Modified model reference adaptive observer‐based control without assumptions on uncertain parameter bounds

Abstract

AbstractThis paper proposes a Modified model reference adaptive controller and observer (MMRACO) for unknown linear time‐invariant (LTI) systems. The recent literature, and in particular the so‐called MRACO approach, has demonstrated how some deficiencies in standard model reference adaptive control can be overcome by using a combination of modified reference models and observers, but this is done at the expense of knowing bounds on certain unknown parameters. Here, a novel adaptive observer/controller combination is presented which removes the need to know the above bounds but preserves the other desirable features of the MRACO approach. A Lyapunov analysis of the closed‐loop system ensures asymptotic convergence of both tracking and observer errors, with uniform boundedness of parameter estimation errors. A key advantage of the scheme is that the design involves only solutions of two Lyapunov equations (or linear matrix inequalities) and does not require the selection of a “high gain” parameter. The effectiveness of the approach is illustrated in some numerical examples.