Multiobjective Complementary Control

This article proposes a novel multiobjective control framework for linear time-invariant systems in which performance and robustness can be achieved in a complementary way instead of a tradeoff. In particular, a state-space solution is first established for a new stabilizing control structure consisting of two independently designed controllers coordinated with a Youla-type operator <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm Q}$</tex-math></inline-formula>. It is then shown by performance analysis that these two independently designed controllers operate in a naturally complementary way for a tracking control system, due to the coordination function of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm Q}$</tex-math></inline-formula> driven by the residual signal of a Luenberger observer. Moreover, it is pointed out that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm Q}$</tex-math></inline-formula> could be further optimized with an additional gain factor to achieve improved performance, through a data-driven methodology for a measured cost function.