control_parameterized.jl

using DiffEqBase
using OrdinaryDiffEq
using ParameterizedFunctions

params = [0.0]
function dyn_eq(t,u,params,du)
    du .= [0 1;
           0 0]*u + [0;1]*params[1]
end

p_dyn_eq = ParameterizedFunction(dyn_eq,params)

tf = 30.0
tstops = collect(0:1:tf)
function condition_control_loop(t,u,integrator)
    (t in tstops)
end

r = 10.0
k = 0.3
d = 0.8
function control_loop!(integrator)
    params = integrator.f.params

    p = integrator.u[1]
    v = integrator.u[2]

    params[1] = k*(r-p) + d*(0.0-v)
end

cb = DiscreteCallback(condition_control_loop, control_loop!)

u0   = [0.0; 0.0]
prob = ODEProblem(p_dyn_eq, u0, (0.0, tf))
sol  = solve(prob, Tsit5(), callback = cb, tstops=tstops)

using Plots; pyplot()
plot(sol)