Locally Expanded Constraint Boundary based Adaptive Composite Control of a Constrained Nonlinear System with Time-varying Actuator Fault

In this paper, an adaptive composite tracking control strategy is proposed for a class of nonlinear systems with asymmetric time-varying state constraints and time-varying actuator faults. Based on the idea of fuzzy logic system (FLS), a FL based-membership function is constructed to realize the local expanded constraint boundary. State constraint problem is solved by constructing a transformation function which can avoid feasibility conditions of barrier Lyapunov function (BLF). At the same time, as the reference command is slightly beyond the border, the output still can track the reference command via locally expanding the constraint boundary. In addition, the boundaries of other states can be expanded automatically. The unknown nonlinear functions are solved by radial basis function neural network (RBFNN) and time-varying actuator faults are handled by adaptive technique. Then backstepping method based control scheme is proposed, which ensures the output track the out-of-bounds reference command and the constraints of remaining states can also be expanded. In the framework of Lyapunov theory, it is proven that the closed-loop system can eventually be bounded stable and the tracking error converges to an arbitrarily small vicinity of zero. At the end, simulation results are given to show the validity of the proposed control scheme.