Pole placement control for nonlinear systems via neural networks

This paper extends pole placement control of conventional linear systems to a class of nonlinear dynamical systems via neural networks. An application of typical inverted pendulum illustrates the design method. Multi-layer neural networks are selected to approach nonlinear components arbitrarily, and then are represented by linear difference inclusion (LDI) format. With pole placement regions formed in linear matrix inequalities (LMIs), quadratic stability theory is used as a basic analysis and synthesis methodology. Pole placement controllers via state feedback are derived by numerical solutions of a set of coupled LNIs. Applying common back propagation algorithm (BP) for networks training and interior point computation for LMI solving, some simulation results show the validity of pole placement control.