Convergence properties of the modified renormalization algorithm based adaptive control supported by ancillary methods

Abstract

A new branch of computational cybernetics seems to emerge on the principles akin to that of the traditional soft computing (SC). In the paper the essential differences between the conventional and the novel approach are summarized. At the cost of the use of a simple dynamic model, a priori known, uniform, lucid, structure of reduced size, machine learning by a simple and short explicit algebraic procedure, especially fit to real time applications, considerable computational advantages can be achieved. The key element of the approach the modified renormalization transformation supported by the application of a simple linear transformation, and the use of a simple prediction technique. How the satisfactory conditions of the complete stability can be guaranteed, and how the convergence properties can be improved by the ancillary methods, is analyzed. Simulation examples are presented for the control of a 3 DOF SCARA arm by the use of partially stretched orthogonal transformations.