Fault-tolerant control for a class of hybrid systems with uncontrollable switching

Abstract

This article focuses on the fault-tolerant control (FTC) problem for a class of hybrid systems modelled by hybrid automata. An observer-based FTC framework is proposed for the hybrid system with uncontrollable state-dependent switching and without full continuous state measurements. Two kinds of faults are considered: continuous faults that affect each mode and discrete faults that affect the mode transition. Sufficient conditions are given such that the hybrid system can be stabilised in the sense of LaSalle invariance principle. Simulation results of example of CPU processing control show the efficiency of the proposed method.

Keywords:

• hybrid-systems
• fault-tolerant control
• observer
• fault diagnosis
• fault detection and isolation
• hybrid automata

Acknowledgements

This work is partially supported by National Natural Science Foundation of China (60874051,60811120024), Natural Science Foundation of Jiangsu Province (BK2007195) and Graduate innovation research funding of Jiangsu Province (CX07B-112z).

Notes

Notes

1. Recall that a positive definite radially unbounded smooth function V : ℜ ⁿ → ℜ is called a control Lyapunov function for the system , x ∈ ℜ ⁿ , if we have inf _u∈𝒰{L _f V + L _G V _u } < 0 ∀x ≠ 0.

2. recall that class 𝒦 is a class of strictly increasing and continuous functions [0, ∞) → [0, ∞), class 𝒦_∞ is the subset of 𝒦 consisting of all those functions that are unbounded, a function β : [0, ∞) × [0, ∞) → [0, ∞) is class 𝒦ℒ if β(·, t) is of class 𝒦.

3. In some literatures, e.g. Tomlin et al. (2003), ‘mode’ is also called ‘location’, that defines the discrete state space of the system.

4. The state of system when a sufficiently long time has passed after booting the system is defined as the equilibrium state of this model.