Simple Hybrid Automata

New to Julia
1

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 <=0,v<=0], vars)  # Trigger mode switch when x == 0
    transition_map =  Dict(v=>-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)
2

Please consider enclosing your source code within triple backticks.

3

done

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