Output-feedback binary adaptive control of MIMO systems using monitoring function

Abstract

The problem of adaptive control design for multivariable linear time-invariant plants with unknown control direction is considered. A solution is proposed based on the SDU factorization of the high frequency gain matrix (HFG) and the monitoring function approach. The adaptation scheme is the binary model reference adaptive control (BMRAC) which utilizes parameter projection and sufficiently high adaptation gains. The signs of the leading principal minors of the HFG define the control directions, and the lack of knowledge of which is a major challenge in the multivariable framework. The role of the monitoring function is to monitor the output error transient and then provide the necessary changes of the adaptation gain signs to guarantee a stable adaptive control. In addition to proving the signal boundedness of the resulting closed-loop system, the output tracking error is shown to be asymptotically as well as exponentially practically stable, i.e., exponentially stable with respect to a small residual compact set of size inversely proportional to the BMRAC adaptation gain. The latter implies good transient properties of the output tracking error in contrast to conventional adaptive laws which only guarantee asymptotic stability but can lead to extremely slow error convergence. The extension of the proposed approach to matched disturbances is also briefly discussed following the classical paradigm of disturbance estimators. Numerical results with a visual servoing application illustrate the efficiency of the proposed method.