Model reference control of non-linear systems via implicit function emulation

Abstract

Narendra and Parthasarathy (1990) demonstrated that neural networks can be used effectively for the identification and control of non-linear dynamical systems. The structure of the controller used was dependent on the structure of the non-linear system under consideration, of which some partial knowledge was assumed. This work is extended by considering a unified approach for the control of higher order systems where full state information is not available, and where no specific information about the structure of the system is assumed. In this case the controller merely emulates the implicit function of some appropriate error criterion. This unified approach includes, as special cases, those systems with special structure previously considered in Narendra and Parthasarathy (1990). Specialization of the method to linear systems allows swift convergence by virtue of a certain convexity property. Extensive simulations confirm the feasibility and effectiveness of the proposed method.