In this post, we have a new take on nonlinear MPC in Simulink using CasADi.

# Interpreter mode

In an earlier post on MPC in Simulink, we used an interpreted 'Matlab system' block in the simulink diagram. This is flexible, but slow because of interpreter overhead.

# code-generation mode

In an earlier post on S-Functions, we showed how Casadi-generated C code can be embedded efficiently in a Simulink diagram using S-functions. The result is fast, but has restrictions: only SqpMethod combined with Qrqp or Osqp solver can be code-generated (as of 3.5), not e.g. ipopt.

# C api mode

Here, we will work with CasADi's C API (new since 3.5) and make Ipopt run within Simulink.

## Constructing a Function

After constructing an Ipopt solver, we create a $\mathbb{R}^2$ symbol to represent current state, and call the solver with symbolic lower and upper variable bounds:

solver = nlpsol('solver', 'ipopt', prob, options);

s0 = MX.sym('s0',2);

lbw_sym = MX(lbw);
ubw_sym = MX(ubw);
lbw_sym(1:2) = s0;
ubw_sym(1:2) = s0;

sol_sym = solver('x0', w0, 'lbx', lbw_sym, 'ubx', ubw_sym,...
'lbg', lbg, 'ubg', ubg);

The resultant expression graph, which has the NLP solver embedded, is used to create a Function mapping from current state to optimal control action to be applied:

f = Function('f',{s0},{sol_sym.x(3)});

Next, we save the Function to the disk. It should be noted that the steps up to here could as well be done from Python, or using different modeling techniques (e.g. Opti).

f.save('f.casadi');

## C API

Classic CasADi codegen gives you an API with C functions for querying dimensions of inputs and outputs and evaluating. Those C functions are prefixed with the CasADi Function name:

#include "f.h"

int_T n_in  = f_n_in();
int_T n_out = f_n_out();
int_T sz_arg, sz_res, sz_iw, sz_w;
f_work(&sz_arg, &sz_res, &sz_iw, &sz_w);

f(arg,res,iw,w,0);


The C API mirrors this syntax, but uses an identifier argument instead of prefixing:

#include <casadi/casadi_c.h>



This identifier is obtained from loading the saved file from disk, and specifying a particular Function by name:

int ret = casadi_c_push_file("f.casadi");
int id = casadi_c_id("f");

Calling the function involves checking out and releasing thread-local memory:

int mem = casadi_c_checkout_id(id);
casadi_c_eval_id(id, arg, res, iw, w, mem);
casadi_c_release_id(id, mem);

## Compilation

Different from code-generation, our S-function is still dependent on the CasADi runtime.

We'll need to compile the S-function using appropriate include and link flags:

lib_path = GlobalOptions.getCasadiPath();
mex('-v',['-I' inc_path],['-L' lib_path],'-lcasadi', 'casadi_fun.c')