7 research outputs found
Towards data-driven stochastic predictive control
Data-driven predictive control based on the fundamental lemma by Willems et
al. is frequently considered for deterministic LTI systems subject to
measurement noise. However, little has been done on data-driven stochastic
control. In this paper, we propose a data-driven stochastic predictive control
scheme for LTI systems subject to possibly unbounded additive process
disturbances. Based on a stochastic extension of the fundamental lemma and
leveraging polynomial chaos expansions, we construct a data-driven surrogate
Optimal Control Problem (OCP). Moreover, combined with an online selection
strategy of the initial condition of the OCP, we provide sufficient conditions
for recursive feasibility and for stability of the proposed data-driven
predictive control scheme. Finally, two numerical examples illustrate the
efficacy and closed-loop properties of the proposed scheme for process
disturbances governed by different distributions
Behavioral Theory for Stochastic Systems? A Data-driven Journey from Willems to Wiener and Back Again
The fundamental lemma by Jan C. Willems and co-workers, which is deeply
rooted in behavioral systems theory, has become one of the supporting pillars
of the recent progress on data-driven control and system analysis. This
tutorial-style paper combines recent insights into stochastic and
descriptor-system formulations of the lemma to further extend and broaden the
formal basis for behavioral theory of stochastic linear systems. We show that
series expansions -- in particular Polynomial Chaos Expansions (PCE) of
-random variables, which date back to Norbert Wiener's seminal work --
enable equivalent behavioral characterizations of linear stochastic systems.
Specifically, we prove that under mild assumptions the behavior of the dynamics
of the -random variables is equivalent to the behavior of the dynamics of
the series expansion coefficients and that it entails the behavior composed of
sampled realization trajectories. We also illustrate the short-comings of the
behavior associated to the time-evolution of the statistical moments. The paper
culminates in the formulation of the stochastic fundamental lemma for linear
(descriptor) systems, which in turn enables numerically tractable formulations
of data-driven stochastic optimal control combining Hankel matrices in
realization data (i.e. in measurements) with PCE concepts.Comment: 30 pages, 8 figure
Pathwise turnpike and dissipativity results for discrete-time stochastic linear-quadratic optimal control problems
We investigate pathwise turnpike behavior of discrete-time stochastic
linear-quadratic optimal control problems. Our analysis is based on a novel
strict dissipativity notion for such problems, in which a stationary stochastic
process replaces the optimal steady state of the deterministic setting. The
analytical findings are illustrated by a numerical example
Turnpike and dissipativity in generalized discrete-time stochastic linear-quadratic optimal control
We investigate different turnpike phenomena of generalized discrete-time
stochastic linear-quadratic optimal control problems. Our analysis is based on
a novel strict dissipativity notion for such problems, in which a stationary
stochastic process replaces the optimal steady state of the deterministic
setting. We show that from this time-varying dissipativity notion, we can
conclude turnpike behaviors concerning different objects like distributions,
moments, or sample paths of the stochastic system and that the distributions of
the stationary pair can be characterized by a stationary optimization problem.
The analytical findings are illustrated by numerical simulations
A Polynomial Chaos Approach to Stochastic LQ Optimal Control: Error Bounds and Infinite-Horizon Results
The stochastic linear-quadratic regulator problem subject to Gaussian
disturbances is well known and usually addressed via a moment-based
reformulation. Here, we leverage polynomial chaos expansions, which model
random variables via series expansions in a suitable
probability space, to tackle the non-Gaussian case. We present the optimal
solutions for finite and infinite horizons. Moreover, we quantify the
truncation error and we analyze the infinite-horizon asymptotics. We show that
the limit of the optimal trajectory is the unique solution to a stationary
optimization problem in the sense of probability measures. A numerical example
illustrates our findings
ALADIN-α—An open-source MATLAB toolbox for distributed non-convex optimization
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
ALADIN- -- An open-source MATLAB toolbox for distributed non-convex optimization
This paper introduces an open-source software for distributed and
decentralized non-convex optimization named ALADIN-. ALADIN- is
a MATLAB 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-