Real-time optimum control design using Maple Non-Linear Model Predictive Control Design

Do you have issues like these?

I want to deal with a non-linear optimum control problem but am unsure of the analysis method to employ.
The algorithms are difficult and it takes time to create programs.
I want to perform real-time optimum control but the calculations involved are extensive and take a long time.



Non-linear model predictive control solves the problem of optimum control up to the finite-time future in each instant of time, and is a form of state feedback control that determines the control input. While deriving the optimal solution and performing feedback control in real-time is regarded as difficult to do realistically, using a high-speed solution known as the 鼎/GMRES method・which combines the continuous deformation method with the GMRES, real-time control has become possible. CYBERNET SYSTEMS has developed a non-linear model predictive control design tool using Maple, a software package supervised by Kyoto University professor Toshiyuki Ohtsuka.

A simulation program is automatically generated in the C language based on state equations and evaluation functions given in Maple format. Then, the solution is processed at once from compilation to calculation results on the Maple worksheet.

Advantages of the Solution

By using a non-linear model predictive control design worksheet through Maple, which utilizes the C/GMRES method, the following effects are expected.

  • Non-linear optimum control problem analysis can be performed by simply setting the parameters depending on the problem
  • Automation of cumbersome differential calculations and reduced labor for problem development
  • Results of calculations can be displayed in a short time due to the use of high-speed algorithms

Overview of Analysis Using the Solution

Problem setting and parameter input

State equations, evaluation functions and parameters are set.

Maple-based automatic code generation

Maple formula manipulation is used to calculate the necessary functions and simplify the equations, and a C-language simulation program is automatically created.

C compiler execution and display of results

The generated C-language simulation problem is compiled and executed, and the calculation results are displayed. Either Microsoft Visual C++ compiler or GNU gcc compiler needs to be set as the C compiler.

Example: Hovercraft Position Control

Hovercraft materials (Ohtsuka Lab.)

Videos of the hovercraft experiments are presented on this webpage.

Required Products

Maple Formula Manipulation and Mathematical Model Design Environment

  • C compiler environment: Visual Studio C++ compiler or GNU gcc compiler
  • OS environment: 64-bit Windows
  • Maple version 17 or later recommended.


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