Unfalsified adaptive control for resettable systems

A switching algorithm in the framework of unfalsified adaptive control is formulated for an uncertain system whose state can be reset in a certain set repeatedly. The behavior of the system with its state in or around the set is of interest and the reset process is performed when a switching occurs. The traditional meaning of a feasible controller is modified and, hence, a candidate controller that locally stabilizes the uncertain system with its state in or around the set for small reference signals, becomes a feasible controller. In addition to a cost function in a switching algorithm for unfalsified adaptive control, a secondary cost function is constructed and is utilized in the switching algorithm. At each switching moment, this secondary cost function supports the selection process of the switching algorithm by providing an additional selecting criterion for candidate controllers with small primary cost values. Even with the introduction of the secondary cost function, the number of switchings is still guaranteed to be finite, provided that the primary cost function satisfies assumptions.