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Structurally and procedurally simplified soft computing for real time control

The present state of development of a new branch of soft computing (SC) developed for the adaptive control of a special class of nonlinear coupled MIMO systems is reported. Its uniform structures are obtained from certain Lie groups, unlike that of the traditional SC approaches. The advantages include: a priori known, very much reduced in size, and increased in lucidity; and the parameter tuning or learning is replaced by a simple and short explicit algebraic procedure. The only disadvantage is a limited circle of applicability. Convergence considerations are also discussed for MIMO and SISO systems. Simulation examples are presented for the control of an inverted pendulum by using the generalized Lorentzian matrices. It is concluded that the method is promising and probably imposes acceptable convergence requirements in many practical cases.