Optimised backstepping control for the nonlinear strict-feedback system having unknown control dead-zone

In this article, the optimised backstepping (OB) strategy is extended to deal with the dead-zone control problem for a class of the nonlinear strict feedback systems. Since the dead-zone phenomenon is frequently encountered in the control of nonlinear strict feedback system, it is very necessary to consider the effect of dead-zone in the OB control. However, the published OB control methods are to rarely deal with the dead-zone problem because of the complex algorithm of reinforcement learning (RL). In this OB control, the dead-zone problem is effectively solved by utilising a simplified RL algorithm. For effective eliminating the effect of dead-zone, an adaptive compensation of dead-zone function's remainder is added to this RL. Since the RL under identifier-critic-actor architecture is implemented in every backstepping step, the requirement of complete dynamic acknowledge is released. Ultimately, the validity of this OB method is certified both theory and simulation.