Stable indirect adaptive control of continuous-time systems with no a priori knowledge on the parameters

Abstract

A crucial drawback of indirect adaptive control is the stabilizability or controllability of the estimated plant model which is required in order to calculate the controller parameters. Loss of stabilizability at a particular instant of time may lead to unbounded signals. In this paper, we propose an indirect adaptive control scheme that overcomes the stabilizability problem, and meets the control objective exactly with no additional a priori knowledge on the unknown plant other than its order. The control scheme switches from the usual certainty equivalence control law to a rich open loop control input, according to an adjustable lower bound for the degree of stabilizability of the estimated plant model. The switching terminates in finite time after which no loss of stabilizability can occur, and the certainty equivalence control law is on for the rest of the time. In contrast to previous schemes, the proposed scheme, referred to as the switched-excitation approach, requires no knowledge of bounds for the stabilizability degree of the unknown plant and guarantees closed-loop stability and zero residual tracking error.