Performance and Constraint Satisfaction in Robust Economic Model Predictive Control
Florian A. Bayer
Cite this publication as
Florian A. Bayer, Performance and Constraint Satisfaction in Robust Economic Model Predictive Control (2017), Logos Verlag, Berlin, ISBN: 9783832592561
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Description / Abstract
In this thesis, we develop a novel framework for model predictive control (MPC) which combines the concepts of robust MPC and economic MPC. The goal of this thesis is to develop and analyze MPC schemes for nonlinear discrete-time systems which explicitly consider the influence of disturbances on arbitrary performance criteria. Instead of regarding the two aspects separately, we propose robust economic MPC approaches that integrate information which is available about the disturbance directly into the economic framework.
In more detail, we develop three concepts which differ in which information about the disturbance is used and how this information is taken into account. Furthermore, we provide a thorough theoretical analysis for each of the three approaches. To this end, we present results on the asymptotic average performance as well as on optimal operating regimes. Optimal operating regimes are closely related to the notion of dissipativity, which is therefore analyzed for the presented concepts. Under suitable assumptions, results on necessity and sufficiency of dissipativity for optimal steady-state operation are established for all three robust economic MPC concepts. A detailed discussion is provided which compares the different performance statements derived for the approaches as well as the respective notions of dissipativity.
In more detail, we develop three concepts which differ in which information about the disturbance is used and how this information is taken into account. Furthermore, we provide a thorough theoretical analysis for each of the three approaches. To this end, we present results on the asymptotic average performance as well as on optimal operating regimes. Optimal operating regimes are closely related to the notion of dissipativity, which is therefore analyzed for the presented concepts. Under suitable assumptions, results on necessity and sufficiency of dissipativity for optimal steady-state operation are established for all three robust economic MPC concepts. A detailed discussion is provided which compares the different performance statements derived for the approaches as well as the respective notions of dissipativity.
Table of content
- BEGINN
- 1 Introduction
- 1.1 Model predictive control
- 1.2 Motivation for robust economic MPC
- 1.3 Contributions and outline of this thesis
- 2 Background
- 2.1 Stabilizing MPC
- 2.2 Robust stabilizing MPC
- 2.3 Economic MPC
- 2.4 Summary
- 3 Min-max robust economic MPC
- 3.1 Economic MPC in classical min-max setup
- 3.2 Economic MPC in min-max setup based on tubes
- 3.3 Discussion comparing the approaches
- 3.4 Numerical examples
- 3.5 Summary
- 4 Tube-based robust economic MPC
- 4.1 Problem setup and performance result
- 4.2 Optimal steady-state operation
- 4.3 Asymptotic stability
- 4.4 Average constraints
- 4.5 Numerical examples
- 4.6 Summary
- 5 Improving robust economic MPC using stochastic information
- 5.1 Problem setup and performance result
- 5.2 Finding an appropriate quadratic terminal cost
- 5.3 Optimal steady-state operation
- 5.4 Tube-based robust economic MPC with RPI-distribution
- 5.5 Summary
- 6 Comparison of the approaches
- 6.1 Optimality based on comparison functions
- 6.2 Comparison of optimality notions
- 6.3 Numerical example
- 6.4 Summary
- 7 Conclusions
- 7.1 Summary
- 7.2 Future work
- A Technical proofs