Efficient delay and parameter estimation for nonlinear systems based on lifted IRK integrators with inexact Jacobians

For continuous nonlinear systems with multiple state delays, this paper proposes an efficient optimization algorithm for delay and parameter estimation based on a novel implicit Runge-Kutta integrator. As the integrator is in form, integral step not restricted to be less than all delays. To improve computational efficiency, lifting scheme employed integrated programming solver such that number of Newton iterations solving collocation equations can reduced. Moreover, simplified-Newton single-Newton methods are applied reduce cost LU decomposition iterations. Complexity analysis shows that, problems middle or large scale, requires much function evaluation sequential traditional A problem gene regulatory network demonstrates obtain estimates efficiently satisfactory accuracy. The speedup factor $ 2 $-$ 3 $.