Workflow of ParNMPC

Preparation

1. Choose a compiler that supports code generation with OpenMP by mex -setup.
2. Edit Timer.m to specify your own timer function.

NMPC Problem Formulation

Example

./NMPC_Problem_Definition.m

1. Formulate an OCP using Class OptimalControlProblem

   % Create an OptimalControlProblem object
   OCP = OptimalControlProblem(dim.u,...  % inputs dim
                               dim.x,...  % states dim
                               dim.p,...  % parameters dim
                               N);        % num of discretization grids
   
   % Give names to x, u, p (optional)                          
   [~] = OCP.setStateName(~);
   [~] = OCP.setInputName(~);
   [~] = OCP.setParameterName(~);
   
   % Set the prediction horizon T 
   OCP.setT(~);
   
   % Set the dynamic function f
   OCP.setf(~);
   
   % Set the matrix M (optional for, e.g., Lagrange model)
   OCP.setM(~);
   
   % Set the equality constraint function C (optional)
   OCP.setC(~);
   
   % Set the cost function L
   OCP.setL(~);
   
   % Set the polytopic constraint G (optional)
   OCP.setG(~);
   
   % Generate necessary files
   OCP.codeGen();
   

2. Configure the solver using Class NMPCSolver

   % Create a NMPCSolver object
   nmpcSolver = NMPCSolver(OCP);
   
   % Configurate the Hessian approximation method
   nmpcSolver.setHessianApproximation(~);
   
   % Configurate the descent regularization parameter (optional)
   nmpcSolver.setDescentRegularization(~);
   
   % Generate necessary files
   nmpcSolver.codeGen();
   

3. Solve the very first OCP offline to provide an accurate initial guess

   % Set the initial state
   x0 = [~];
   
   % Set the parameters
   p  = [~];
   
   % Create an initial guess
   solutionInitGuess = [~];
   
   % Solve the optimal control problem for given values of x0 and p 
   % with barrier parameter rho
   solution = NMPC_SolveOffline(x0,p,solutionInitGuess,rho,maxIter);
   
   
   % Save to file for Simu_Matlab.m
   save GEN_initData.mat dim x0 p N
   
   % Set initial guess
   global ParNMPCGlobalVariable
   ParNMPCGlobalVariable.solutionInitGuess = solution;
   

4. Define the controlled plant using Class DynamicSystem (optional for simulation)

   % Create a DynamicSystem object
   plant = DynamicSystem(dim.u,dim.x,dim.p);
   
   % Give names to x, u, p (optional)
   [~] = plant.setStateName(~);
   [~] = plant.setInputName(~);
   [~] = plant.setParameterName(~);
   
   % Set the dynamic function f
   plant.setf(~);
   
   % Set the matrix M (optional for, e.g., Lagrange model)
   plant.setM(~);
   
   % Generate necessary files
   plant.codeGen();
   

Configuration Table:

	Configurable discretization method	Configurable Hessian approximation method
M enabled	'Euler'	'GaussNewton'
M disabled	All	All

Closed-loop Simulation

In order to do the closed-loop simulation for the problem defined above, two functions are provided:

• NMPC_Solve: function of the NMPC solver. See Interfaces > Functions > NMPC_Solve.

• SIM_Plant_RK4: one-step simulation of the controlled plant based on the 4-th order Runge-Kutta method. See Interfaces > Functions > SIM_Plant_RK4.

Code Generation and Deployment

MATLAB

Here, assume your closed-loop simulation is performed in Simu_Matlab.m.

Example

./Simu_Matlab.m

Code generation

Example

./Simu_Matlab_Codegen.m

An executable file that performs the closed-loop simulation will be generated automatically.

Simulink

Here, assume your closed-loop simulation is performed in Simulink. You can call the generated C/C++ solver function NMPC_Solve directly to compute the optimal input.

Code generation

Example

./Simu_Simulink_Setup.m

1. Define and configurate options for NMPC_Solve:

   options = createOptions();
   

2. Generate code:

   NMPC_Solve_CodeGen(~,~,options);
   

Deployment

Example

./Simu_Simulink.slx

This example shows how to call the generated C interface in Simulink using the coder.cevel function within a MATLAB Function block. You can also call the C/C++ interface using S-function.

1. Open the Simulation Target pane in the Simulink Editor: Simulation > Model Configuration Parameters > Simulation Target.

2. Add #include "NMPC_Solve.h" to Insert custom C code in generated: Header file.

3. Add NMPC_Solve_initialize(); to Insert custom C code in generated: Initialize function.

4. Add NMPC_Solve_terminate(); to Insert custom C code in generated: Terminate function.

5. Add the following directory to Additional Build Information: Include directories:

   ./codegen/~/NMPC_Solve
   

6. Add NMPC_Solve.lib (NMPC_Solve.so in linux) to Additional Build Information: Libraries.

7. Call the generated C function in a MATLAB Function block in Simulink:

   output = createOutput();
   solution = createNonemptySolution();
   coder.ceval('NMPC_Solve',...
                x0,...
                p,... % (optional)
                coder.wref(solution),...
                coder.wref(output));
   

Note

Alternatively, steps 1-6 can be done using the following commands.

Simu_Simulink
set_param('Simu_Simulink', 'SimCustomHeaderCode', '#include "NMPC_Solve.h"')
set_param('Simu_Simulink', 'SimCustomInitializer', 'NMPC_Solve_initialize();')
set_param('Simu_Simulink', 'SimCustomTerminator', 'NMPC_Solve_terminate();')
set_param('Simu_Simulink', 'SimUserLibraries', 'NMPC_Solve.lib')
set_param('Simu_Simulink', 'SimUserIncludeDirs', './codegen/~/NMPC_Solve')

Accelerating Simulation using MEX-function

1. Code generation

   Example

   ./Simu_Simulink_Setup.m

   Following the code generation for Simulink procedure, MEX-function can be generated by modifying the generation target to mex:

   NMPC_Solve_CodeGen('mex','C',options);
   

2. Deployment

   Example

   ./Simu_Matlab.m

   Modify NMPC_Solve to NMPC_Solve_mex to call the generated mex function and run.

   MEX-function is typically slower than C code. However, it can speed up your simulation to check the closed-loop response.