Energy-based design of dynamic allocation in the presence of saturating actuators⁎This study was financed in part by the Coordenaçao de Aper-feicoamento de Pessoal de Nível Superior - Brasil (Capes) - Finance Code 001, and by ANR project HANDY 18-CE40-0010. Issue 9 (2021) - Lima, T. Alves; Tarbouriech, S.; Nogueira, F.G.; Torrico, B.C.
Abstract: This paper addresses the design of dynamic allocation functions for systems with saturating actuators. The novelty of the proposal relies on the use of an anti-windup loop to drive the state of the allocator, which in some sense dynamically compensates the difference between the computed control signal and the plant input. Furthermore, the co-design of the allocator and anti-windup loop is presented, allowing to deal with the multiple objective of reducing the allocator error and increasing the closed-loop region of stability. Theoretical conditions are derived in terms of linear matrix inequalities (LMIs) and an optimization scheme consisting in the minimization of the energy of the allocator error is proposed. Two examples borrowed from the literature illustrate the proposed technique and show its effectiveness.