No abstract

Data-driven Model Predictive Control (MPC) based on the fundamental lemma by Willems et al. has shown promising results for deterministic LTI systems subject to measurement noise. However, besides measurement noise, stochastic disturbances might also directly affect the dynamics. In this paper, we extend deterministic data-driven MPC towards stochastic systems. Leveraging Polynomial Chaos Expansions (PCE), we propose a novel variant of the fundamental lemma for stochastic LTI systems. This extension allows to predict future distributions of the behaviors for stochastic LTI systems based on the knowledge of previously recorded behavior realizations and based on the knowledge of the noise distribution. Finally, we propose a framework for data-driven stochastic MPC which is applicable to a large class of noise distributions with finite variance. Numerical examples illustrate the efficacy of the proposed scheme.

This article introduces an open-source software for distributed and decentralized non-convex optimization named ALADIN-𝛼. ALADIN-𝛼 is a MATLAB implementation of tailored variants of the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm. It is user interface is convenient for rapid prototyping of non-convex distributed optimization algorithms. An improved version of the recently proposed bi-level variant of ALADIN is included enabling decentralized non-convex optimization with reduced information exchange. A collection of examples from different applications fields including chemical engineering, robotics, and power systems underpins the potential of ALADIN-𝛼.

This paper studies optimal control problems of unknown linear systems subject to stochastic disturbances of uncertain distribution. Uncertainty about the stochastic disturbances is usually described via ambiguity sets of probability measures or distributions. Typically, stochastic optimal control requires knowledge of underlying dynamics and is as such challenging. Relying on a stochastic fundamental lemma from data-driven control and on the framework of polynomial chaos expansions, we propose an approach to reformulate distributionally robust optimal control problems with ambiguity sets as uncertain conic programs in a finite-dimensional vector space. We show how to construct these programs from previously recorded data and how to relax the uncertain conic program to numerically tractable convex programs via appropriate sampling of the underlying distributions. The efficacy of our method is illustrated via a numerical example.

This paper introduces an open-source software for distributed and decentralized non-convex optimization named ALADIN-α. ALADIN-α is a MAT-LAB implementation of the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm, which is tailored towards rapid prototyping for non-convex distributed optimization. An improved version of the recently proposed bi-level variant of ALADIN is included enabling decentralized non-convex optimization. A collection of application examples from different applications fields including chemical engineering, robotics, and power systems underpins the application potential of ALADIN-α.