Adaptive Optimization With Decaying Periodic Dither Signals

Real-time optimization in cyber–physical network systems with unknown system parameters must integrate optimization and parameter estimation, leading to adaptive optimization problems. Such problems encounter fundamental conflict between optimization and system identifiability. Recently, a new method of employing a stochastic or periodic dither has been introduced to resolve this conflict and achieve convergence toward optimal solutions. However, adding a dither introduces persistent disturbances to the optimal solution, resulting in an essential tradeoff between convergence rate and steady-state error. This article introduces a method of adding decaying periodic dither signals into the cyber–physical system, which can still provide sufficient excitations for estimating the unknown parameters and, at the same time, asymptotically reduce optimality errors down to zero without affecting negatively on identifiability. The convergence properties of parameter estimation and optimization updates are provided simultaneously, first for noise-free and model uncertain free cases, followed by general systems that include observation noise and modeling errors. A simulation example is used to illustrate the adaptive optimization algorithms and the main properties.