Adaptive Constrained Control of Uncertain ARMA-Systems based on Set Membership Identification

In this article an adaptive constrained finite time optimal (CFTO) controller design is presented for unknown, discrete-time linear systems, whose dynamics are identified via set-membership identification (SMI) algorithms. The controller consists of two modules: a) the set membership(SM)-identifier that identifies the system´s dynamics through the extended recursive least squares (eRLS) while providing the vertices of an orthotope that contains the nominal identification parameter vector, and b) the CFTO-controller; the tuning of the controller is based on a batch tuning procedure. The controller´s feasible operating region remains unchanged for: a) all SM-orthotopes that are subsets of the last orthotope for which the controller´s tuning was based, and b) the calculated CFTO-controller remains constant for a large period of time. In the opposite case the control partition of the controller is re-calculated (batch process) based on the current vertices of the identified SM-orthotope. Simulation results are presented that prove the efficacy and the validity of the suggested control scheme