Observer-based fault reconstruction for continuous-time piecewise-affine systems: a novel iterative learning approach

In this paper, the issue of fault reconstruction is investigated for a class of continuous-time piecewise-affine (PWA) systems against actuator faults. First, to overcome the slow response issue of the conventional iterative learning law to the fault estimation error, a novel iterative accelerator and a new triggering condition, which together constitute a more efficient accelerated iterative learning law, are proposed. Then, based on the PWA iterative learning observer, the $M$-th accelerated iterative learning law, including a first accelerated iterative learning law as a special case, is constructed. A novel learning law updating algorithm is developed to depict the iterative procedure of fault reconstruction, the triggering process for the iterative accelerator, and the updating process. Moreover, sufficient conditions for ensuring asymptotic stability with guaranteed $\mathcal{H}_{\infty}$ performance are derived for the augmented PWA estimation error dynamics subject to region mismatch between the faulty system and the iterative learning observer. Finally, two examples, including a case study of a tunnel diode circuit system, are presented to fully verify the effectiveness and superiority of the proposed accelerated iterative learning method.