Event-Triggered Multiobjective Control and Fault Diagnosis: A Unified Framework

Abstract

In the area of robust control, fault diagnosis, and fault tolerant control of linear systems, many fundamental problems can be recast as $H_\infty$ , $l_1$ and generalized $H_2$ control frameworks leading to the so-called mixed norm or multiobjective optimization problems. This paper develops a new linear matrix inequality (LMI) approach to the problems of event-triggered multiobjective synthesis of feedback controllers and fault diagnosis filters through a unified framework. Toward this end, at first a general problem known as event-triggered integrated fault detection, isolation and control (E-IFDIC) is defined. By utilizing a filter to represent, characterize, and specify the E-IFDIC module, a multiobjective formulation of the problem is developed based on $H_\infty$ , $H_{-}$ , $l_1$ and generalized $H_2$ performance criteria. It is shown that when an event-triggered strategy is applied to both the sensor and E-IFDIC module, the amount of data that is sent through the sensor-to-E-IFDIC module and E-IFDIC module-to-actuator channels are dramatically reduced. A set of LMI feasibility conditions is derived to ensure the solvability of the problem, as well as to simultaneously obtain the E-IFDIC module parameters and the event-triggered conditions. Finally, it is shown that certain existing problems in the fields of time and event-triggered control and fault diagnosis can be considered as special cases of our proposed methodology. Two industrial case studies are also provided to illustrate and demonstrate the effectiveness of our proposed design methodology when compared with available work in the literature.