$H_2$ /$H_\infty$ Simultaneous Fault Detection and Control for Markov Jump Linear Systems With Partial Observation

Abstract

We focus on the Simultaneous Fault Detection and Control (SFDC) in the context of Markov Jump Linear Systems (MJLS). The main novelty of the paper is the design of H ∞ and H 2 SFDC under the MJLS framework considering partial observation of the Markov chain. Both designs are obtained via Bilinear Matrix Inequalities optimization problem. As secondary results we provide a Mixed H 2 /H ∞ SFDC under the same set up, as well as the implementation of a coordinated descent algorithm to solve the optimization problem formulated as Bilinear Matrix Inequalities (BMI). To illustrate the viability of the proposed solution a numerical example is provided. INDEX TERMS Markovian jump linear systems, simultaneous fault detection and control, hidden markov mode, H ∞ norm, H 2 norm.

Gain-Scheduled Fault Detection Filter for Discrete-Time LPV Systems

“…In the following theorem we present the design of LPV FDF via LMI in order to obtain a guaranteed H ∞ upper bound of the augmented system in (16). Theorem 2: If there exist a scalar γ > 0 and symmetric positive definite matrices W 11θ , and W 22θ and matrices W 12θ , K 1 θ , K 2 θ , Kθ , Ω θ , ∇ θ , Γ θ , C η θ , D η θ with compatible dimensions and a given scalar parameter ξ such that (27) holds for all feasible θ, β, θ then the LPV FDF (13) with…”

“…[26] present the design of a fuzzy fault-tolerant control for MJS, where the faults are reconstructed using proportional integral observers. In [27], the authors study the design of a simultaneous FDF and state-feedback control for MJS under the premise that the transition matrix is partially unknown. The paper [28] provides the design of a Fault Accommodation Control for hidden-MJS assuming that the transition matrix in the Markov chain is partially unknown.…”

Fault accommodation controller under Markovian jump linear systems with asynchronous modes

“…For solving these optimization problems with BMI constraints, there are a number of approaches presented in literature, to name a few Reference 27 or 28. In this article, we use the coordinate descent algorithm (CDA) for solving the problems which is also used and presented in References 21 and 29. The CDA is presented below.…”

Observer‐based adaptive neural networks control for Markovian jump nonlinear systems with partial mode information and input saturation

“…This means that Markov mode cannot directly access, but the mode information of Markov chain can be detected by an associated detector, 26 which is more practical and useful. Under this concept, there are some excellent results that have been reported concerning mean square stability, or control for Markovian jump linear systems 27–31 . In addition, some researchers have considered the control issue for systems with immeasurable state variables and meaningful control schemes have been proposed 12,32,33 .…”