Editing Forward algorithm (section)

==Variants of the algorithm==
* '''Hybrid Forward Algorithm''':<ref>Peng, Jian-Xun, Kang Li, and De-Shuang Huang. "A hybrid forward algorithm for RBF neural network construction." ''Neural Networks, IEEE Transactions'' on 17.6 (2006): 1439-1451.</ref> A variant of the Forward Algorithm called Hybrid Forward Algorithm (HFA) can be used for the construction of radial basis function (RBF) neural networks with tunable nodes. The RBF neural network is constructed by the conventional subset selection algorithms. The network structure is determined by combining both the stepwise forward network configuration and the continuous RBF parameter optimization. It is used to efficiently and effectively produce a parsimonious RBF neural network that generalizes well. It is achieved through simultaneous network structure determination and parameter optimization on the continuous parameter space. HFA tackles the mixed integer hard problem using an integrated analytic framework, leading to improved network performance and reduced memory usage for the network construction.

* '''Forward Algorithm for Optimal Control in Hybrid Systems''':<ref>Zhang, Ping, and Christos G. Cassandras. "An improved forward algorithm for optimal control of a class of hybrid systems." ''Automatic Control, IEEE Transactions'' on 47.10 (2002): 1735-1739.</ref> This variant of Forward algorithm is motivated by the structure of manufacturing environments that integrate process and operations control. We derive a new property of the optimal state trajectory structure which holds under a modified condition on the cost function. This allows us to develop a low-complexity, scalable algorithm for explicitly determining the optimal controls, which can be more efficient than Forward Algorithm.

* '''Continuous Forward Algorithm''':<ref>Peng, Jian-Xun, Kang Li, and George W. Irwin. "A novel continuous forward algorithm for RBF neural modelling." ''Automatic Control, IEEE Transactions'' on 52.1 (2007): 117-122.</ref> A continuous forward algorithm (CFA) can be used for nonlinear modelling and identification using radial basis function (RBF) neural networks. The proposed algorithm performs the two tasks of network construction and parameter optimization within an integrated analytic framework, and offers two important advantages. First, the model performance can be significantly improved through continuous parameter optimization. Secondly, the neural representation can be built without generating and storing all candidate regressors, leading to significantly reduced memory usage and computational complexity.