Finite form realizations of adaptive control algorithms

We suggest a new method to design adaptation algorithms that guarantee improved performance and are applicable for a class of plants with nonconvex parameterization. The main idea of the method is, first, to augment the tuning error (possibly using uncertainty-dependent signals) of the known adaptive schemes in such a way that the desired characteristics of the adaptive system are guaranteed. Then we search for realization of the proposed schemes in an integral-differential form similar to the PI (proportional-integral) rules. Such adaptation schemes in the paper are called adaptive algorithms in finite forms. For this new description, neither dependence on state derivatives, nor unknown parameters is required. Sufficient conditions for existence of new finite form realizations of adaptive algorithms are proposed.