Adaptive fault tolerant tracking control for a class of stochastic nonlinear systems with output constraint and actuator faults

In this work, we present a novel control algorithm for a class of stochastic nonlinear systems with constraint requirement on the system output tracking error. The gain functions are not totally known, and the systems are subject to actuator faults. A novel structure of barrier Lyapunov function is proposed to deal with the constraint requirement in stochastic systems. We show that under the proposed control scheme, convergence of the system output tracking error into a small set around zero is guaranteed in the sense of mean quartic value. The constraint requirement on the system output tracking error will not be violated during operation in the sense of probability. The proposed scheme is also a unified approach, which can handle both deterministic and stochastic nonlinear systems of a particular structure, and can also handle nonlinear systems with or without system output constraint requirements. An illustrative example with both deterministic and stochastic nonlinear systems is presented to further demonstrate the effectiveness of the proposed control scheme.