In this chapter, the authors provide fundamental principles of Higher Order Neural Units (HONUs) and Higher Order Neural Networks (HONNs) for modeling and simulation. An essential core of HONNs can be found in higher order weighted combinations or correlations between the input variables and HONU. Except for the high quality of nonlinear approximation of static HONUs, the capability of dynamic HONUs for the modeling of dynamic systems is shown and compared to conventional recurrent neural networks when a practical learning algorithm is used. In addition, the potential of continuous dynamic HONUs to approximate high dynamic order systems is discussed, as adaptable time delays can be implemented. By using some typical examples, this chapter describes how and why higher order combinations or correlations can be effective for modeling of systems.

In this chapter, we provide fundamental principles of higher order neural units (HONUs) and higher order neural networks (HONNs). An essential core of HONNs can be found in higher order weighted combinations or correlations between the input variables. By using some typical examples, this chapter describes how and why higher order combinations or correlations can be effective.

A knowledge-based system is defined that ensures network radiality during reconfiguration of a power distribution system. Network radiality heuristics identify a pair of switching operations that preserves radiality. A matrix-structured knowledge base with five distinct rule bases is used. Rule base A is used in determining which other rule bases to activate. Rule base B is used in considering whether to open a switch and rule base C is used in finding a corresponding initially open switch to close to assume the load transfer that would be necessitated by the switch opening. Rule base D is used in considering whether to close a switch and rule base E is used in finding a corresponding initially closed switch to open because of the load transfer that would be necessitated by the switch closing. In the interest of brevity, only rule bases A, D, and E are described