Multivariable adaptive control with unknown signs of the high-frequency gain matrix using novel Nussbaum functions

Multivariable adaptive control with less prior information of the high-frequency gain matrix (HFGM) is a longstanding problem of both theoretical and practical importance. In this paper, a solution is presented by proposing a novel output-feedback adaptive backstepping control scheme. Our scheme only requires the leading principal minors of the HFGM to be nonzero and allows their signs to be unknown, which significantly relaxes the assumptions on the HFGM in conventional multivariable adaptive control schemes. To cope with the unknown signs, we propose novel Nussbaum functions with some nice properties and construct periodical intervals in which the effects of the multiple Nussbaum functions reinforce rather than counteract each other. With these efforts, global stability of the closed-loop system and asymptotical convergence to zero of the tracking error are successfully achieved. Simulation results illustrate the effectiveness of the proposed control scheme.