Learning-based Model Predictive Control with closed-loop guarantees
Raffaele Soloperto
Cite this publication as
Raffaele Soloperto, Learning-based Model Predictive Control with closed-loop guarantees (2023), Logos Verlag, Berlin, ISBN: 9783832583132
Descripción / Abstract
The performance of model predictive control (MPC) largely depends on the accuracy of the prediction model and of the constraints the system is subject to. However, obtaining an accurate knowledge of these elements might be expensive in terms of money and resources, if at all possible. In this thesis, we develop novel learning-based MPC frameworks that actively incentivize learning of the underlying system dynamics and of the constraints, while ensuring recursive feasibility, constraint satisfaction, and performance bounds for the closed-loop.
In the first part, we focus on the case of inaccurate models, and analyze learning-based MPC schemes that include, in addition to the primary cost, a learning cost that aims at generating informative data by inducing excitation in the system. In particular, we first propose a nonlinear MPC framework that ensures desired performance bounds for the resulting closed-loop, and then we focus on linear systems subject to uncertain parameters and noisy output measurements. In order to ensure that the desired learning phase occurs in closed-loop operations, we then propose an MPC framework that is able to guarantee closed-loop learning of the controlled system. In the last part of the thesis, we investigate the scenario where the system is known but evolves in a partially unknown environment. In such a setup, we focus on a learning-based MPC scheme that incentivizes safe exploration if and only if this might yield to a performance improvement.
In the first part, we focus on the case of inaccurate models, and analyze learning-based MPC schemes that include, in addition to the primary cost, a learning cost that aims at generating informative data by inducing excitation in the system. In particular, we first propose a nonlinear MPC framework that ensures desired performance bounds for the resulting closed-loop, and then we focus on linear systems subject to uncertain parameters and noisy output measurements. In order to ensure that the desired learning phase occurs in closed-loop operations, we then propose an MPC framework that is able to guarantee closed-loop learning of the controlled system. In the last part of the thesis, we investigate the scenario where the system is known but evolves in a partially unknown environment. In such a setup, we focus on a learning-based MPC scheme that incentivizes safe exploration if and only if this might yield to a performance improvement.
Índice
- BEGINN
- 1 Introduction
- 1.1 Motivation
- 1.2 Related work
- 1.3 Contribution and outline
- 2 Preliminaries
- 2.1 Nominal MPC with terminal ingredients
- 2.2 Nominal tracking MPC without terminal ingredients
- 2.3 Disturbances and uncertainty in MPC
- 2.4 Summary
- 3 Dual adaptive MPC
- 3.1 Augmenting MPC schemes with active learning
- 3.2 Dual adaptive MPC for linear systems
- 3.3 Summary
- 4 Guaranteed closed-loop learning in MPC
- 4.1 Problem setup
- 4.2 MPC framework for closed-loop learning
- 4.3 Theoretical analysis
- 4.4 Application to learning approaches
- 4.5 Numerical example
- 4.6 Summary
- 5 Learning the constraints through safe exploration
- 5.1 Problem setup
- 5.2 Preliminaries for MPC scheme
- 5.3 Proposed MPC framework
- 5.4 Theoretical analysis
- 5.5 Numerical example
- 5.6 Summary
- 6 Conclusions
- 6.1 Summary
- 6.2 Future work
- A Technical results for Section 2:2:3
- A.1 Proof of Proposition 2:1
- A.2 Proof of Proposition 2:2
- A.3 Proof of Theorem 2:4
- A.4 Proof of Proposition 2:3
- B Additional results for Chapter 4
- B.1 MPC scheme with nominal cost function
- B.2 Lemma B1
- Bibliography