Order reduction of n for robust adaptive control design of SISO linear systems

In this paper, we propose an order-reduction design methodology to simplify the adaptive controller obtained in Z. Pan and T. Basar (2000) by n integrators. We study the same class of linear systems as Z. Pan and T. Basar (2000), make the same assumptions, and have the same formulation and approach to the problem. The main difference between our design methodology and that of Pan and T. Basar (2000) lies in the step O of the control design step. In this paper, we skip step O and immediately start the integrator backstepping procedure without stabilizing the filtered dynamics of the output. This relieves us from generating the reference trajectory for the filtered dynamics of the output and thus reducing the controller order by n. The trade-off for this order reduction Ls that the worst-case estimate for the expanded state vector has to be chosen as a suboptimal choice, rather than the optimal choice. Exactly the same robustness properties can be established for the reduced-order controllers as those of Z. Pan and T. Basar (2000). There is no definite performance comparison that can be made theoretically between the reduced-order controller and the full-order controller of Z. Pan and T. Basar (2000). Based on a few simulation examples, we observe that the reduced-order controller does not perform better than the full-order controller.