Thesis: robust adaptive model predictive control with ellipsoidal tubes


ETH Zürich

Robust adaptive MPC is a technique where model parameters are learned online using measurements. To ensure robustness, techniques from tube MPC are generally used. In this project, we aim to investigate novel ways to improve the design of these controllers by using ellipsoidal tubes.

Keywords: model predictive control, robust control, adaptive control

Model predictive control (MPC) algorithms require a model of the system to be controlled. When the model of the true system is unavailable, robust MPC methods are used to ensure that the performance is robust to model uncertainties. However, these methods are conservative when the uncertainties are large. Robust adaptive MPC (RAMPC) techniques ameliorate this conservatism by reducing the uncertainty online using measurements.

Most RAMPC methods in literature use polytopic tubes to ensure that the state trajectories are robust to all the model uncertainties. However, the size of the MPC optimization problem grows exponentially in the number of parameters and state variables.

This issue can be addressed by parameterizing the state tube using ellipsoids. This is because an ellipsoid can be specified by a single matrix as opposed to polytopes, which are specified by hyperplanes (and thus their complexity grows exponentially for higher dimensional spaces). Ellipsoids have an interesting connection to Lyapunov stability and terminal sets, because an ellipsoidal terminal set can be easily computed along with a terminal controller. Another benefit of considering ellipsoidal tubes is the possibility to include Linear Fractional Transformation (LFT) type of uncertainty descriptions, which is a flexible paradigm widely used in Robust Control. The project aims to exploit these properties of ellipsoids to improve the scaling of the existing RAMPC methods.

Please submit your CV, transcripts and a reference contact along with your application.

  1. Study existing literature on ellipsoidal MPC approaches, and familiarize with semidefinite programming.
  2. Extend the ellipsoidal tube MPC to allow scaling of tubes to increase the feasible region of the controller. Efficiently implement the method and compare performance to the unscaled tube version.
  3. Study robust adaptive MPC methods, and modify the developed robust MPC method to allow adaptation of parameters.
  4. Implement the robust adaptive MPC method, and compare the performance and computational complexity to a polytopic approach.
  5. (If time permits) Apply the developed control strategy to a practical example (e.g. building control, quadrotor control, etc).

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