I want to use jump and guard conditions for my hybrid automata. But it is not working. Can anyone help? using ReachabilityAnalysis, Symbolics # Define the variables: height (x), velocity (v), and time (t) @variables x v t const vars = [x, v] # Define the constants const g = 9.81 # gravity (m/s^2) const c = 0.8 # restitution coefficient (energy loss during bounce) # Mode 1: Falling dynamics function falling!(du, u, p, t) x, v = u du[1] = v # x' = v (position derivative) du[2] = -g # v' = -g (velocity derivative due to gravity) return du end # Mode 2: Bouncing dynamics (after hitting the ground) function bouncing!(du, u, p, t) x, v = u du[1] = v # x' = v du[2] = -g # v' = -g (same as falling, but with new initial velocity) return du end # Define the hybrid automaton function bouncing_ball() n = 2 # number of dimensions (x, v) automaton = GraphAutomaton(2) # 2 modes: falling and bouncing # Mode 1: Falling invariant_falling = HalfSpace(x >= 0, vars) # Ball cannot go below ground level falling_system = @system(x' = falling!(x), dim:2, x ∈ invariant_falling) # Mode 2: Bouncing invariant_bouncing = HalfSpace(x >= 0, vars) # Also, ball cannot go below ground bouncing_system = @system(x' = bouncing!(x), dim:2, x ∈ invariant_bouncing) # Transition from falling to bouncing when ball hits the ground (x = 0) guard = HPolyhedron([x -c*v,x=>x) # Bounce with reduced velocity add_transition!(automaton, 1, 2, 1) # Mode 1 (falling) -> Mode 2 (bouncing) # Transition from bouncing back to falling after the bounce add_transition!(automaton, 2, 1, 2) # Mode 2 (bouncing) -> Mode 1 (falling) # Create the hybrid system H = HybridSystem(; automaton=automaton, modes=[falling_system, bouncing_system], resetmaps=[transition_map]) # Initial conditions: ball starts from height 10 meters, with 0 initial velocity X0 = Hyperrectangle([1.0, 0.0], [1, 0.0]) init = [(1, X0)] # Start in mode 1 (falling) at initial condition println(1) return InitialValueProblem(H, init) end # Solve the hybrid system prob = bouncing_ball() sol = solve(prob, tspan=(0.0, 2.0), alg=TMJets21a(; abstol=1e-5, maxsteps=10_000, orderT=5, orderQ=1)) # Overapproximate the solution using zonotopes solz = overapproximate(sol, Zonotope)

Simple Hybrid Automata

zdenek_hurak September 30, 2024, 5:20pm 2

Please consider enclosing your source code within triple backticks.

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