Fault reconstruction and fault tolerant control design for a network of dynamical systems

This paper investigates the problems of the fault reconstruction and fault compensation controller design for a network of dynamic systems in which subsystems are interconnected through each subsystem’s outputs. First, under some assumptions, we prove that the minimum phase system condition, the observer matching condition and the controllability can be kept for the overall system. Second, an augmented descriptor system is constructed and we further prove that the minimum phase system condition, the observer matching condition are kept, and then a reduced-order observer is designed for the augmented system to obtain the estimates of the overall system states and the sensor faults simultaneously. Third, an interval observer is designed for the measured output, and based on the interval observer, an asymptotical actuator fault reconstruction method is developed. Finally, an observer-based H infinite and fault compensation scheme is designed and the stability of the closed-loop system is analyzed. We point out that the closed-loop system satisfies the so-called separation property. In the end, a simulation example is given to demonstrate the effectiveness of the proposed methods.

Integrated Fault Estimation and Fault-Tolerant Control for Dynamic Positioning of Ships

An integrated fault estimation and fault-tolerant control scheme is developed in this paper for dynamic positioning of ships in the presence of an actuator fault. First, an auxiliary derivative output of dynamic positioning ships is constructed in order to satisfy the so-called observer matching condition, and a high-gain observer is designed to exactly estimate the auxiliary derivative outputs. Then, a fault-tolerant controller is developed for dynamic positioning ships based on the iterative learning observer. By means of Lyapunov–Krasovskii stability theory, it is proved that the proposed fault-tolerant controller is able to estimate the total fault effects and states of ships accurately via the iterative learning observer and also to stabilize the closed-loop system. In addition, the parameter design of the proposed fault-tolerant control system can be conveniently solved in terms of linear matrix inequalities. Finally, simulation studies for dynamic positioning ships with actuator faults are carried out, and the results validate the effectivity of the proposed fault-tolerant control scheme.

On the observer matching condition and unknown input observer design based on the system left-invertibility concept

This paper considers the problems of unknown input observer (UIO) designs when the so-called observer matching condition (OMC) is not satisfied. Firstly, the system left-invertibility (SLI) concept is investigated in detail and some new criteria are given. Secondly, based on the SLI concept, an augmented output vector formed partly by the original measurable output and partly by the auxiliary output is obtained. By this constructed output vector, the new system is allowed to be transformed into an equivalent linear dynamic system which contains no unknown input, and thus a simple Luenberger observer can be constructed to simultaneously estimate the original states and unknown inputs. Compared with the existing results, the present UIO design can be taken under the single strong detectability condition and the OMC is not needed any more. Finally, the simulations of a single-link flexible joint robotic model and a linearized vertical take-off and landing helicopter model are given to show the effectiveness of our method and its superiority over existing ones.

Adaptive observer-based fault estimation for a class of Lipschitz nonlinear systems

Fault input channels represent a major challenge for observer design for fault estimation. Most works in this field assume that faults enter in such a way that the transfer functions between these faults and a number of measured outputs are strictly positive real (SPR), that is, the observer matching condition is satisfied. This paper presents a systematic approach to adaptive observer design for joint estimation of the state and faults when the SPR requirement is not verified. The proposed method deals with a class of Lipschitz nonlinear systems subjected to piecewise constant multiplicative faults. The novelty of the proposed approach is that it uses a rank condition similar to the observer matching condition to construct the adaptation law used to obtain fault estimates. The problem of finding the adaptive observer matrices is formulated as a Linear Matrix Inequality (LMI) optimization problem. The proposed scheme is tested on the nonlinear model of a single link flexible joint robot system.