{"action":"created","comment":{"url":"https://api.github.com/repos/JuliaReach/ReachabilityBenchmarks/pulls/comments/255353804","pull_request_review_id":201919990,"id":255353804,"node_id":"MDI0OlB1bGxSZXF1ZXN0UmV2aWV3Q29tbWVudDI1NTM1MzgwNA==","diff_hunk":"@@ -0,0 +1,114 @@\n+# =================================================\n+# Platooning model\n+# See https://easychair.org/publications/paper/3QLs\n+# =================================================\n+using LinearAlgebra, SparseArrays, HybridSystems, MathematicalSystems, LazySets,\n+      Reachability\n+using LazySets: HalfSpace  # resolve name-space conflicts with Polyhedra\n+\n+\"\"\"\n+    platooning(;\n+               [deterministic_switching]::Bool=true,\n+               [time_horizon]::Float64=20.,\n+               [allowed_distance]::Float64=50.)\n+\n+Construct the platooning model consisting of three vehicles.\n+\n+### Input\n+\n+- `deterministic_switching` -- (optional, default: `true`) flag to use\n+                               deterministic transitions\n+- `time_horizon`            -- (optional, default: `20.`) time horizon\n+- `allowed_distance`        -- (optional, default: `50.`) specification of\n+                               allowed distance between the vehicles\n+\"\"\"\n+function platooning(;\n+                    deterministic_switching::Bool=true,\n+                    time_horizon::Float64=20.,\n+                    allowed_distance::Float64=50.)\n+    # three variables for each vehicle, (ei, d(et)/dt, ai) for\n+    # (spacing error, relative velocity, speed), and the last dimension is time\n+    n = 9 + 1\n+\n+    c1 = c2 = 5.   # clock constraints\n+    tb = 10.       # lower bound for loss of communication\n+    tc = tr = 20.  # upper bound for loss of communication (tc) and reset time (tr)\n+\n+    # transition graph\n+    automaton = LightAutomaton(2)\n+    add_transition!(automaton, 1, 2, 12)\n+    add_transition!(automaton, 2, 1, 21)\n+\n+    # common inputs\n+    B = sparse([2], [1], [1.], n, 1)\n+    BB = Matrix(1.0I, size(B, 1), size(B, 1))\n+    U = Interval(-9., 1.)  # acceleration of the lead vehicle\n+\n+    # common invariant\n+    X = HPolyhedron([HalfSpace(sparsevec([n], [1.], n), 20.)])","path":"models/ARCH/AFF/Platooning/Platooning.jl","position":48,"original_position":48,"commit_id":"c42f78a26d1cd9a29cd6ff29c4a5025337d5c755","original_commit_id":"c42f78a26d1cd9a29cd6ff29c4a5025337d5c755","user":{"login":"schillic","id":9656686,"node_id":"MDQ6VXNlcjk2NTY2ODY=","avatar_url":"https://avatars2.githubusercontent.com/u/9656686?v=4","gravatar_id":"","url":"https://api.github.com/users/schillic","html_url":"https://github.com/schillic","followers_url":"https://api.github.com/users/schillic/followers","following_url":"https://api.github.com/users/schillic/following{/other_user}","gists_url":"https://api.github.com/users/schillic/gists{/gist_id}","starred_url":"https://api.github.com/users/schillic/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/schillic/subscriptions","organizations_url":"https://api.github.com/users/schillic/orgs","repos_url":"https://api.github.com/users/schillic/repos","events_url":"https://api.github.com/users/schillic/events{/privacy}","received_events_url":"https://api.github.com/users/schillic/received_events","type":"User","site_admin":false},"body":"Replace this invariant and use a `Universe` instead.","created_at":"2019-02-10T20:23:18Z","updated_at":"2019-02-10T20:23:18Z","html_url":"https://github.com/JuliaReach/ReachabilityBenchmarks/pull/65#discussion_r255353804","pull_request_url":"https://api.github.com/repos/JuliaReach/ReachabilityBenchmarks/pulls/65","author_association":"MEMBER","_links":{"self":{"href":"https://api.github.com/repos/JuliaReach/ReachabilityBenchmarks/pulls/comments/255353804"},"html":{"href":"https://github.com/JuliaReach/ReachabilityBenchmarks/pull/65#discussion_r255353804"},"pull_request":{"href":"https://api.github.com/repos/JuliaReach/ReachabilityBenchmarks/pulls/65"}}},"pull_request":{"url":"https://api.github.com/repos/JuliaReach/ReachabilityBenchmarks/pulls/65","id":249397620,"node_id":"MDExOlB1bGxSZXF1ZXN0MjQ5Mzk3NjIw","html_url":"https://github.com/JuliaReach/ReachabilityBenchmarks/pull/65","diff_url":"https://github.com/JuliaReach/ReachabilityBenchmarks/pull/65.diff","patch_url":"https://github.com/JuliaReach/ReachabilityBenchmarks/pull/65.patch","issue_url":"https://api.github.com/repos/JuliaReach/ReachabilityBenchmarks/issues/65","number":65,"state":"open","locked":false,"title":"Platooning model","user":{"login":"schillic","id":9656686,"node_id":"MDQ6VXNlcjk2NTY2ODY=","avatar_url":"https://avatars2.githubusercontent.com/u/9656686?v=4","gravatar_id":"","url":"https://api.github.com/users/schillic","html_url":"https://github.com/schillic","followers_url":"https://api.github.com/users/schillic/followers","following_url":"https://api.github.com/users/schillic/following{/other_user}","gists_url":"https://api.github.com/users/schillic/gists{/gist_id}","starred_url":"https://api.github.com/users/schillic/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/schillic/subscriptions","organizations_url":"https://api.github.com/users/schillic/orgs","repos_url":"https://api.github.com/users/schillic/repos","events_url":"https://api.github.com/users/schillic/events{/privacy}","received_events_url":"https://api.github.com/users/schillic/received_events","type":"User","site_admin":false},"body":"There is a statement in the ARCH-COMP report which IMO is wrong.\r\n\r\n> There seems to be no reason why the upper bound tc should be greater than tb. Loss of communication after a time longer than tb is included by reestablishing communication in zero time. Tools could possibly exploit this by minimizing the model before the analysis.\r\n\r\nI claim that for tb = 10 and tc = 10, one cannot get to the rhs location at time 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