Adaptive Tracking of Uncertain Markovian Jump Nonlinear Systems with Random Actuator Faults

This article deals with the adaptive fault-tolerant tracking problem for uncertain Markovian jump nonlinear systems (MJNSs) in a stochastic framework. A joint and a scalar Markovian process are employed to describe behaviors of the unknown parameters and actuator faults, respectively, thereby characterizing uncertainties in a random manner. With the aid of the backstepping technique, an adaptive tracking controller as well as the corresponding parameter update laws is constructed by treating the regimes of all Markovian variables as constants. It is shown that with appropriate design parameters, the output tracking error can converge into a small adjustable residual set in the sense of mean quadratic value while all closed-loop signals are bounded in probability, regardless of infinite number of random abrupt jumps in both uncertain parameters and the control input. An illustrative example is provided to show the effectiveness of the theoretical results.