Functional optimization problems can be solved analytically only if special assumptions are verified; otherwise, approximations are needed. The approximate method that we propose is based on two steps. First, the decision functions are constrained to take on the structure of linear combinations of basis functions containing free parameters to be optimized (hence, this step can be considered as an extension to the Ritz method, for which fixed basis functions are used). Then, the functional optimization problem can be approximated by nonlinear programming problems. Linear combinations of basis functions are called approximating networks when they benefit from suitable density properties. We term such networks nonlinear (linear) approximating networks if their basis functions contain (do not contain) free parameters. For certain classes of d-variable functions to be approximated, nonlinear approximating networks may require a number of parameters increasing moderately with d, whereas linear approximating networks may be ruled out by the curse of dimensionality. Since the cost functions of the resulting nonlinear programming problems include complex averaging operations, we minimize such functions by stochastic approximation algorithms. As important special cases, we consider stochastic optimal control and estimation problems. Numerical examples show the effectiveness of the method in solving optimization problems stated in 1

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Automatic taxonomic categorisation of 23 species of dinoflagellates was demonstrated using field-collected specimens. These dinoflagellates have been responsible for the majority of toxic and noxious phytoplankton blooms which have occurred in the coastal waters of the European Union in recent years and make severe impact on the aquaculture industry. The performance by human 'expert' ecologists/taxonon~ists in identifying these species was compared to that achieved by 2 art~fi-cial neural network classifiers (multilayer perceptron and radial basis function networks) and 2 other statistical techniques, k-Nearest Neighbour and Quadratic Dlscnm~nant Analysis The neural network classifiers outperform the classical statistical techniques. Over extended trials, the human experts averaged 85% while the radial basis network achieved a best performance of 83%, the multilayer perceptron 66 %, k-Nearest Neighbour 60%, and the Quadratic Discriminant Analysis 56 %.

Large-scale traffic networks can be modeled as graphs in which a set of nodes are connected through a set of links that cannot be loaded above their traffic capacities. Traffic flows may vary over time. Then the nodes may be requested to modify the traffic flows to be sent to their neighboring nodes. In this case, a dynamic routing problem arises. The decision makers are realistically assumed 1) to generate their routing decisions on the basis of local information and possibly of some data received from other nodes, typically, the neighboring ones and 2) to cooperate on the accomplishment of a common goal, that is, the minimization of the total traffic cost. Therefore, they can be regarded as the cooperating members of informationally distributed organizations, which, in control engineering and economics, are called team organizations. Team optimal control problems cannot be solved analytically unless special assumptions on the team model are verified. In general, this is not the case with traffic networks. An approximate resolutive method is then proposed, in which each decision maker is assigned a fixed-structure routing function where some parameters have to be optimized. Among the various possible fixed-structure functions, feedforward neural networks have been chosen for their powerful approximation capabilities. The routing functions can also be computed (or adapted) locally at each node. Concerning traffic networks, we focus attention on store-and-forward packet switching networks, which exhibit the essential peculiarities and difficulties of other traffic networks. Simulations performed on complex communication networks point out the effectiveness of the proposed method.

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