Fault accommodation controller under Markovian jump linear systems with asynchronous modes

• Published in: International journal of robust and nonlinear control Vol. 30; no. 18; pp. 8503 - 8520
• Main Authors: Carvalho, L. P., Rosa, T. E., Jayawardhana, B., Costa, O. L. V.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.12.2020
• Subjects: Accommodation; Algorithms; Controllers; fault‐tolerant control; Linear systems; Markov analysis; Markov chains; Optimization; robust linear matrix inequalities; stochastic control
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5252

Summary We tackle the fault accommodation control (FAC) in the Markovian jump linear system (MJLS) framework for the discrete‐time domain, under the assumption that it is not possible to access the Markov chain mode. This premise brings some challenges since the controllers are no longer allowed to depend on the Markov chain, meaning that there is an asynchronism between the system and the controller modes. To tackle this issue, a hidden Markov chain (θ(k), θ^(k)) is used where θ(k) denotes the Markov chain mode, and θ^(k) denotes the estimated mode. The main novelty of this work is the design of ℋ∞ and ℋ2 FAC under the MJLS framework considering partial observation of the Markov chain. Both designs are obtained via bilinear matrix inequalities optimization problems, which are solved using coordinate descent algorithm. As secondary results, we present simulations using a two‐degree of freedom serial flexible joint robot to illustrate the viability of the proposed approach.