Problem 6.8
An open problem in adaptative nonlinear
control theory
Leonid S. Zhiteckij
Int. Centre of Inform. Technologies and Systems
Institute of Cybernetics
40 Prospect Akademika Glushkova
MSP03680 Kiev 187
1 STATEMENT OF THE PROBLEM
2 MOTIVATION
In contrast to the adaptive control of nonlinear continuous-time systems, where substantial breakthroughs in the theoretical area have been achieved by the middle of the 1990s (see, e.g., [3], [5], etc.), very few similar works are available in the literature that address the global stable adaptive control design for discrete-time systems with nonlinearities [1], [2], [4], [6]-[8]. One of the inherent difficulties of discrete-time adaptive control is that the Lya-punov stability techniques typically exploited in the continuous time case may not be straightforwardly extended to its discrete-time counterpart, as detailed in [4], [6], [8]. It has been shown in Section II of [4], and in [8] and [9] that the so-called Key Technical Lemma, which has played a key role in analyzing the adaptation algorithms of type (5)-(7) applied to linear discrete-time systems, can be used to derive the stabilizability properties of adaptive nonlinear LP systems with a nonlinearity whose growth rate (2)
3 RELATED RESULTS
