Adaptive cross backstepping control for a class of nonstrict feedback nonlinear systems with partial state constraints

Abstract

AbstractThe tracking control problem for a class of partial state constrained nonlinear system is studied in this article. The system is divided into two semistrict feedback nonlinear subsystems, one is state constrained and the other is state free. By means of state transformation, the state constraint problem is transformed into the bounded problem of the transformed function. Compared with the barrier Lyapunov function (BLF) method, it not only solves the state constraint problem but also circumvents the feasibility check on virtual controllers. Based on the cross backstepping control, the constrained controller and unconstrained controller are designed simultaneously. It solves the coupling problem effectively in the design of cross processing control. On the other hand, dynamic surface control is used which effectively avoids “computation explosion” caused by backstepping control. The designed controllers can ensure the error signals converge to a small neighbourhood of zero and keep the asymmetric time‐varying constraints on system partial states are satisfied for all the time. Finally, simulation experiments are carried out on a hyperchaotic Rössler system to verify the efficacy of the control scheme.