Abstract
A new branch of Soft Computing (SC) designed for the adaptive control of a special class of non-linear coupled multivariable systems is reported. In contrast to traditional SC its uniform structures are obtained from certain abstract geometry-related Lie groups. Adavantages are: a priori known and reduced structure size, increase in lucidity; simple, short, and explicit algebraic procedure instead of intricate learning. Disadvantage is: limited circle of applicability. Convergence consideratons for the new approach are discussed. Simulations are presented for the control of the inverted pendulum using the generalized Lorentz Group. It is concluded that the method is promising and probably imposes acceptable convergence requirements in many practical cases.
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