A General Approach for Solving Dynamic Sensor Activation Problems - PowerPoint PPT Presentation

A General Approach for Solving Dynamic Sensor Activation Problems for a Class of Properties Xiang Yin and Stéphane Lafortune EECS Department, University of Michigan 54th IEEE CDC, Dec 15-18, 2015, Osaka, Japan 0/17 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Introduction • Dynamic Sensor Activation Problem 2 3 0 4 𝑡 1 5 Plant G 𝑄 𝑄(𝑡) Observer 1/17 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Introduction • Dynamic Sensor Activation Problem 2 3 0 4 𝑡 1 5 Sensor Activation Plant G Module 𝝏 𝑄 𝑄 𝜕 (𝑡) Observer 1/17 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Introduction • Dynamic Sensor Activation Problem 2 3 0 4 𝑡 1 5 Sensor Activation Plant G Module 𝝏 𝑄 𝑄 𝜕 (𝑡) Property √ Observer 1/17 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 2/17 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 • Σ = Σ 𝑝 ∪ Σ 𝑡 ∪ Σ 𝑣𝑝 • A sensing decision is a set of events 𝜄 ∈ 2 Σ s.t. Σ 𝑝 ⊆ 𝜄 ⊆ Σ 𝑝 ∪ Σ 𝑡 Θ denotes the set of sensing decisions • Information mapping 𝜕: ℒ 𝐻 → Θ 𝜕 : ℒ 𝐻 → Σ 𝑝 ∪ Σ 𝑡 ∗ denotes the corresponding projection 𝑄 • A sensor activation policy is an information mapping 𝜕: ℒ 𝐻 → Θ s.t. ∀𝑡, 𝑢 ∈ ℒ 𝐻 : 𝑄 𝜕 𝑡 = 𝑄 𝜕 𝑢 ⇒ 𝜕 𝑡 = 𝜕(𝑢) 2/17 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Information-State-Based Property Information State: a set of states, 𝐽 ≔ 2 𝑅 Information-State-Based Property • Let 𝐻 be the system automaton and 𝜕: ℒ 𝐻 → Θ be a sensor activation policy. An IS-based property w.r.t. 𝐻 is a function 𝜒: 2 𝑅 → *0,1+ We say that 𝜕 satisfies 𝜒 w.r.t. 𝐻 , denoted by 𝜕 ⊨ 𝐻 𝜒 , if 𝐻 𝑡 ) = 1 ∀𝑡 ∈ ℒ 𝐻 : 𝜒(ℰ 𝜕 where 𝐻 𝑡 = *𝑟 ∈ 𝑅: ∃𝑢 ∈ 𝑀 𝑡. 𝑢. 𝑄 ℰ 𝜕 𝜕 𝑢 = 𝑄 𝜕 𝑡 ∧ 𝜀 𝑟 0 , 𝑢 = 𝑟+ 3/17 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

IS-based Properties • Information-State-Based Properties • Opacity: privacy applications • Diagnosability: fault detection and isolation • Predictability: fault prognosis • Detectability: state estimation • Anonymity: privacy applications • Etc. 4/17 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Example 1 𝑓 𝑝 1 2 3 7 𝑔 𝜏 1 𝑝 𝑓 𝜏 2 𝑝 𝑓, 𝜏 1 4 5 6 IS-based Property 𝜒: 2 𝑅 → *0,1+ • ∀ 𝑗 ∈ 2 𝑅 : 𝜒 𝑗 = 1 ⇔ ,∄𝑟 ∈ 1,4,5,6 : 3, 𝑟 ⊆ 𝑗- 5/17 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Example 1 𝑓 𝑝 1 2 3 7 𝑔 𝜏 1 𝑝 𝑓 𝜏 2 𝑝 𝑓, 𝜏 1 4 5 6 IS-based Property 𝜒: 2 𝑅 → *0,1+ • ∀ 𝑗 ∈ 2 𝑅 : 𝜒 𝑗 = 1 ⇔ ,∄𝑟 ∈ 1,4,5,6 : 3, 𝑟 ⊆ 𝑗- • Sensor Activation Policy 𝜕: ℒ 𝐻 → Θ ∀𝑡 ∈ ℒ 𝐻 : 𝜕 𝑡 = *𝑝+ 5/17 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Example 1 𝑓 𝑝 1 2 3 7 𝑔 𝜏 1 𝑝 𝑓 𝜏 2 𝑝 𝑓, 𝜏 1 4 5 6 IS-based Property 𝜒: 2 𝑅 → *0,1+ • ∀ 𝑗 ∈ 2 𝑅 : 𝜒 𝑗 = 1 ⇔ ,∄𝑟 ∈ 1,4,5,6 : 3, 𝑟 ⊆ 𝑗- • Sensor Activation Policy 𝜕: ℒ 𝐻 → Θ ∀𝑡 ∈ ℒ 𝐻 : 𝜕 𝑡 = *𝑝+ • The IS-based property is not satisfied, i.e., 𝜕 ⊭ 𝜒 𝐻 𝑓𝑝 = *𝟒, 𝟕+ ℰ 𝜕 5/17 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Example 1 𝑓 𝑝 1 2 3 7 𝑔 𝜏 1 𝑝 𝑓 𝜏 2 𝑝 𝑓, 𝜏 1 4 5 6 IS-based Property 𝜒: 2 𝑅 → *0,1+ • ∀ 𝑗 ∈ 2 𝑅 : 𝜒 𝑗 = 1 ⇔ ,∄𝑟 ∈ 1,4,5,6 : 3, 𝑟 ⊆ 𝑗- • Sensor Activation Policy 𝜕: ℒ 𝐻 → Θ ∀𝑡 ∈ ℒ 𝐻 : 𝜕 𝑡 = *𝑝+ • The IS-based property is not satisfied, i.e., 𝜕 ⊭ 𝜒 𝐻 𝑓𝑝 = *𝟒, 𝟕+ ℰ 𝜕 • State-disambiguation problem 5/17 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Example 2 IS-based Property 𝜒: 2 𝑅 → *0,1+ • ∀ 𝑗 ∈ 2 𝑅 : 𝜒 𝑗 = 1 ⇔ ,𝑗 ⊈ 𝑌 𝑇𝑓𝑑𝑠𝑓𝑢 - , where 𝑌 𝑇𝑓𝑑𝑠𝑓𝑢 ⊆ 𝑌 • Opacity problem 𝑢 𝑡 𝑄 𝜕 𝑡 = 𝑄 𝜕 (𝑢) S NS 6/17 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Problem Formulation • Minimal Sensor Activation Problem for IS-Based Properties Let 𝐻 = (𝑅, Σ, 𝜀, 𝑟 0 ) be the system automaton and 𝜒: 2 𝑅 → *0,1+ be an IS-based property w.r.t. 𝐻 . Find a sensor activation policy 𝜕 such that (i) 𝜕 ⊨ 𝐻 𝜒 (IS-based Property) (ii) ∄𝜕 ′ ∈ Ω such that 𝜕 ⊨ 𝐻 𝜒 and 𝜕 ′ < 𝜕 . (Minimality) The Maximal Sensor Activation Problem is also defined analogously. 𝜕 ′ < 𝜕 is defined in terms of set inclusion. 7/17 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Literature Review 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. • 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. • 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. • Dallal, E., & Lafortune, S. (2014). On most permissive observers in dynamic sensor activation problems. Automatic Control, IEEE Transactions on, 59(4), 966-981. • Sears, D., & Rudie, K. (2015). Minimal sensor activation and minimal communication in discrete-event systems. Discrete Event Dynamic Systems, 1-55. 8/17 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Literature Review 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. • 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. • 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. • Dallal, E., & Lafortune, S. (2014). On most permissive observers in dynamic sensor activation problems. Automatic Control, IEEE Transactions on, 59(4), 966-981. • Sears, D., & Rudie, K. (2015). Minimal sensor activation and minimal communication in discrete-event systems. Discrete Event Dynamic Systems, 1-55. • Different approaches for different properties • The sensor activation problems for some properties have not been considered • Need general approach 8/17 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015

Bipartite Dynamic Observer Bipartite Dynamic Observer (BDO) • 𝒫 , ℎ 𝑎𝑍 𝒫 , 𝐹, Γ, 𝑧 0 𝒫 , 𝑅 𝑎 𝒫 , ℎ 𝑍𝑎 ) A bipartite dynamic observer 𝒫 w.r.t. G is a 7-tuple 𝒫 = (𝑅 𝑍 𝒫 ⊆ 𝐽 is the set of Y-states; • 𝑅 𝑍 𝒫 ⊆ 𝐽 × Θ is the set of Z-states so that z = (𝐽 𝑨 , Θ 𝑨 ) ; • 𝑅 𝑎 𝒫 : 𝑅 𝑍 𝒫 × Θ → Q 𝑎 𝒫 represents the unobservable reach; • ℎ 𝑍𝑎 𝒫 : 𝑅 𝑎 𝒫 × Σ → Q 𝑍 𝒫 represents the observable reach; • ℎ 𝑎𝑍 = *𝑟 0 + is the initial state. • 𝑧 0 9/17 X.Yin & S.Lafortune (UMich) CDC 2015 Dec 2015