Min–Max Dynamic Programming Control for Systems with Uncertain Mathematical Models via Differential Neural Network Bellman’s Function Approximation

This research focuses on designing a min–max robust control based neural dynamic programming approach using class of continuous differential networks (DNNs). The proposed controller solves the optimization cost function that depends trajectories system with an uncertain mathematical model satisfying non-linear perturbed systems. formulation enables concerning bounded modelling uncertainties and disturbances. Hamilton–Jacobi–Bellman (HJB) equation’s value function, approximated by DNN, permits to estimate closed-loop controller. design is estimated state trajectory worst possible uncertainties/perturbations provide degree robustness learning laws for time-varying weights in DNN produced studying HJB partial equation. uses solution obtained Riccati A recurrent algorithm Kiefer–Wolfowitz method leads adjusting initial conditions satisfy final condition given function. suggested this work evaluated numerical example confirming optimizing approximate Bellman’s