Composite hierarchical control for Markovian jump systems with multiple disturbances and time-varying fault

Abstract

We investigate a robust fault-tolerant control problem for continuous-time Markovian jump systems with an actuator fault and multiple disturbances (one is norm-bounded, whereas the other can be modelled by an exogenous system). Our aim is to construct, simultaneously, a model-dependent disturbance observer for modelling the disturbance estimate and a model-dependent fault diagnosis observer for the time-varying fault estimate and then propose a composite hierarchical control scheme by integrating the fault and disturbance estimates using a state feedback control strategy. Application of the H ∞ control methodology ensures stochastic stability of the resulting composite system with fault compensation, disturbance attenuation and rejection performances. On the basis of Lyapunov stability theory, the existence conditions of the disturbance observer, fault diagnosis observer and composite controller are derived from the solution to a convex optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed techniques.

A novel full-order and reduced-order fault detection filters design method for continuous-time singular Markov jump systems with complexity transition rates

“…It is known that Markov jump systems (MJSs) as a special class of hybrid systems can simulate the uncontrolled configuration and parameter unexpected changes of real dynamic systems (Feng and Zheng, 2016; Gao et al, 2018; Wei et al, 2017c; Yao et al, 2020; Zhang et al, 2016). Over the past few decades, MJSs have attracted much attention and a lot of relevant results have been reported (Li et al, 2015; Li et al, 2016; Shen et al, 2019; Wei et al, 2017; Wei et al, 2017b).…”

Disturbance-observer-based control for semi-Markovian jump systems with time-varying delay and generally uncertain transition rate

“…Over the past few decades, Markovian jump systems (MJSs) can be seen as a perfect example of random jump system; such a system transformed from one set of subsystem to another by the Markov chain (Hou et al, 2017; Kocer, 2013). The analysis results based on MJS has been obtained in Yao et al (2019), Qi et al (2017), and Zhang et al (2019). However, MJSs still have some limitations when dealing with special systems.…”