Control of nonlinear system with input saturation based on Gaussian potential function network

The authors present a novel approach to the neural-network-based control of a nonlinear system, or in particular for the neural-network-based regulation of a nonlinear system subject to input saturation. This 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 makes it possible to overcome the structural limitations of a network and also the local minima problem in learning