Classical/neural synthesis of nonlinear control systems

Classical/neural synthesis of control systems combines the most effective elements of old and new design concepts with the promise of producing better control systems. There is considerable precedent for applying gain-scheduled linear controllers to nonlinear systems, especially those that can be locally approximated as linear- parameter-varying systems; however, a means for transferring the insights gained from these linear controllers to nonlinear controllers remains to be identified. The approach taken here is to design nonlinear control systems that take advantage of prior knowledge and experience gained from linear controllers, while capitalizing on the broader capabilities of adaptive, nonlinear control theory and computational neural networks. Central to this novel approach is the recognition that the gradients of a nonlinear control law must represent the gain matrices of an equivalent, locally linearized controller. In this paper we focus on the initial specification for the control law, which consists of a set of hypersurfaces expressed as neural networks that represent satisfactory linear controllers designed over the plant's operating range. Along the way, a new neural network training method consisting solely of solving algebraic linear systems of equations is developed, and its effectiveness is demonstrated on a case study.