Control and Estimation by Real-Time Optimization

Optimal control problems of nonlinear systems generally cannot be solved explicitly, and their numerical solutions are computationally expensive. Therefore, implementing an optimal control in the form of feedback has long been regarded as impossible. However, we have developed efficient numerical algorithms for a class of nonlinear optimal control problems, i.e., model predictive control (receding horizon control), and succeeded in implementing optimal feedback control with a sampling period in the order of milliseconds, which is one of the world's first real-time optimization algorithms tailored for model predictive control. Since then, our algorithms have also been applied to various systems such as autopilot systems of ships and airplanes. Applications of real-time optimization are not limited to control but expand to estimation, differential games, adaptation, learning, and their integration. Our research topics include not only numerical algorithms but also automatic code generation by symbolic computation, tuning of performance indexes, parallel computing, and so on.



Figure: A model hovercraft.



Figure: Autopilot for a ship (Photo: Kawasaki Heavy Industry)

■ Keywords

Nonlinear systems, Optimal control, Real-time optimization, Numerial computation, Symbolic computation.

References

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  • T. Ohtsuka (Ed.): Practical Applications of Control by Real-Time Optimization, Corona Publishing (2015) (in Japanese) ISBN:978-4-339-03210-9
  • Automatic Code Generation System, AutoGenU [Maple Version] [Mathematica Version; Matlab Interface] [Python Version]
  • Maplesoft Webinar: Real Time Code Generation for Nonlinear Model Predictive Control [YouTube]
  • H.Deng, and T. Ohtsuka: A Parallel Newton-type Method for Nonlinear Model Predictive Control, Automatica, Vol. 109, No. 12, 108560 (2019) DOI:10.1016/j.automatica.2019.108560
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  • A Parallel Computing Toolbox ParNMPC [GitHub]