Identification and control of delayed unstable and integrative LTI MIMO systems using pattern search methods

In this paper, we develop a multi-model adaptive control strategy to be applied on delay compensation schemes for stable/unstable LTI MIMO systems. The only requirement is that the delay should be bounded and decoupled from the control strategy. The delay identification problem is formulated as an optimization one, and it is framed on the abstract definition of the Generalized Pattern Search Method (GPSM). Taking advantage of the global convergence analysis presented by GPSM, we make a stability analysis of the proposed approach and delay identification capabilities. Simulation examples show the usefulness of the proposed strategy proving that the scheme is capable of identifying the delay and stabilizing the system even with a larger delay. The capabilities of the approach are tested on a second-order delayed unstable process, a MIMO unstable systems and an irrigation channel model. Additionally, simulation examples on an irrigation channel with time-varying delay are presented.