Fault-Tolerant Control and Adaptive Estimation Schemes for Sensors with Bounded Faults

A novel structure of the state observer with adaptive estimation scheme of sensors and the design of control law to accommodate sensor faults are presented. In this novel approach, based on Lyapunov method, the system is designed, in its feedback loop, to achieve good estimation of the plant states and to adaptively monitor the condition of sensors. Once we have the estimated plant states, the design of control law is straightforward. In our design an error filter and a state observer together with an adaptive law will be used to achieve the estimation of the plant states in the presence of sensor faults. While, in the mean time, the estimation scheme by the adaptive law will be used to monitor the condition of sensors. The sensor faults that we consider in this paper are the signals subject to abrupt jump down toward zero while between each jump the fault is kept at constant value. In such case we prove that a quadratic Lyapunov function is bounded even if the number of jumps is infinite and thus is still applicable to ensure asymptotic stability.