Adaptive control for uncertain nonlinear systems with state-function constraints and input delay - Gao, Lihong; Song, Zhibao; Wang, Zhen; Li, Ping (Applied mathematics and computation, 2023)
•Distinct from most existing output/state constraints problem [13, 20, 21, 22, 32, 33, 34, 35, 36], function constraints on full states in this paper are asymmetric time-varying, and they are dependent of both state and time. This will increase the difficulty of controller design due to their partial derivatives. Moreover, our proposed control scheme has wide applications, that is, symmetric constraints, constant constraints or time-varying constraints are the special cases of function constraints.•Without growth conditions on nonlinear functions, FLS is introduced to estimate some complex terms generated by the derivation of constraint boundary, the auxiliary variable and uncertain nonlinear functions which cannot be directly handled in the constructed controller.•Different from [13, 14, 19, 26, 28, 29, 33], all the control coefficients and their boundaries are not available with respect to state-function constraints. As a consequence, the Nussbaum function involved in [38, 39, 40, 41, 42] is borrowed in the process of controller design.•By incorporating BLF method into the backstepping idea, a novel adaptive fuzzy controller is devised such that the tracking error ultimately changes near the origin and all signals of the closed-loop system are bounded. Meanwhile, full states remain in the asymmetric function-constraint set. The adaptive control problem is studied for nonlinear systems with asymmetric full state-function constraints, unknown control gains, input delay and external disturbances in this paper. Firstly, the effect of input time delay is removed by using Laplace transform and Pade approximation. Then, Nussbaum function and fuzzy logic system (FLS) are recommended to dispose unknown control gains and unknown nonlinear functions, respectively. By incorporating barrier Lyapunov function (BLF) into the backstepping idea, a new adaptive fuzzy controller is presented such that the tracking error finally fluctuates near the origin and all signals of the closed-loop system are bounded. Meanwhile, the asymmetric full state-function constraints do not violate. Ultimately, a numerical example is used to explain the feasibility of the devised control scheme.