Adaptive NN Cross Backstepping Control for Nonlinear Systems With Partial Time-Varying State Constraints and Its Applications to Hyper-Chaotic Systems

This paper proposes a novel cross backstepping technique-based controller design for a class of nonlinear constrained systems with its applications to hyper-chaotic systems. Considering the strict feedback systems with partial time-varying state constraints, we divide the special systems into constrained subsystems and unconstrained subsystems. However, the normal backstepping method is only an effective method structured to control lower-triangular systems. Since the method is strictly limited to the system structure, the previous works cannot solve the problem considered. Thus, we employ the cross backstepping method to solve the problem of partial and alternate time-varying state constraints. For the constrained subsystems, the time-varying barrier Lyapunov function (TVBLF) is employed to ensure that the violation of any time-varying constraint does not occur. Besides, the radial basis function neural network (RBFNN) is used to approximate the uncertainties. Then, based on the stability analysis, it is concluded that the output follows the desired trajectory as closely as possible, all the signals in closed-loop systems are bounded, and the alternate time-varying state constraints are never violated. Finally, the simulation results demonstrate the effectiveness of the proposed strategy.