Genetic algorithms for local model and local controller network design

Local Model Networks (LMNs) provide a global representation of a nonlinear dynamical system by interpolating between a set of locally valid sub-models distributed across the operating range. Training such networks typically involves heuristic selection of the number of sub-models and their structure followed by the combined estimation of the free sub-model and interpolation function parameters. This paper describes a new genetic learning approach to the construction of LMNs comprising ARX local models and normalised Gaussian interpolation functions. In addition to allowing the simultaneous optimisation of the number of sub-models, model parameters and interpolation function parameters, the approach provides a flexible framework for targeting transparency and generalisation. Fuzzy logic is used with special features to provide a directional and dynamic search for the genetic algorithm. Several modifications of the classical genetic algorithm are adopted to optimise each local model separately within the overall global model. A linear direct feedback control scheme is derived from the LMN representation of the nonlinear plant and local stability analysis is discussed. Simulation studies on a pH neutralisation process confirm the excellent nonlinear modelling properties of LM networks and illustrate the potential of the proposed control scheme.