Setting a terminal equality constraint in MATLAB

josipkh · November 27, 2024, 3:53pm

Hi

I am using the MATLAB interface on Windows and trying to do the following:

solve a linear MPC tracking problem using a controller with a longer horizon (N=10)
solve the same linear MPC problem with a shorter horizon (N=1), starting from the results obtained from 1.

Later, I would like to do the same with a nonlinear OCP and a different cost in the second controller.

So far, I have tried using the linear_mpc example with the following:

setup the two OCPs, where the only difference is the horizon and the terminal constraint
solve the first OCP and obtain x^* and u^* (optimal predicted states and inputs)
set the terminal constraint of the second problem equal to x_1^* (first predicted state) with ocp_solver.set('constr_lbx',...,1) and ocp_solver.set('constr_ubx',...,1)
set the initial guess of the second solver to x^* and u^*
solve the second OCP

However, the control input obtained from the second controller is not the same (in fact, it is approximately zero).

Is it possible to set the terminal equality constraint in that way? I guess that an alternative would be to use parameters, but that would complicate the formulation a bit.

A working example can be found here:

github.com

josipkh/acados/blob/terminal_equality_constraint/examples/acados_matlab_octave/linear_mpc/terminal_equality_constraint/main.m

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This file has been truncated. show original

Thanks in advance!

Kind regards,
Josip

kaethe · November 27, 2024, 7:33pm

Don’t you need to get the second entry of the state trajectory here?

github.com

josipkh/acados/blob/79003ce302bcf62763882d70ceee6231f0499201/examples/acados_matlab_octave/linear_mpc/terminal_equality_constraint/main.m#L102


      
              warning(['acados ocp solver failed with status ',num2str(status)]);
          end
          
          sol1_x = ocp_solver.get('x');
          sol1_u = ocp_solver.get('u');
          
          % --------------------------
          % use the second solver (results should be the same)
          ocp_solver_2.set('constr_x0',x);
          ocp_solver_2.set('cost_y_ref_e', xr, 1);    % terminal state reference
          x1 = sol1_x(:,1);                           % first predicted optimal state
          ocp_solver_2.set('constr_lbx', x1, 1);      % terminal equality constraint
          ocp_solver_2.set('constr_ubx', x1, 1);      % terminal equality constraint
          ocp_solver_2.set('init_x', sol1_x(:,1:2));  % use the prediction
          ocp_solver_2.set('init_u', sol1_u(:,1));    % use the prediction
          
          ocp_solver_2.solve();
          if ocp_solver_2.get('status') ~= 0
              warning(['ocp solver 2 failed with status ',num2str(status)]);
          end

josipkh · November 27, 2024, 8:03pm

Oh that’s right, thank you very much Katrin!

Best regards,
Josip