Adaptive Failure Compensation Control for Uncertain Systems With Stochastic Actuator Failures

Adaptive fault-tolerant stabilization for nonlinear systems with Markovian jumping actuator failures and stochastic noises

“…Then it can be obtained that ∥x(t)∥ < l in the interval [t 0 , t l ] a.s., which implies that V (x(t), r(t)) is bounded on [t 0 , t l ] a.s. by (20). From (19), it is obvious that LV (x(t), r(t)) is also bounded on [t 0 , t l ] a.s. Then according to Property 2.2 in Fan et al (2014) and (19), we obtain…”

“…In the spacecraft system, different values of the function ψ j (r j (t)) represent different modes of the jth reaction wheel and the transition among the modes follows a Markovian process. Additionally, the stuck case has been concerned in the actuator fault model (8) which is different from the one considered in Fan et al (2014) and extra challenges are hereby arose in the controller design.…”

“…However, compared with the deterministic counterpart, the FTC problem for stochastic nonlinear systems has seldom been discussed. In Fan, Liu, Shen, and Wang (2014), the adaptive failure compensation problem has been studied for a class of nonlinear uncertain systems subjected to stochastic actuator failures and unknown parameters, in which the stuck case and stochastic noises are not involved. In Chen and Shen (2012), the robust reliable H ∞ control problem has been studied for a class of nonlinear stochastic Markovian jump systems.…”

Supervisory switching‐based prescribed performance control of unknown nonlinear systems against actuator failures

“…In spite of hysteretic actuators operating in faulty modes, the output tracking with preassigned accuracy was achieved. Contrary to deterministic failure compensation problems studied in References and , an approach to dealing with actuator failures in a stochastic manner such as abrupt changes was formulated in Reference . With the help of projection adaptation design and nonlinear damping techniques, the challenge caused by the possibly infinite number of failures was conquered in References and .…”

“…Compared with the existing results, the established one is of the following superiorities. Only one monitoring function is constructed to implement failure detection, contrary to the multiple monitoring functions designed in References and . There is no need to compute analytic derivatives of virtual control signals, in contrast to References , , and . No adaptive techniques or approximating structures (eg, neuro/fuzzy systems) are involved in the control design, despite model uncertainties. …”