Mixtures of adaptive controllers based on Markov chains: a future of intelligent control?

Estimation of linear auto-regression models with external inputs (ARX) and certainty-equivalence design are mostly used in contemporary adaptive controllers. In spite of the successes of such controllers, they face difficulties whenever the controlled process is nonlinear or the range of inputs is restricted. Using a sort of gain scheduling a piecewise linearization is often possible. The input restrictions, however, are coped with with difficulty. Thus, it is worth searching for an alternative class of adaptive controllers that take these restrictions into account. We try to complement ARX models by controlled Markov chains (CMC). By their nature, the gained controllers are able to cope both with nonlinear systems and restricted data ranges. To make them, however, practicable the "curse of dimensionality" inherent to CMCs has to be beaten. The outlined way indicates that such possibility exists.