The stability guaranteed active fault-tolerant control against actuators failures and plant uncertainties in networked control systems (NCSs) is addressed. A detailed design procedure is formulated as a convex optimization problem which can be efficiently solved by existing software. An illustrative example is given to show the efficiency of the proposed method for network-based control for uncertain systems.

Fault-tolerant
control (FTC) techniques against actuator faults can be classified into two
groups [

In contrast to passive FTC systems, AFTC techniques
rely on a real-time fault detection and isolation (FDI) scheme and a controller
reconfiguration mechanism. Such techniques allow a flexibility to select different controllers according to different component failures, and therefore
better performance of the closed-loop system can be expected. However, this
holds true when the FDI process does not make an incorrect or delayed decision
[

The outline of the paper is as follows. In Section

Figure

Networked control system with actuator failures.

The delays induced by the network in the closed-loop
control system are modeled as time-varying quantities

We further assume that the time-varying delays

If there exists a control law

In Section

construct a
fault-tolerant controller (i.e., a robust controller), with structure as given
by (

redesign that
part of the above controller associated to only one fault-free actuator
in order to improve the robust performance without loss of the stability
property of the design in step (i); step (ii) repeats for all

In this subsection,
we establish a sufficient condition for the existence of a guaranteed cost
network-based controller for the uncertain plant (

If there exist a gain matrix

See the appendix.

The “

Note that
the upper bound in (

Now, we derive the guaranteed cost controller in terms of the feasible solutions to a set of linear matrix inequalities.

Using Sherman-Morrison matrix inversion formula, we
have

Suppose that for a prescribed
scalar

From (

Given a prescribed
scalar

Based on the
controller designed in Theorem

If there exist a gain matrix

The proof is similar to the proof
of Theorem

Proceeding as
in step (i), we restrict

Suppose that for a prescribed scalar

Given a prescribed
scalar

The dynamics are described by the following matrices:

Disturbance, actuator failures, and state response.

the dotted line
represents the state response for controller-switching sequence N^{°}

the solid line
represents the state response for controller-switching sequence N^{°}

the dot-dashed line represents the state response under the fault tolerant control (i.e., robust control) of step (i).

^{°}

In this paper, the stability guaranteed active fault tolerant control against actuators failure in networked control system with time-varying but bounded delays has been addressed. Plants with norm-bounded parameter uncertainty have been considered, where the uncertainty may appear in the state matrix. Modelling network-induced delays as communication delays between sensors and actuators, linear memoryless state feedback fault-tolerant controllers have been developed through LMI-based methods. A simulation example has been presented to show the potentials of the proposed method for fault-tolerant control in networked control systems.

The following
matrix inequalities are essential for the proof of Theorem

Assume that

Let

Note that

The authors would like to thank the anonymous reviewers for their constructive comments and suggestions that have improved the quality of the manuscript. This work is supported by the French National Research Agency (Agence Nationale de la Recherche, ANR) project SafeNECS (Safe-Networked Control Systems) under Grant no. ANR-ARA SSIA-NV-15.