Receding Horizon Decision Making

Model Predictive Control Algorithms (MPC)


Control and decision making algorithms based on receding horizon information and online (real-time) optimization, such as model predictive control (MPC) and moving horizon estimation (MHE), have recently received a lot of attention in both academia and industrial application. Based on a receding horizon policy idea, which has its origin in economics, MPC computes online the current control input by solving at each sampling instant a suitably defined finite-horizon open loop optimal control problem and applying then only the first part of the resulting input sequence to the considered plant. MPC schemes usually assume that the required optimal control input can be computed at each sampling instant exactly and in a negligible amount of time. Especially in the context of fast system dynamics or restricted hardware specifications, this idealizing assumption may not be valid anymore, which makes it hard to give stability or constraint satisfaction guarantees when it comes to the practical implementation of MPC. Thus, there is a well-founded need for efficient algorithmic MPC implementations that allow a rapid computation of the optimal control input - or at least of a sufficiently good approximation - while still being able to give guarantees on system theoretic properties of the overall closed-loop system, which now consists of the combined dynamics of both plant and optimization algorithm. Consequently, our research focus lies at the intersection of the areas systems theory, predictive control, and optimization algorithms. In particular, the overall goal is the development and analysis of so-called anytime barrier function based MPC approaches in conjunction with suitable, or even specifically tailored, optimization algorithms. By taking the dynamics of the underlying optimization into account, the resulting MPC algorithms allow to guarantee properties like closed-loop stability and constraint satisfaction for in principle arbitrary fast system dynamics. Recent implementations in autonomous driving tasks have shown that the developed approach performs very well in practice.

  • Some publications:
  • L. Schwenkel, M. Gharbi, S. Trimpe, C. Ebenbauer. Online learning with stability guarantees: A memory-based real-time model predictive controller, (preprint:, to appear in Automatica.
  • C. Feller and C. Ebenbauer. Sparsity-exploiting anytime algorithms for model predictive control: A relaxed barrier approach. IEEE Transactions on Control Systems Technology, 1-11, 2018.
  • C. Feller and C. Ebenbauer. A stabilizing iteration scheme for model predictive control based on relaxed barrier functions. Automatica, 80:328–339, June 2017.
  • C. Feller and C. Ebenbauer. Relaxed logarithmic barrier function based model predictive control of linear systems. IEEE Transactions on Automatic Control, 62:1223–1238, March 2017.


Moving Horizon Estimation Algorithms (MHE)

Estimation is fundamental in many areas  (c) such as identification, learning and control. For dynamical systems, the aim is to reconstruct the underlying state at each sampling instant from available measurements. One powerful method for constrained state estimation is moving horizon estimation (MHE). MHE is an online optimization-based approach that computes an estimate of the state by solving at each sampling instant a suitable optimization problem. Hereby, a fixed number of recent measurements is taken into account. As a new measurement becomes available, the considered horizon of measurements is shifted forward in time in a receding horizon fashion. The goal of our research is to develop MHE formulations with inherent stability guarantees under minimal assumptions, which is not jeopardized by the flexibility of the design of the underlying optimization problem. From a computational point of view, we aim for an efficient MHE implementation that offers the freedom to choose between optimality and a reduced computational burden without endangering stability. In the spirit of anytime relaxed barrier function based MPC, the overall goal of our research is the design of a unified approach for anytime estimation-based MPC algorithms.

  • Some publications:
  • M. Gharbi, B. Gharesifard, C. Ebenbauer. Anytime Proximity Moving Horizon Estimation: Stability and Regret, (preprint:, 2020.
  • M. Gharbi and C. Ebenbauer. Proximity moving horizon estimation for linear time-varying systems and a Bayesian filtering view. In Proc. of the 58th CDC, Nice, France, 2019.
  • M. Gharbi and C. Ebenbauer. A proximity approach to linear moving horizon estimation. In Proc. of the 6th IFAC NMPC Conference 2018, pages 649–655, Madison, USA, 2018.
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