Unfalsified Adaptive Control for Nonlinear Time-Varying Plants

The Battistelli–Hespanha–Mosca–Tesi (BHMT) adaptive reset switching algorithm is enhanced to admit bumpless transfer and to control a nonlinear time-varying plant using the broad class of two-degree-of-freedom nonlinear time-varying controllers. Performance, including stability and exponential stability, is proved given only that the adaptive stabilization problem is
$\lambda$
-feasible, which means at every time, there exists at least one exponentially stabilizing controller. We relax two restrictive BHMT assumptions: i) the plant is linear time-invariant (LTI) over most intervals and has finite order and ii) each controller is LTI. And, we expand the scope to include a broad class of bumpless switching algorithms. An example is provided to support the improved results.