Abstract
Adaptive control approaches are effective system-theoretical methods for guaranteeing both the stability and the performance of physical systems subject to uncertainties. However, the stability and performance of these approaches can be severely degraded by the presence of unmodeled dynamics. Motivated by this standpoint, the previous work of the authors introduced a model reference adaptive control architecture based on the direct uncertainty minimization method for systems with additive input uncertainties and unmodeled dynamics. In particular, the proposed approach not only guaranteed the closed-loop stability predicated on a sufficient stability condition but also improved the closed-loop performance. The purpose of this paper is to generalize this previous work of the authors. Specifically, a model reference adaptive control architecture is given and it is system-theoretically analyzed for systems with unmodeled dynamics, and both additive input and control effectiveness uncertainties (we refer to Theorems 1 and 2 of this paper). The sufficient stability condition of the resulting architecture relies on linear matrix inequalities and this architecture can be effective in achieving not only stability but also a desired level of closed-loop system performance. Finally, we also provide an illustrative numerical example, which demonstrates the given theoretical results. (This research was supported by the Air Force Research Laboratory Aerospace Systems Directorate under the Universal Technology Corporation Grant 162642-20-25-C1.)
Stabilisation of Discrete-Time Piecewise Homogeneous Markov Jump Linear System with Imperfect Transition Probabilities
