  This paper deals with an isoperimetric optimal control problem for nonlinear
control-affine systems with periodic boundary conditions. As it was shown
previously, the candidates for optimal controls for this problem can be
obtained within the class of bang-bang input functions. We consider a
parametrization of these inputs in terms of switching times. The control-affine
system under consideration is transformed into a driftless system by assuming
that the controls possess properties of a partition of unity. Then the problem
of constructing periodic trajectories is studied analytically by applying the
Fliess series expansion over a small time horizon. We propose analytical
results concerning the relation between the boundary conditions and switching
parameters for an arbitrary number of switchings. These analytical results are
applied to a mathematical model of non-isothermal chemical reactions. It is
shown that the proposed control strategies can be exploited to improve the
reaction performance in comparison to the steady-state operation mode.
