Active fault diagnosis: A multi-parametric approach

This paper considers the design of an input signal for minimizing the time and energy required to detect and isolate faults in the outputs of a system. Faults are represented by discrete switches between affine models with bounded disturbances and bounded measurement errors. Within this framework, previous work has demonstrated that a minimally harmful input guaranteeing fault diagnosis can be obtained by solving a Mixed Integer Quadratic Program (MIQP). A closed-loop approach allows to reduce the length and/or norm of this input by solving an MIQP at each time instant with the newly available measurements. However, solving such programs online can be computationally demanding. In this paper, we employ multi-parametric (mp) programming to move most of the computation offline, thus allowing the application of the closed-loop approach to fast processes. Still, the mp-MIQP complexity becomes quickly prohibitive as the number of faulty models increases. In order to overcome this problem, we propose a strategy based on mp-optimization and graph theory that takes into account only two models at a time. While this approach is suboptimal compared to the case in which all the models are considered simultaneously, simulations show that, in practice, the performance is comparable.