Stable artificial neural networks for robust pole assignment

Given a linear control system, it is expected that the system poles can be assigned robustly and efficiently. In this paper we propose two artificial neural networks for robust pole assignment by state feedback and output feedback controllers, respectively, based on two gradient flows. By embedding the negative gradient flows and the dynamical systems associated with the matrix inverse together into higher dimensional spaces, we obtain two modified gradient systems. Without involving the direct computation of the matrix inverse, those modified systems are readily to be realized using recurrent neural networks. Furthermore, the trajectories of the modified gradient flows are guaranteed to converge to the equilibrium sets of the original flows by appropriately choosing a design parameter. The architecture of the corresponding neural networks is discussed. Simulation results are also included to show the effectiveness of the proposed approach.