Application of local deformations in adaptive control — A comparative survey

In this paper a brief survey is provided on a novel approach to adaptive nonlinear control developed at Budapest Te c h in the past few years. The most popular branches of the classical and novel adaptive approaches are analyzed in comparison with methods needing complete, accurate, and permanent models or applying only partial, incomplete, temporal, and situation-dependent ones that require continuous refreshment via observing the behavior of the controlled system in the actual situation. It will be shown how simple geometric considerations can be used for developing iterative learning control. It will also be shown that in the case of the novel approach the conditions of convergence normally can be satisfied by choosing very primitive initial system models and roughly chosen control parameters on the basis of simple geometric considerations. It will be pointed out that while the traditional adaptive approaches are applicable only for learning linearly separable dynamical system parameters and fail for the permanent presence of unknown external disturbances and linearly non-separable (e.g. friction model) parameters, the novel approach can well compensate the simultaneous effects of imprecise and linearly non-separable model parameters and external perturbations, too. Since in contrast to the traditional solutions that normally guarantee global (asymptotic) stability by using Lyapunov functions, the novel approach can assure only local region of stability that in principle can be left by the system´s state, a real time simulation tool has been developed to study the robustness of the novel control versus the variation of the adaptive control parameters. It will also be stressed that the traditional approaches have a huge number of adaptive control parameters that generally cannot optimally be set, the novel approach have only a few control parameters that can easily be tuned by observing the behavior of the controlled system. The already achieved results will be e- xemplified by simulation studies using the same paradigm.