Create transmissionlinecircuits.jl

models/TransmissionLineCircuit/transmissionlinecircuits.jl

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+#=
+This is Non-linear transmission line circuits model,
+Originally considered by Chen et al [1]
+and then adapted to be hybrid case studies [2, 3]
+
+[1] https://www.researchgate.net/publication/2538345_A_Quadratic_Method_for_Nonlinear_Model_Order_Reduction
+
+[2] https://ieeexplore.ieee.org/document/1174092
+
+[3] C. Gu. Model Order Reduction of Nonlinear Dynamical Systems. 
+    PhD thesis, University of California, Berkeley, 2011   
+=#
+
+using MathematicalSystems, Reachability, HybridSystems
+using Reachability: solve
+using TaylorIntegration
+
+@taylorize function transmission_line_circuits_one!(t, x, dx)
+   local α = 5
+   dx[1] = (-2*x[1] + x[2]) + ((2 - exp(α*x[1])) + (2 - exp(α*(x[1] - x[2]))))
+   dx[2] = (-2*x[2] + x[1]) + ((x[3] + exp(α*(x[1] - x[2]))) - exp(α*(x[2] - x[3])))
+   dx[3] = (-2*x[3] + x[2]) + ((x[4] + exp(α*(x[2] - x[3]))) - exp(α*(x[3] - x[4])))
+   dx[4] = (-2*x[4] + x[3]) + ((x[5] + exp(α*(x[3] - x[4]))) - exp(α*(x[4] - x[5])))
+   dx[5] = (-2*x[5] + x[4]) + ((x[6] + exp(α*(x[4] - x[5]))) - exp(α*(x[5] - x[6])))
+   dx[6] = (-x[6] + x[5]) + (exp(α*(x[5] - x[6])) - 1)
+   dx[7] = one(x[7])
+   return dx
+end
+
+@taylorize function transmission_line_circuits_two!(t, x, dx)
+   local α = 5
+   dx[1] = (-2*x[1] + x[2]) + ((2 - exp(α*x[1])) + ((3 - exp(α*(x[1] - x[2]))) - x[7]))
+   dx[2] = (-2*x[2] + x[1]) + ((x[3] + exp(α*(x[1] - x[2]))) - exp(α*(x[2] - x[3])))
+   dx[3] = (-2*x[3] + x[2]) + ((x[4] + exp(α*(x[2] - x[3]))) - exp(α*(x[3] - x[4])))
+   dx[4] = (-2*x[4] + x[3]) + ((x[5] + exp(α*(x[3] - x[4]))) - exp(α*(x[4] - x[5])))
+   dx[5] = (-2*x[5] + x[4]) + ((x[6] + exp(α*(x[4] - x[5]))) - exp(α*(x[5] - x[6])))
+   dx[6] = (-x[6] + x[5]) + (exp(α*(x[5] - x[6])) - 1)
+   dx[7] = one(x[7])
+   return dx
+end
+
+@taylorize function transmission_line_circuits_three!(t, x, dx)
+   local α = 5
+   dx[1] = (-2*x[1] + x[2]) + ((2 - exp(α*x[1])) + (1 - exp(α*(x[1] - x[2]))))
+   dx[2] = (-2*x[2] + x[1]) + ((x[3] + exp(α*(x[1] - x[2]))) - exp(α*(x[2] - x[3])))
+   dx[3] = (-2*x[3] + x[2]) + ((x[4] + exp(α*(x[2] - x[3]))) - exp(α*(x[3] - x[4])))
+   dx[4] = (-2*x[4] + x[3]) + ((x[5] + exp(α*(x[3] - x[4]))) - exp(α*(x[4] - x[5])))
+   dx[5] = (-2*x[5] + x[4]) + ((x[6] + exp(α*(x[4] - x[5]))) - exp(α*(x[5] - x[6])))
+   dx[6] = (-x[6] + x[5]) + (exp(α*(x[5] - x[6])) - 1)
+   dx[7] = one(x[7])
+   return dx
+end
+
+
+function circuits()
+
+   automaton = LightAutomaton(3) #three modes
+
+   inv_one = HPolyhedron([HalfSpace([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0], 1.0)]) 
+
+   inv_two = HPolyhedron([HalfSpace([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0], 2.0), 
+                          HalfSpace([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0], -1.0)]) 
+
+   inv_three = HPolyhedron([HalfSpace([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0], -2.0)]) 
+
+
+   m1 = ConstrainedBlackBoxContinuousSystem(transmission_line_circuits_one!, 7, inv_one)
+
+   m2 = ConstrainedBlackBoxContinuousSystem(transmission_line_circuits_two!, 7, inv_two)
+
+   m3 = ConstrainedBlackBoxContinuousSystem(transmission_line_circuits_three!, 7, inv_three)
+
+   modes = [m1, m2, m3]  #modes
+
+
+   add_transition!(automaton, 1, 2, 1)    # first transion
+   add_transition!(automaton, 2, 3, 2)    # second transion
+
+   G_first = Hyperplane([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0], 1.0)
+   G_second = Hyperplane([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0], 2.0)
+
+   R_first = ConstrainedIdentityMap(7, G_first)
+   R_second = ConstrainedIdentityMap(7, G_second)
+   # resetmaps
+   resetmaps = [R_first, R_second]
+   # switchings
+   switching = AutonomousSwitching()
+   switchings = fill(switching, 2)
+
+   ℋ = HybridSystem(automaton, modes, resetmaps, switchings)
+
+   X0 = Hyperrectangle(low = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], high = [0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.01])
+   # initial condition 
+   initial_condition = [(1, X0)]  
+
+   system = InitialValueProblem(ℋ, initial_condition)
+
+   options = Options(:mode=>"reach", :T=>3.5, :plot_vars=>[1, 2], :project_reachset=>false)
+
+   return (system, options)
+end
+
+
+problem, options = circuits();
+
+options = Options(:mode=>"reach", :T=>3.0, :plot_vars=>[1, 2], :project_reachset=>false, :verbosity => "info")
+
+@time sol_TMJets = solve(problem, options, TMJets(:orderT=>5, :orderQ=>2, :abs_tol=>1e-10),LazyDiscretePost(:check_invariant_intersection=>true));
+
+plot(sol_TMJets, xlab="x", ylab="v", alpha=.5, color=:lightblue)