Adaptive Estimation Algorithms of FCN Parameters

In this chapter, adaptive estimation algorithms are proposed, which estimate the FCN parameters based on sampled data that correspond to FCN equilibrium points. First, we assume that the only parameters that have to be estimated are the FCN weights. This requires the development of estimation algorithms that are based on a linear parametric model of the FCN equilibrium equation. Discrete time repetitive weight estimation laws are derived based on Lyapunov stability analysis and appropriate projection methods are employed to guarantee that the weight updating procedure does not compromise the conditions of existence and uniqueness of solutions, derived in the previous chapter. Next, we assume that apart from the FCN weights, the sigmoid inclination parameter of each node has to be appropriately estimated. This leads to bilinear parametric modeling of the FCN equilibrium equation and the derivation of respective adaptation algorithm. Similar to the linear case, appropriate projection methods are derived and it is proved that they do not compromise the stability results of the estimation error dynamics. Simulations and comparisons between the two approaches are given, which highlight the benefit of each of them.