Hybrid neural control systems: Some stability properties

Nonlinear control with feedforward neural networks is usually designed by means of model based control strategies, which make explicit use of (direct or inverse) models of the controlled system. In this framework, a typical control problem consists in reducing the effects of the inevitable errors introduced by neural network approximation. In a non-adaptive setting, modeling errors can be compensated by hybrid control schemes, where the approximate neural controller is complemented with an integral type regulator connected in parallel. However, in this way, the model based control paradigm is partially lost and stability properties of the control system may be degraded. In this paper a stability analysis of such hybrid schemes is performed, which shows that control system stability can be achieved provided each of the two control blocks obeys a specific condition. Furthermore, a modified hybrid scheme is proposed to enhance the cooperation between the two control blocks: a nonlinear static filter is employed to modulate the integral action so that it becomes significant only when the neural controller has approached the equilibrium. Stability analysis is extended to this case. The hybrid scheme where the two control blocks are connected hierarchically in cascade is finally discussed.