8 research outputs found
Offline Uncertainty Sampling in Data-driven Stochastic MPC
In this work, we exploit an offline-sampling based strategy for the
constrained data-driven predictive control of an unknown linear system subject
to random measurement noise. The strategy uses only past measured, potentially
noisy data in a non-parametric system representation and does not require any
prior model identification. The approximation of chance constraints using
uncertainty sampling leads to efficient constraint tightening. Under mild
assumptions, robust recursive feasibility and closed-loop constraint
satisfaction is shown. In a simulation example, we provide evidence for the
improved control performance of the proposed control scheme in comparison to a
purely robust data-driven predictive control approach.Comment: This work has been accepted for presentation at IFAC World Congress
202
Controller design for robust invariance from noisy data
For an unknown linear system, starting from noisy open-loop input-state data
collected during a finite-length experiment, we directly design a linear
feedback controller that guarantees robust invariance of a given polyhedral set
of the state in the presence of disturbances. The main result is a necessary
and sufficient condition for the existence of such a controller, and amounts to
the solution of a linear program. The benefits of large and rich data sets for
the solution of the problem are discussed. A numerical example about a
simplified platoon of two vehicles illustrates the method
A novel constraint-tightening approach for robust data-driven predictive control
In this paper, we present a data-driven model predictive control (MPC) scheme that is capable of stabilizing unknown linear time-invariant systems under the influence of process disturbances. To this end, Willems' lemma is used to predict the future behavior of the system. This allows the entire scheme to be set up using only a priori measured data and knowledge of an upper bound on the system order. First, we develop a state-feedback MPC scheme, based on input-state data, which guarantees closed-loop practical exponential stability and recursive feasibility as well as closed-loop constraint satisfaction. The scheme is extended by a suitable constraint tightening, which can also be constructed using only data. In order to control a priori unstable systems, the presented scheme contains a prestabilizing controller and an associated input constraint tightening. We first present the proposed data-driven MPC scheme for the case of full state measurements, and also provide extensions for obtaining similar closed-loop guarantees in case of output feedback. The presented scheme is applied to a numerical example
Combining Prior Knowledge and Data for Robust Controller Design
We present a framework for systematically combining data of an unknown linear
time-invariant system with prior knowledge on the system matrices or on the
uncertainty for robust controller design. Our approach leads to linear matrix
inequality (LMI) based feasibility criteria which guarantee stability and
performance robustly for all closed-loop systems consistent with the prior
knowledge and the available data. The design procedures rely on a combination
of multipliers inferred via prior knowledge and learnt from measured data,
where for the latter a novel and unifying disturbance description is employed.
While large parts of the paper focus on linear systems and input-state
measurements, we also provide extensions to robust output-feedback design based
on noisy input-output data and against nonlinear uncertainties. We illustrate
through numerical examples that our approach provides a flexible framework for
simultaneously leveraging prior knowledge and data, thereby reducing
conservatism and improving performance significantly if compared to black-box
approaches to data-driven control