upper bounded by some unknown constant, as in [33,37,9,10,14,12,11,41,8]; (vi) the control gain is assumed upper bounded by a known function, as in [13,32].…”