Adaptive control-based Barrier Lyapunov Functions for a class of stochastic nonlinear systems with full state constraints

An adaptive control scheme is developed in the paper for nonlinear stochastic systems with unknown parameters. All the states in the systems are required to be constrained in a bounded compact set, i.e., the full state constraints are considered in the systems. It is for the first time to control nonlinear stochastic systems with the full state constraints. In contrast to deterministic systems, the stochastic systems with the full state constraints are more difficult to be stabilized and the design procedures are more complicated. By constructing Barrier Lyapunov Functions (BLF) in symmetric and asymmetric forms, it can be ensured that all the states of the stochastic systems are not to transgress their constraint bounds. Thus, the proposed scheme not only solves the stability problem of stochastic systems, but also overcomes the effect of the full state constraints on the control performance. Finally, it is proved that all the signals in the closed-loop system are semi-global uniformly ultimately bounded (SGUUB) in probability, the system output is driven to follow the reference signals, and all the states are ensured to remain in the predefined compact sets. The validity of the proposed scheme is verified by a simulation example.