Barrier Lyapunov Function Based Adaptive Cross Backstepping Control for Nonlinear Systems with Time-varying Partial State Constraints

This paper focuses on an adaptive cross-backstepping control for a class of nonstrict-feedback nonlinear systems affected by time-varying partial state constraints. The nonstrict-feedback nonlinear systems considered in this paper are divided into two strict-feedback nonlinear subsystems. One constrained subsystems and another unconstrained subsystems. In view of the normal backstepping method is only an effective method to control lower-triangular systems, cross-backstepping control is introduced which successfully solves the problem of alternate time-varying state constraints. For the constrained subsystems, novel time-varying tan-type barrier Lyapunov function (TBLF) is employed in each step of backstepping design to guarantee the boundedness of the fictitious or actual state tracking errors. Besides, proper adaptive laws are designed for the upper bound of uncertain parameters, which successfully neutralize the influence of parametric uncertainties. Based on the stability analysis, it is concluded that the states of the closed-loop system maintain in the predefined time-varying compact sets and the output can be guaranteed to be as close to the desired trajectory as possible. The effectiveness of the proposed technique is illustrated by a constrained hyperchaotic system in two cases.