The paper introduces linear dynamic-order extended time-delay dynamic neural unit (DOE TmD-DNU) whose adaptation by the dynamic backpropagation learning rule is enhanced by the genetic algorithm. DOE TmD-DNU is a possible customization of novel class of artificial neurons called time-delay dynamic neural units (TmD-DNU). In standalone implementations, these artificial dynamic neural architectures can be viewed as analogies to continuous time-delay differential equations, where the equation parameters are unknown and are adaptable such as neural weights and other parameters of artificial neurons. Time delays on neural inputs of a unit and in the state feedback of a unit are also considered as unit’s adaptable neural parameters. These new neural units equipped with adaptable time delays can identify all parameters of a continuous time-delay dynamic system including unknown time delays both in the unit’s inputs as well as in its state variables. Incorporation of adaptable time delays into neural units significantly increases approximation capability of individual neural units. It results in simplification of a neural architecture and minimization of the number of neural parameters, and thus possibly in better understanding the obtained neural model. It has been shown, that stable adaptation of all parameters of TmD-DNU including time delays can be achieved by dynamic modification of backpropagation learning algorithm. However, sometimes the relatively slow convergence rate of the neural parameters and the convergence rather toward local minima of error function can be considered as drawbacks of the adaptation. This paper focuses the improvement of the backpropagation learning algorithm of TmD-DNU by the genetic algorithm and its application to heat transfer system modeling. The adaptation learning algorithm based on the simultaneous combination of dynamic backpropagation and genetic algorithm has been designed to accelerate the convergence of time-delay parameters of a neural unit and to achieve the global character of minimization of error function. The neural weights and parameters, except the time-delays, are adapted by dynamic modification of backpropagation learning algorithm, and those that represent time-delays can be adapted by the genetic algorithm. Results on system identification of an unknown system with dynamics of higher-order including unknown time delays are shown in comparison to achievements by common identification methods applied to the same system. The robust identification capabilities, the aspects of network implementation of TmD-DNU, and the prospects of their nonlinear versions, i.e. higher-order nonlinear time delay dynamic neural units (TmD-HONNU) are briefly discussed with respect to the learning technique presented in this paper.
Optimised control using proportional-integral-derivative controller tuned using internal model control
