Discrete-Time Periodic Adaptive Control

Abstract

In this study a periodic adaptive control approach is discussed for a class of nonlinear discrete-time systems with time-varying parametric uncertainties which are periodic, and the only prior knowledge is the periodicity. The adaptive controller updates the parameters and the control signal periodically in a pointwise manner over one entire period, in the sequel achieves the asymptotic tracking convergence. The result is further extended to a scenario with mixed time-varying and time-invariant parameters, and a hybrid classical and periodic adaptation law is proposed to handle the scenario more appropriately. Extension of the periodic adaptation to systems with unknown input gain, higher order dynamics, and tracking problems are also discussed.