Several algorithms for finite-model adaptive control partial answers to finite-model adaptive control problem

Finite-model adaptive control problem is studied for a class of discrete-time nonlinear uncertain systems. This problem was motivated by recent efforts on the capability and limitation of feedback mechanism and has the characteristics of "essentially" finite internal uncertainties. To solve this type of problem, based on different ideas, we introduce several approaches, controller falsification, controller combination, and pseudo-parameter estimation, to design the feedback control law and rigorously establish the stability of closed-loop system for several typical algorithms in these approaches. Our results show that, under reasonably weak conditions, capable feedback control laws exist dealing with the finite internal uncertainties of the system. These results together with related results in companion papers provide partial answers to the finite-model adaptive control problem and may lead to deeper understanding on the capability of the whole feedback mechanism.