Observer-Based Safety Monitoring of Nonlinear Dynamical Systems with Neural Networks via Quadratic Constraint Approach

The safety monitoring for nonlinear dynamical systems with embedded neural network components is addressed in this paper. The interval-observer-based safety monitor is developed consisting of two auxiliary neural networks derived from the neural network components of the dynamical system. Due to the presence of nonlinear activation functions in neural networks, we use quadratic constraints on the global sector to abstract the nonlinear activation functions in neural networks. By combining a quadratic constraint approach for the activation function with Lyapunov theory, the interval observer design problem is transformed into a series of quadratic and linear programming feasibility problems to make the interval observer operate with the ability to correctly estimate the system state with estimation errors within acceptable limits. The applicability of the proposed method is verified by simulation of the lateral vehicle control system.