Adaptive tracking control for stochastic nonlinear systems with asymmetric full state constraints

This article addresses the problem of adaptive tracking control for stochastic nonlinear systems with asymmetric full state constraints. Different from the traditional log-type or tan-type barrier Lyapunov functions (BLFs), a new asymmetric BLF is proposed in this article. Then, a state feedback controller is constructed with backstepping method so that all signals of the closed-system are bounded and the asymmetric state constraint is well kept all the time. Without changing the structure of the controller, the design and the analysis for constrained and unconstrained systems are unified. Finally, the effectiveness of proposed control strategy has been demonstrated by simulations of numerical example and the single-link robot arm model.

Automated summary

This article proposes a new asymmetric barrier Lyapunov function for adaptive tracking control of stochastic nonlinear systems with asymmetric full state constraints. A state feedback controller is constructed using the backstepping method to ensure bounded signals and the maintenance of the asymmetric state constraint. The design and analysis for constrained and unconstrained systems are unified without changing the controller structure. The effectiveness of the proposed control strategy is demonstrated through simulations.