Automatic Differentiation Applied for Optimization of Dynamical Systems

Simulation is ubiquitous in many scientific areas. Applied for dynamic systems usually by employing differential equations, it gives the time evolution of system states. In order to solve such problems, numerical integration algorithms are often required. Automatic differentiation (AD) is introduced as a powerful technique to compute derivatives of functions given in the form of computer programs in a high-level programming language such as FORTRAN, C, or C++. Such technique fits perfectly in combination with gradient-based optimization algorithms, provided that the derivatives are evaluated with no truncation or cancellation error. This paper intends to use AD employed for numerical integration schemes of dynamic systems simulating electromechanical actuators. Then, the resulting derivatives are used for sizing such devices by means of gradient-based constrained optimization.