Data-Driven Fault Estimation and Control for Unknown Discrete-Time Systems via Multiobjective Optimization Method
Xiaojian Li, Ning Wang
Abstract
This article investigates the fault estimation and control problem for linear discrete-time systems with completely unknown system dynamics. The considered problem is formulated into a multiobjective composite optimization one and a data-driven <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }/H_{\infty }$ </tex-math></inline-formula> controller is then designed to ensure the fault estimation and control performances. Different from the existing multiobjective optimization strategies, where only one system performance can be optimized, a two-step design method is introduced in this article to optimize different system performances. Especially, each step design contains a novel constraint-type optimization algorithm, and the matrix inequality involved in the constraint condition has no structure restriction. In addition, by applying policy iterations (PIs) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -learning techniques, the controller parameters are obtained by solving a set of linear matrix inequalities (LMIs) only relying on the system states and inputs. Finally, the effectiveness of the proposed approach is illustrated through three examples.