MPT3 allows to export parametric solutions in two ways:
Arbitrary parametric solutions can be exported to a standalone m-file by the PolyUnion/toMatlab method (see help PolyUnion/toMatlab for more information). The exported code is completely MPT-independent and, more importantly, much faster to execute compared to built-in MPT function-evaluation code (which needs to perform lots of sanity checks which slow down the evaluation process).
The general syntax is as follows:
The method takes any PolyUnion object (or an array thereof) and exports the function function_to_export to file name_of_file, resolving tiebreak (when a particular point is contained in multiple regions) using the function tiebreak_function. If you have a single optimizer that is continuous, you can use set tiebreak_function='first-region'. Here, the search for a region that contains a particular point is finished upon hitting the first such region.
The exported parametric solution can then be evaluated by
where x is the vector of parameters at which to evaluate, z is the value of the optimizer at x, and region is the index of the region that constains x. If there is no region containing x, then z=NaN and region=0.
To export explicit MPC feedbacks, use the following syntax:
This tells MPT to export the primal optimizer (stored as the primal function of the optimizer field of the controller), resolving tiebreaks using the cost function of the controller (stored as the obj function of controller.optimizer).
Note that, by default, the toMatlab method exports the full open-loop optimizer. In the case of explicit MPC this implies that the output of z=name_of_file(x) will be an {$ N n_u \times 1$} vector, where {$ N $} is the prediction horizon and {$ n_u $} is the number of control inputs. Then the closed-loop control action is given by u = z(1:nu). Alternatively, you can ask toMatlab() to only export the closed-loop optimizer. This can be achieved by:
Here, trimFunction('primal', nu) will change the primal function such that it only returns the closed-loop optimizer (i.e., the first nu components of the open-loop optimizer). The added benefit is in decreased memory consumption.
Full example:
The BinTreePolyUnion/toMatlab method exports a given binary tree to a pure Matlab code, similarly to the procedure above. Note that the method has following limitations:
BinTreePolyUnion object
Example:
EMPCController objectThe EMPCController object contains a method exportToC that exports PWA control law stored in the optimizer property to C language. The syntax of exportToC method is given as
where output is the base name for the C-files to be generated in directory. In the new directory there will be three files located:
output.c - pure C-code with PWA control law
output_mex.c - mex interface for fast evaluation in Matlab
output_sfunc.c - Simulink interface for fast evaluation in Simulink
The output.c contains the pure C-code that can be ported to target application. For fast evaluation in Matlab (Simulink), one may be interested to compile the mex (Simulink) interfaces by issuing the command
The compiled files can be called from Matlab (Simulink) as any other function. For the above example, the compiled function output_mex evaluates to the same output as the generated Matlab files
From version 3.0.14 we have introduced toC() methods that export general PWA/PWQ functions to C language. The basic sequential search (including tie-breaking) is exported using the toC() method operating over PolyUnion object. The binary search trees are exported in BinTreePolyUnion/toC() method. The syntax for code generation applied for the example above is given as
The first argument represents the PWA/PWQ function to export, the second argument is the base name for the files to be generated and the third argument is the tie-breaking function to deal with multiple valued cases. The generated mex-file can be compiled:
and evaluated inside Matlab
The result gives the same output as evaluating the Matlab file mycontroller in the above example.
One straightforward way to obtain a C-code representation of parametric solutions is to use the Matlab Coder toolbox:
where nx is the number of parameters. The coder function will generate the mex-function controller_mex() which is much faster to execute compared to executing controller.m.
For explicit MPC controllers you can obtain nx by nx=controller.xinitFormat.n_xinit (this number already includes any additional parameters introduced by free reference tracking and/or by the {$ \Delta u $} formulation).