Nonlinear system control based on Gaussian potential function network

A new approach for the neural network-based control of a nonlinear system subject to input saturation, is presented. The approach is based on: 1) the training of a Gaussian potential function network (GPFN) to model nonlinear system dynamics based on the hierarchically self-organizing learning (HSOL) algorithm; and 2) the planning of a path from the initial state to the goal state which ensures the state reachability under input saturation and the satisfaction of performance criteria. Path planning is done in the regulatable region associated with the feasible state transition region based on a potential field method. The advantage of using GPFN with HSOL compared to backpropagation networks is due to the capability of HSOL to recruit a required number of Gaussian hidden units automatically and incrementally by monitoring network performance. This allows the structural limitation of a network and the local minima problem in learning to be overcome. Simulation results are shown for the regulation of first-order SISO (single-input single-output) nonlinear plants