Global stability and performance of a simplified adaptive algorithm†

What is it about?

Most self-tuning and adaptive control algorithms usually use reference models, controllers, or identifiers of about the same order as the controlled plant. Since the dimension of the plants in the real world may be very large or unknown, implementation of adaptive control procedures may be difficult, or sometimes impossible. In this paper, we prove global stability for a simple adaptive algorithm that can use low-order model reference and controllers, since no observers or identifiers are used in the adaptation process. The algorithm is basically fitted for systems that are denominated as 'almost positive real'. It is shown that, at the price of bounded rather than vanishing output tracking errors, the simple algorithm can be applied in systems that can be stabilized via constant output feedback. These procedures are believed to reduce considerably the effort required for implementation of adaptive control in practical applications, especially in multivariable large-scale systems.

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