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.

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

State equations, evaluation functions and parameters are set.

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

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.

http://www.symlab.sys.i.kyoto-u.ac.jp/~ohtsuka/research_j.htm

Videos of the hovercraft experiments are presented on this webpage.

**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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