Barrier Lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems

Abstract In this paper, an adaptive controller design is studied for single-input–single-output (SISO) nonlinear systems with parameter uncertainties and the systems are enforced to subject to the full state constraints. A remarkable feature of the constrained systems is that the so-called control direction is unknown, or in other words, the signs of control gains are unknown. In the existing results, we discover that all the state constraint control results are required to determine a priori knowledge of control direction. It will be inevitable to bring about a different design procedure and a difficult task when no a priori knowledge of control direction is known. To stabilize this class of systems, two parameter adaptive controllers with Nussbaum gain technique are constructively framed to overcome the unknown control direction problem, and the novel symmetric and asymmetric Barrier Lyapunov Functions (BLFs) are adopted to guarantee that the states are not to violate their constraints. Then, the proposed BLF strategy can be to conquer the conservatism of the traditional BLF-based controls for the full state constraints. Finally, two theorems are provided to show that all the signals in the closed-loop system are bounded, the outputs are driven to follow the reference signals and all the states are ensured to remain in the predefined compact sets. The effectiveness of the proposed scheme is performed via a simulation example.