Adjoint based Hessians for optimization problems in system identification

An adjoint sensitivity based approach to determine the gradient and Hessian of cost functions for system identification is presented. The motivation is the development of a computationally efficient approach relative to the direct differentiation technique and which overcomes the challenges of the step size selection in finite difference approaches. The discrete time measurements result in discontinuities in the Lagrange multipliers. The proposed approach is illustrated on the Lorenz 63 model where part of the initial conditions and model parameters are estimated.