Hessian Matrix Estimation in Hybrid Systems Based on an Embedded FFNN

This paper describes the Hessian matrix estimation of nonsmooth nonlinear parameters by the identifier based on a feedforward neural network (FFNN) embedded in a hybrid system, which is modeled by the differential-algebraic-impulsive-switched (DAIS) structure. After identifying full dynamics of the hybrid system, the FFNN is used to estimate second-order derivatives of an objective function
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with respect to the nonlinear parameters from the gradient information, which are trajectory sensitivities. Then, the estimated Hessian matrix is applied to the optimal tuning of a saturation limiter used in a practical engineering system.