L<inf>1</inf> adaptive controller for systems with input quantization

Abstract

This paper quantifies performance bounds of L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> adaptive controllers for linear uncertain systems with input quantization. Two basic types of quantizers are considered: uniform quantizers and logarithmic quantizers. The performance bounds of the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> adaptive controller in the presence of input quantization proved to have an additional term, dependent upon the quality of quantization. The signals of the closed-loop L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> adaptive systems can be rendered arbitrarily close to the corresponding signals of a bounded reference system by increasing the adaptation rate and improving the quantizer. Simulations confirm the theoretical results.