Constructive methods in nonlinear control theory problems

We consider nonlinear control problems of transferring a substance from one state to the other given boundary data. We define second order differential operators with three time-independent coefficients. Our constructive analytical methods use in particular the Burman–Lagrange inversion formula for analytic functions. We give formulas for solutions to control problems in some particular cases of initial and boundary data. In addition to theoretical study we attempt, basing on a symbolic computation system, to implement some algorithms and programs to automatically generate the formulas that yield solutions to control problems.