A stable indirect adaptive control scheme for a first-order plants with no prior knowledge on the parameters

An indirect adaptive control scheme for first-order linear time-invariant plant with unknown parameters is presented and analyzed. The scheme requires no prior knowledge about the sign or bounds of the plant parameters. A discontinuous control law is used to avoid any singularities due to lack of stabilizability of the estimated model. The scheme guarantees signal boundedness and zero residual tracking error. It is shown that, after a finite time, no switching of the control law is required and the estimate of the high frequency gain remains bounded away from zero for the rest of the time