Topology Optimization for Piecewise Dynamic Models Using a Genetic Algorithm

It has been demonstrated in the previous research that the node connectivity in the graph encoding the topological neighborhood relationships between local models in a piecewise dynamic model may significantly affect the cooperative learning process. It was shown that a graph with a larger connectivity leads to a quicker learning adaption due to more rapidly decaying transients of the estimation of local model parameters. In the same time, it was shown that the accuracy could be degraded by a larger bias in the asymptotic portion of the estimations of local model parameters. The efforts in topology optimization should therefore strive towards a high accuracy of the asymptotic portion of the estimator of local model parameters while simultaneously accelerating the decay of the estimation transients. In this paper, we pursue minimization of the residual sum of squares of a piecewise dynamic model after a predetermined number of training steps. The optimization of inter-model topology is implemented via a genetic algorithm that manipulates adjacency matrices of the graph underlying the piecewise dynamic model. An example of applying the topology optimization procedure on a peicewise linear model of a highly nonlinear dynamic system is provided to show the efficacy of the new method.