Tailored Output Layers of Neural Networks for Satisfaction of State Constraints in Nonlinear Control Systems

This work considers the synthesis of state feedback controllers established as deep artificial feed-forward neural networks for the control of discrete-time nonlinear but input-affine systems. The idea is to design output layers of particular structure to guarantee the satisfaction of state constraints in form of control-invariant ellipsoids. Since an analytical expression can be derived for the resulting neural network controller, the latter can be stored and evaluated efficiently. Moreover, the proposed output layer guarantees the satisfaction of the considered state constraints for each specification of the parameter vector. Numerical examples are provided for illustration and evaluation of the approach, in which the approximation of a nonlinear model predictive control law is considered as application.