Pointwise conditions for improving control on a known region of asymptotic stability

A learning control system may be defined as: a control system in which the performance of the system is improved with experience. A key aspect of such a system is the improvement of control on a known region of asymptotic stability. Improving control implies that some metric of the system performance is reduced, and that the system remains asymptotically stable. Pointwise conditions for improvement while maintaining stability are looked at for a class of nonlinear regulators.