  The problem of optimal switching between nonlinear autonomous subsystems is
investigated in this study where the objective is not only bringing the states
to close to the desired point, but also adjusting the switching pattern, in the
sense of penalizing switching occurrences and assigning different preferences
to utilization of different modes. The mode sequence is unspecified and a
switching cost term is used in the cost function for penalizing each switching.
It is shown that once a switching cost is incorporated, the optimal cost-to-go
function depends on the already active subsystem, i.e., the subsystem which was
engaged in the previous time step. Afterwards, an approximate dynamic
programming based method is developed which provides an approximation of the
optimal solution to the problem in a feedback form and for different initial
conditions. Finally, the performance of the method is analyzed through
numerical examples.
