Robustness of the combined MRAC using knowledge of a bound on ||0*||

The combined model reference adaptive control (CMRAC) scheme, that brings together direct and indirect adaptive control methods has been extensively studied in the ideal case. Under non ideal conditions this algorithm has also been tested and quite good performance was also detected. In this paper the CMRAC is modified in order to include the knowledge of a bound on the norm of the desired controller parameter vector, which is somehow related to the actual plant parameters. This information is used to modify both control adaptive laws as well as identification adaptive laws. It is shown that the modified CMRAC gives a stable adaptive scheme in the presence of bounded external disturbances. Thus, CMRAC suitably modified is also useful to face this kind of robust adaptive control problems. The study is done for the continuous-time case and a first order plant is treated in detail. Extension of the method to high order plants is also included. A comparison with the direct MRAC using this kind of extra information indicates that transient response is improved if the modified CMRAC is used. The main contribution of the paper is the presentation of a new robust MRAC method based on the combination of direct and indirect adaptive control philosophies, which is globally stable in the presence of bounded external perturbations acting on the input and/or output of the plant. The advantage over the direct MRAC lies on the fact that a better transient response can be obtained with the proposed method due to flexibility in the choice of design parameters and adaptive gains.