How can one implement multimode systems that also include continuous events effectively?

[zalanzsiboras]

How can one implement multimode systems that also include continuous events effectively❓

I would like to create a multimode system, where the derivative of some unknowns depend on the (discrete) mode, and where the mode is changed by continuous events.

1. Firstly, should mode be a time-dependent parameter, or a variable/unknown❓

On the one hand, if mode is a time-dependent parameter, then according to the Event Handling and Callback Functions tutorial it needs to be marked as a discrete parameter within the continuous event. However, using the @continuous_events macro does not seem to set mode as a discrete parameter, and it also does not seem to accept SymbolicContinuousCallback().

using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D

@mtkmodel MultiModeSystem begin
    @parameters begin
        mode(t)::Bool = false
    end
    @variables begin
        # Depends on "mode"
        x(t) = 0.0
        # Event triggerer var. - "mode" depends on it
        v(t) = 0.0
        d_v(t) = 10.0
    end
    @equations begin
        # Depends on "mode"
        D(x) ~ mode * 1.0
        # Event triggerer var. - "mode" depends on it
        D(v) ~ d_v
        D(d_v) ~ 0.0
    end
    @continuous_events begin
        [v ~ 10.0] => [v ~ 0.0, d_v ~ -10.0, mode ~ true]
        [v ~ -10.0] => [v ~ 0.0, d_v ~ 10.0, mode ~ false]
    end
end

@mtkcompile sys = MultiModeSystem()
prob = ODEProblem(sys, [], (0, 3.0))

using OrdinaryDiffEq: solve
sol = solve(prob)
# Incorrect solution because "x" does not change!

Using SymbolicContinuousCallback() within @continuous_events results in the following error during system definition:

ERROR: LoadError: Malformed continuous event ModelingToolkit.SymbolicContinuousCallback([v ~ 10.0] => [v ~ 0.0, d_v ~ -10.0, mode ~ true], discrete_parameters = [mode]).
Stacktrace:
 [1] error(s::String)
   @ Base .\error.jl:35
 [2] parse_continuous_events!(c_evts::Vector{Any}, dict::Dict{Symbol, Any}, body::Expr)
   @ ModelingToolkit ..\.julia\packages\ModelingToolkit\hlGut\src\systems\model_parsing.jl:1164
 [3] parse_model!(exprs::Vector{…}, comps::Vector{…}, ext::Vector{…}, eqs::Vector{…}, icon::Base.RefValue{…}, vs::Vector{…}, ps::Vector{…}, sps::Vector{…}, c_evts::Vector{…}, d_evts::Vector{…}, cons::Vector{…}, costs::Vector{…}, dict::Dict{…}, mod::Module, arg::Expr, kwargs::OrderedCollections.OrderedSet{…}, where_types::Vector{…})
   @ ModelingToolkit ..\.julia\packages\ModelingToolkit\hlGut\src\systems\model_parsing.jl:667
 [4] _model_macro(mod::Module, fullname::Symbol, expr::Expr, isconnector::Bool)
   @ ModelingToolkit ..\.julia\packages\ModelingToolkit\hlGut\src\systems\model_parsing.jl:82
 [5] var"@mtkmodel"(__source__::LineNumberNode, __module__::Module, fullname::Union{Expr, Symbol}, body::Any)
   @ ModelingToolkit ..\.julia\packages\ModelingToolkit\hlGut\src\systems\model_parsing.jl:33
in expression starting at ..\Coding\ModularEnergySystemSim.jl\dev\features\dev_degmin_calc_with_events.jl:7

On the other hand, if mode is a variable/unknown an additional equation needs to be added. This could be D(mode) ~ 0, however D() unsurprisingly only supports continuous variable/unknown.

2. During the previous question, I assumed that mode is discrete (is of type bool or int). Would it help if it was treated as a continuous parameter or variable/unknown❓

3. If so, how could one implement the "mode conditions" within equations robustly❓
   For example, if mode is a variabe/unknown a tiny numerical error ifelse(mode == 1.0, cond_true_eq, cond_false_eq) could still "trigger" the use of "cond_false_eq" equations even if D(mode) ~ 0 and mode is set to 1.0 by a continuous event. (In production code I also would like to avoid the use of isapprox().) Whereas, if mode is a continuous parameter, then the continuous events cannot be defined with the @continuous_events macro.

I also think that a tutorial on multimode systems (using events) could be a great addition to the documentation and I would be happy to help with that if we can find an effective solution.