Minimization of Sensor Activation in Decentralized Fault Diagnosis - PowerPoint PPT Presentation

Minimization of Sensor Activation in Decentralized Fault Diagnosis of Discrete Event Systems Xiang Yin and Stéphane Lafortune EECS Department, University of Michigan 54th IEEE CDC, Dec 15-18, 2015, Osaka, Japan 0/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Introduction 𝑡 2 3 0 4 𝑡 𝑡 1 5 Plant G 𝑄 𝑄 2 1 𝑄 1 (𝑡) 𝑄 2 (𝑡) Agent 1 𝐸 1 Agent 2 𝐸 2 Coordinator Fault Alarm 1/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Introduction 𝑡 2 3 0 4 𝑡 𝑡 1 5 Plant G Ω 1 Ω 2 𝑄 𝑄 2 1 𝑄 Ω 1 (𝑡) 𝑄 Ω 2 (𝑡) Agent 1 𝐸 1 Agent 2 𝐸 2 Coordinator Fault Alarm 1/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

System Model 𝐻 = (𝑅, Σ, 𝜀, 𝑟 0 ) is a deterministic FSA • 𝑅 is the finite set of states; • Σ is the finite set of events; • 𝜀: 𝑅 × Σ → 𝑅 is the partial transition function; • 𝑟 0 is the initial state. 2/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

System Model 𝐻 = (𝑅, Σ, 𝜀, 𝑟 0 ) is a deterministic FSA • 𝑅 is the finite set of states; • Σ is the finite set of events; • 𝜀: 𝑅 × Σ → 𝑅 is the partial transition function; • 𝑟 0 is the initial state. Sensor activation policy Ω = (𝐵, 𝑀) , where 𝐵 = (𝑅 𝐵 , Σ 𝑝 , 𝜀 𝐵 , 𝑟 0,𝐵 ) and 𝑀: 𝑅 𝐵 → 2 Σ 𝑝 ; - ∗ - Projection 𝑄 Ω : ℒ 𝐻 → Σ 𝑝 𝐻 𝑡 State estimate ℰ Ω - , 𝐽 𝑦 ∈ 2 𝑅 . 𝐵 𝑦 ∈ 𝑅 𝐵 - Observer 𝑃𝑐𝑡 Ω 𝐻 = 𝑌, Σ 𝑝 , 𝑔, 𝑦 0 , and 𝑦 = 𝐽 𝑦 , 𝐵 𝑦 𝑝 𝑔 𝑝 ( 1,3,5,7 , 1) 2 1 3 𝑝 𝑐 𝑔 𝑝 𝑏 𝑏 ( 2,4,7 , 2) 1 2 3 4 5 𝑏 𝑏 𝑐 *𝑝+ *𝑏+ ∅ 𝑝 𝑝 ( 6 , 3) 6 7 𝑯 𝛁 𝑷𝒄𝒕 𝜵 𝑯 2/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Decentralized Diagnosis Problem = Ω 1 , Ω 2 with Σ 𝑝,1 and Σ 𝑝,2 • Two agents ℐ = *1,2+ , Ω • A fault event 𝑓 𝑒 ∈ Σ ∖ (∪ 𝑗=1,2 Σ 𝑝,𝑗 ) Ψ 𝑓 𝑒 = *𝑡𝑓 𝑒 ∈ ℒ 𝐻 : 𝑡 ∈ Σ ∗ + • 3/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Decentralized Diagnosis Problem = Ω 1 , Ω 2 with Σ 𝑝,1 and Σ 𝑝,2 • Two agents ℐ = *1,2+ , Ω • A fault event 𝑓 𝑒 ∈ Σ ∖ (∪ 𝑗=1,2 Σ 𝑝,𝑗 ) Ψ 𝑓 𝑒 = *𝑡𝑓 𝑒 ∈ ℒ 𝐻 : 𝑡 ∈ Σ ∗ + • • K -Codiagnosability: and 𝑓 𝑒 if A live language ℒ 𝐻 is said to be 𝐿 -codiagnosable w.r.t. Ω • 𝑌 is the finite set of states; (∀𝑡 ∈ Ψ(𝑓 𝑒 ))(∀𝑢 ∈ ℒ 𝐻 /𝑡), 𝑢 ≥ 𝐿 ⇒ 𝐷𝐸- • 𝐹 is the finite set of events; where the codiagnosability condition 𝐷𝐸 is • 𝑔: 𝑌 × 𝐹 → 𝑌 is the partial transition function; • 𝑌 0 is the set of initial states. ∃𝑗 ∈ *1,2+ ∀𝜕 ∈ ℒ 𝐻 𝑄 Ω 𝑗 𝑥 = 𝑄 Ω 𝑗 𝑡𝑢 ⇒ 𝑓 𝑒 ∈ 𝜕 . 3/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Problem Formulation Decentralized Minimization Problem • Let 𝐻 be the system with fault event 𝑓 𝑒 . For each agent 𝑗 ∈ 1,2 , let Σ 𝑝,𝑗 ⊆ Σ be the set of observable events. Find a sensor activation policy ∗ = ,Ω 1 • 𝑌 is the finite set of states; ∗ , Ω 2 ∗ - such that Ω • 𝐹 is the finite set of events; ∗ C1. ℒ 𝐻 is 𝐿 -codiagnosable w.r.t. Ω and e d ; • 𝑔: 𝑌 × 𝐹 → 𝑌 is the partial transition function; ′ < Ω ∗ ∗ that satisfies (C1). C2. Ω is minimal, i.e., there does not exist another Ω • 𝑌 0 is the set of initial states. ′ < Ω ∗ is defined in terms of set inclusion. • Ω 4/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Literature Review Decentralized Fault Diagnosis • Debouk, R., Lafortune, S., & Teneketzis, D. (2000). Coordinated decentralized protocols for failure diagnosis of discrete event systems. Discrete Event Dynamic Systems, 10(1-2), 33-86. • Qiu, W., & Kumar, R. (2006). Decentralized failure diagnosis of discrete event systems. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 36(2), 384-395. • Kumar, R., & Takai, S. (2009). Inference-based ambiguity management in decentralized decision-making: Decentralized diagnosis of discrete-event systems. IEEE Transactions on Automation Science and Engineering, 6(3), 479-491. • Moreira, M. V., Jesus, T. C., & Basilio, J. C. (2011). Polynomial time verification of decentralized diagnosability of discrete event systems. IEEE Transactions on Automatic Control, 56(7), 1679-1684. Dynamic Sensor Activation Problem • Thorsley, D., & Teneketzis, D. (2007). Active acquisition of information for diagnosis and supervisory control of discrete event systems. Discrete Event Dynamic Systems, 17(4), 531-583. • Cassez, F., & Tripakis, S. (2008). Fault diagnosis with static and dynamic observers. Fundamenta Informaticae, 88(4), 497-540. • Cassez, F., Dubreil, J., & Marchand, H. (2012). Synthesis of opaque systems with static and dynamic masks. Formal Methods in System Design, 40(1), 88-115. • Shu, S., Huang, Z., & Lin, F. (2013). Online sensor activation for detectability of discrete event systems. IEEE Transactions on Automation Science and Engineering, 10(2), 457-461. • Wang, W., Lafortune, S., Lin, F., & Girard, A. R. (2010). Minimization of dynamic sensor activation in discrete event systems for the purpose of control. IEEE Transactions on Automatic Control, 55(11), 2447-2461. • Wang, W., Lafortune, S., Girard, A. R., & Lin, F. (2010). Optimal sensor activation for diagnosing discrete event systems. Automatica, 46(7), 1165-1175. 5/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Solution Overview Person by Person Approach Agent 1 Agent 2 𝟏 𝟏 𝛁 𝟑 𝛁 𝟐 6/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Solution Overview Person by Person Approach Agent 1 Agent 2 𝟏 𝟏 𝛁 𝟑 𝛁 𝟐 𝟏 𝛁 𝟐 6/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Solution Overview Person by Person Approach Agent 1 Agent 2 𝟏 𝟏 𝛁 𝟑 𝛁 𝟐 𝟏 𝟐 𝛁 𝟐 𝛁 𝟑 6/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Solution Overview Person by Person Approach Agent 1 Agent 2 𝟏 𝟏 𝛁 𝟑 𝛁 𝟐 𝟏 𝟐 𝛁 𝟐 𝛁 𝟑 𝟐 𝛁 𝟑 6/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Solution Overview Person by Person Approach Agent 1 Agent 2 𝟏 𝟏 𝛁 𝟑 𝛁 𝟐 𝟏 𝟐 𝛁 𝟐 𝛁 𝟑 𝟐 𝟐 𝛁 𝟐 𝛁 𝟑 6/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Solution Overview Person by Person Approach Agent 1 Agent 2 𝟏 𝟏 𝛁 𝟑 𝛁 𝟐 𝟏 𝟐 𝛁 𝟐 𝛁 𝟑 𝟐 𝟐 𝛁 𝟐 𝛁 𝟑 6/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Solution Overview Person by Person Approach Agent 1 Agent 2 𝟏 𝟏 𝛁 𝟑 𝛁 𝟐 𝟏 𝟐 𝛁 𝟐 𝛁 𝟑 𝟐 𝟐 𝛁 𝟐 𝛁 𝟑 ∗ ∗ 𝛁 𝟐 𝛁 𝟑 6/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Solution Overview Person by Person Approach Challenges & Solutions Agent 1 Agent 2 𝟏 𝟏 𝛁 𝟑 𝛁 𝟐 • Constrained minimization problem 𝟏 𝟐 𝛁 𝟐 𝛁 𝟑 𝟐 𝟐 𝛁 𝟐 𝛁 𝟑 ∗ ∗ 𝛁 𝟐 𝛁 𝟑 6/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Solution Overview Person by Person Approach Challenges & Solutions Agent 1 Agent 2 𝟏 𝟏 𝛁 𝟑 𝛁 𝟐 • Constrained minimization problem - Full centralized problem - Generalized state-partition automaton 𝟏 𝟐 𝛁 𝟐 𝛁 𝟑 𝟐 𝟐 𝛁 𝟐 𝛁 𝟑 ∗ ∗ 𝛁 𝟐 𝛁 𝟑 6/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Solution Overview Person by Person Approach Challenges & Solutions Agent 1 Agent 2 𝟏 𝟏 𝛁 𝟑 𝛁 𝟐 • Constrained minimization problem - Full centralized problem - Generalized state-partition automaton 𝟏 𝟐 𝛁 𝟐 𝛁 𝟑 • Converge? 𝟐 𝟐 𝛁 𝟐 𝛁 𝟑 ∗ ∗ 𝛁 𝟐 𝛁 𝟑 6/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Solution Overview Person by Person Approach Challenges & Solutions Agent 1 Agent 2 𝟏 𝟏 𝛁 𝟑 𝛁 𝟐 • Constrained minimization problem - Full centralized problem - Generalized state-partition automaton 𝟏 𝟐 𝛁 𝟐 𝛁 𝟑 • Converge? - Yes! 𝟐 𝟐 - Monotonicity property 𝛁 𝟐 𝛁 𝟑 ∗ ∗ 𝛁 𝟐 𝛁 𝟑 6/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Solution Overview Person by Person Approach Challenges & Solutions Agent 1 Agent 2 𝟏 𝟏 𝛁 𝟑 𝛁 𝟐 • Constrained minimization problem - Full centralized problem - Generalized state-partition automaton 𝟏 𝟐 𝛁 𝟐 𝛁 𝟑 • Converge? - Yes! 𝟐 𝟐 - Monotonicity property 𝛁 𝟐 𝛁 𝟑 • Minimal? ∗ ∗ 𝛁 𝟐 𝛁 𝟑 6/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Solution Overview Person by Person Approach Challenges & Solutions Agent 1 Agent 2 𝟏 𝟏 𝛁 𝟑 𝛁 𝟐 • Constrained minimization problem - Full centralized problem - Generalized state-partition automaton 𝟏 𝟐 𝛁 𝟐 𝛁 𝟑 • Converge? - Yes! 𝟐 𝟐 - Monotonicity property 𝛁 𝟐 𝛁 𝟑 • Minimal? - Yes! - Logical optimal (set inclusion) ∗ ∗ 𝛁 𝟐 𝛁 𝟑 6/15 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015