Symbolic algebra toolbox for the design of dynamical adaptive backstepping controllers

The backstepping control design algorithms described by Krstic et al. (1995) provide a systematic framework for the design of regulating strategies suitable for large classes of nonlinear uncertain systems. However, the equations arising at the successive steps are usually too complicated to be computed by hand. We consider here a symbolic toolbox which implements a general algorithm for the design of dynamic adaptive controllers following the basic ideas of backstepping with tuning functions without transformation into canonical forms. This algorithm is applicable to observable minimum phase systems not necessarily in triangular form and also to uncertain nonlinear systems in triangular forms. Additionally the control can be generated by a sliding mode approach