Adaptive Fuzzy Backstepping Design for Nonlinear Systems with Asymmetric Full-State Constraints

When backsteppinng is used to construct controllers for systems with full-state constraints, an open and challenging problem is how to ensure the designed virtual control signals remain in the corresponding state constraints all the time during the operation. This research deals with this problem and presents a novel adaptive fuzzy control method to solve this problem. The designed adaptive fuzzy controller can make sure that all the closed-loop signals keep bounded and the tracking error tends to a small neighborhood of origin, meanwhile, the asymmetric constraints on each system state are not violated during the operation. Finally, the proposed control scheme is further tested by a simulation example.