The optimization of non-linear systems using a new two level method

A new two level method is developed for the optimization of non-linear dynamical systems with a quadratic cost function. This method used an expansion around the equilibrium point of the system to fix the second and higher order terms. These terms are compensated for iteratively at the second level by providing a prediction for the states and controls which form a part of the higher order terms. A proof of the convergence of the algorithm is provided. The algorithm is tested on a problem of synchronous machine excitation where fast convergence is obtained. A comparison is also made with the global solution of the problems using quasi-linearisation. It is seen that the new method takes less than half the computation time of the global solution. © 1976.