[ANN] ModelPredictiveControl.jl

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61

Thanks. I guess I missed this sentence.

all the keyword arguments above but with a first capital letter, except for the terminal constraints, e.g. Ymax or C_Δumin: for time-varying constraints (see Extended Help)

A nicer interface would be something akin to setconstraint!(variable, index, lb, ub).

Or just a mini DSL that can formulate things like x + y \geq a, or x + y = a.

For example for my problem I also need to be able to define constraints of the form:

\begin{align} x_t &\geq a_t - z_t\\ y_t &\geq z_t - a_t \\ x_t, y_t &\geq 0 \end{align}

Is that possible?

For context, I am working on the ‘real’ version of Economic MPC for residential HVAC · DyadControlSystems by Fredrik :slight_smile:

62

What do you mean by “variable” ? Decision variables, outputs, states ? And “index” ? The discrete time step ?

What is x_t, y_t and z_t here ? States, manipulated inputs or outputs ?

63

Was trying to avoid some jargon but the form is:

\begin{align} \underline{u}_t &\geq T^\mathrm{set}_t - T^i_t\\ \overline{u}_t &\geq T^i_t - T^\mathrm{set}_t\\ \underline{u}_t, \overline{u}_t &\geq 0 \end{align}

Where \underline{u}_t and \overline{u}_t are the lower and upper comfort penalties. T^i_t is a state variable, and T^\mathrm{set}_t is a setpoint. Additional slack can be added to create a ‘comfort band’ that a user can define.

I also have constraints of the form:

\begin{align} Q_t^\mathrm{HP} &\leq b_0 + b_1 T^a_t + b_2 T^s_t \end{align}

Where T^s_t is a state variable and Q_t^\mathrm{HP} an input variable. Output thermal power limits typically depend on ambient and water temperatures.

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64

No, this structure is currently not supported by LinMPC object. It may be supported by the LinearMPC.jl package however, see Constraints and add_constraint!. The documentation is scarce but you are interested in Ax, Ar and ks arguments (x for state, r for setpoint and ks for the discrete time steps, starting at 1 for the present time step).

My main priority is to provide a user interface that is easy to use, meaning it is more restrictive in what can be accomplished in terms of objectives and constraints. Currently, if you have complex constraint or objective structures, there is always the NonLinMPC object that allows custom nonlinear constraints (gc and nc kwargs) and objectives (Ewt and JE kwargs). But it will obviously not be the most computationally efficient algorithm if these structures are truly linear and quadratic. And code generation is not supported for NonLinMPC.

That being said, my second priority is to be as flexible as possible. A feature that I could introduce is the possibility to add custom linear inequality constraints in the form of (with \mathbf{\tilde{Z}} being the decision variables augmented with the scalar slack variable \epsilon, if activated):

\mathbf{A_c} \mathbf{\tilde{Z}} \le \mathbf{b_c}

But there are two issues with this:

  • It needs a lot of work from the user (as in, you) to compute the \mathbf{A_c} matrix and \mathbf{b_c} vector.
  • For your specific structure, the \mathbf{b_c} vector will need to be re-computed at each control period k by the user (since the setpoints may change). This feature is not supported by code generation (i.e. there is no C code equivalent of calling setconstraint! online).

A second option would be to introduce an API similiar to LinearMPC’s add_constraint! in ModelPredictiveControl.jl, if it fits your need. And it would obviously support code generation.

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65

The expressiveness of the linear MPC framework is already very limited and the current syntax limits it further. As long as my expression is mathematically valid within the linear MPC framework I think I should be able to define it.

Unfortunately for commercial embedded systems every kilobyte matters so C codegen is a must. I think it’s already a modern miracle we can do MPC with a <200 kB solver (thanks Boyd!).

Yeah this is very tricky but I think a requirement for practical applications. Between mild and cold weather with high supply temperatures maximum output power can drop from 5 to 3 kW.

Maybe you know this already, but cvxpygen will generate a function cpg_update_<param>(idx, val) to update each parameter in your problem. For that to work you would first need to know where the parameters are and there are some rules as to how parameters can enter the problem (DPP compliance).

Now for LinearMPC.jl, you could say everything that is a constant in my problem is a parameter and thus could be updated and included in the codegen. Having both an expressive API and efficient codegen is even more tricky and you’re halveway to a DSL already.

Really thinking out loud here so feel free to shoot this down, but why not use JuMP as the main problem creation interface instead? There’s a DSL, and there is MOI.Parameter.

ps. It goes without saying but I appreciate your work on these packages.

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Flexible linear constraints for MPC and codegen