Nonlinear periodic adaptive control for linear time-varying plants

In adaptive control the goal is to deal with systems that have unknown and/or time-varying parameters. Most techniques are proven in the case in which the time-variation is non-existent or slow, with results pertaining to systems with rapid time-variations limitted to those in which the time-variation is of a known form or for which the plant has stable zero dynamics. Here we propose a new adaptive controller design based on the related area of gain scheduling. We consider the case in which the plant uncertainty is limitted to a scalar variable; under suitable assumptions on the plant under consideration, it is proven that the controller yields a closed loop system which is stable under fast parameter variations with persistent jumps.