Nonlinear system identification employing automatic differentiation

• Automatic differentiation is employed for computing derivatives of general cost functions.
• This approach provides an efficient implementation of an optimization based state and parameter estimation method.
• A strategy for estimating the delay time in delay differential equation models is presented.
• These identification methods are demonstrated with the hyper-chaotic Lorenz-96 model and the Mackey–Glass delay system.

An optimization based state and parameter estimation method is presented where the required Jacobian matrix of the cost function is computed via automatic differentiation. Automatic differentiation evaluates the programming code of the cost function and provides exact values of the derivatives. In contrast to numerical differentiation it is not suffering from approximation errors and compared to symbolic differentiation it is more convenient to use, because no closed analytic expressions are required. Furthermore, we demonstrate how to generalize the parameter estimation scheme to delay differential equations, where estimating the delay time requires attention.