Chapter

Informatics in Control, Automation and Robotics

Volume 24 of the series Lecture Notes in Electrical Engineering pp 239-252

Stochastic Nonlinear Model Predictive Control based on Gaussian Mixture Approximations

  • Florian WeisselAffiliated withIntelligent Sensor-Actuator-Systems Laboratory Institute of Computer Science and Engineering, Universität Karlsruhe (TH)
  • , Marco F. HuberAffiliated withIntelligent Sensor-Actuator-Systems Laboratory Institute of Computer Science and Engineering, Universität Karlsruhe (TH)
  • , Uwe D. HanebeckAffiliated withIntelligent Sensor-Actuator-Systems Laboratory Institute of Computer Science and Engineering, Universität Karlsruhe (TH)

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Abstract

In this paper, a framework for stochastic Nonlinear Model Predictive Control (NMPC) that explicitly incorporates the noise influence on systems with continuous state spaces is introduced. By the incorporation of noise, which results from uncertainties during model identification and measurement, the quality of control can be significantly increased. Since stochastic NMPC requires the prediction of system states over a certain horizon, an efficient state prediction technique for nonlinear noise-affected systems is required. This is achieved by using transition densities approximated by axis-aligned Gaussian mixtures together with methods to reduce the computational burden. A versatile cost function representation also employing Gaussianmixtures provides an increased freedom of modeling. Combining the rediction technique with this value function representation allows closed-form calculation of the necessary optimization problems arising from stochastic NMPC. The capabilities of the framework and especially the benefits that can be gained by considering the noise in the controller are illustrated by the example of a mobile robot following a given path.