Optimal control based on multiple models approach of chaotic switched systems, application to a stepper motor

In this paper, we are interested in the control of chaotic switched systems with application to a stepper motor. The aim of the control is to determine the optimal sequence of switching instants in order to bring the chaotic behaviour of the system to a periodic one. The determination of the optimal sequence will follow two steps using an optimisation algorithm, the Hamiltonian system and the derivative of a performance criterion over the switching instants. The nonlinear switched system is modelled by a multiple linear time-invariant models approach to make possible to calculate the gradient of the cost function and therefore to determine the optimal instants of switches. Simulations are applied to a stepper motor to illustrate the results.