Henk J. van Waarde

Bio: Henk J. van Waarde is an academic researcher from University of Groningen. The author has contributed to research in topics: Identifiability & Graph (abstract data type). The author has an hindex of 11, co-authored 34 publications receiving 441 citations. Previous affiliations of Henk J. van Waarde include Technische Universität München & University of Cambridge.

Data Informativity: A New Perspective on Data-Driven Analysis and Control

Abstract: The use of persistently exciting data has recently been popularized in the context of data-driven analysis and control. Such data have been used to assess system-theoretic properties and to construct control laws, without using a system model. Persistency of excitation is a strong condition that also allows unique identification of the underlying dynamical system from the data within a given model class. In this article, we develop a new framework in order to work with data that are not necessarily persistently exciting. Within this framework, we investigate necessary and sufficient conditions on the informativity of data for several data-driven analysis and control problems. For certain analysis and design problems, our results reveal that persistency of excitation is not necessary. In fact, in these cases, data-driven analysis/control is possible while the combination of (unique) system identification and model-based control is not. For certain other control problems, our results justify the use of persistently exciting data, as data-driven control is possible only with data that are informative for system identification.

Data informativity: a new perspective on data-driven analysis and control

Abstract: The use of persistently exciting data has recently been popularized in the context of data-driven analysis and control. Such data have been used to assess system theoretic properties and to construct control laws, without using a system model. Persistency of excitation is a strong condition that also allows unique identification of the underlying dynamical system from the data within a given model class. In this paper, we develop a new framework in order to work with data that are not necessarily persistently exciting. Within this framework, we investigate necessary and sufficient conditions on the informativity of data for several data-driven analysis and control problems. For certain analysis and design problems, our results reveal that persistency of excitation is not necessary. In fact, in these cases data-driven analysis/control is possible while the combination of (unique) system identification and model-based control is not. For certain other control problems, our results justify the use of persistently exciting data as data-driven control is possible only with data that are informative for system identification.

Willems’ Fundamental Lemma for State-Space Systems and Its Extension to Multiple Datasets

Abstract: Willems et al. ’s fundamental lemma asserts that all trajectories of a linear system can be obtained from a single given one, assuming that a persistency of excitation and a controllability condition hold. This result has profound implications for system identification and data-driven control, and has seen a revival over the last few years. The purpose of this letter is to extend Willems’ lemma to the situation where multiple (possibly short) system trajectories are given instead of a single long one. To this end, we introduce a notion of collective persistency of excitation. We will show that all trajectories of a linear system can be obtained from a given finite number of trajectories, as long as these are collectively persistently exciting. We will demonstrate that this result enables the identification of linear systems from data sets with missing samples. Additionally, we show that the result is of practical significance in data-driven control of unstable systems.

From noisy data to feedback controllers: non-conservative design via a matrix S-lemma

Abstract: We propose a new method to obtain feedback controllers of an unknown dynamical system directly from noisy input/state data. The key ingredient of our design is a new matrix S-lemma that will be proven in this paper. We provide both strict and non-strict versions of this S-lemma, that are of interest in their own right. Thereafter, we will apply these results to data-driven control. In particular, we will derive non-conservative design methods for quadratic stabilization, H_2 and H_inf control, all in terms of data-based linear matrix inequalities. In contrast to previous work, the dimensions of our decision variables are independent of the time horizon of the experiment. Our approach thus enables control design from large data sets.

From noisy data to feedback controllers: non-conservative design via a matrix S-lemma

Abstract: We propose a new method to obtain feedback controllers of an unknown dynamical system directly from noisy input/state data. The key ingredient of our design is a new matrix S-lemma that will be proven in this paper. We provide both strict and non-strict versions of this S-lemma, that are of interest in their own right. Thereafter, we will apply these results to data-driven control. In particular, we will derive non-conservative design methods for quadratic stabilization, H_2 and H_inf control, all in terms of data-based linear matrix inequalities. In contrast to previous work, the dimensions of our decision variables are independent of the time horizon of the experiment. Our approach thus enables control design from large data sets.

Adaptive Control

Abstract: This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

Subspace model identification-Part 1. The output-error state-space model identification class of algorithms

Abstract: In this paper, we present two novel algorithms to realize a finite dimensional, linear time-invariant state-space model from input-output data. The algorithms have a number of common features. They are classified as one of the subspace model identification schemes, in that a major part of the identification problem consists of calculating specially structured subspaces of spaces defined by the input-output data. This structure is then exploited in the calculation of a realization. Another common feature is their algorithmic organization: an RQ factorization followed by a singular value decomposition and the solution of an overdetermined set (or sets) of equations. The schemes assume that the underlying system has an output-error structure and that a measurable input sequence is available. The latter characteristic indicates that both schemes are versions of the MIMO Output-Error State Space model identification (MOESP) approach. The first algorithm is denoted in particular as the (elementary MOESP scheme)...

Data-Driven Model Predictive Control With Stability and Robustness Guarantees

Abstract: We propose a robust data-driven model predictive control (MPC) scheme to control linear time-invariant systems. The scheme uses an implicit model description based on behavioral systems theory and past measured trajectories. In particular, it does not require any prior identification step, but only an initially measured input–output trajectory as well as an upper bound on the order of the unknown system. First, we prove exponential stability of a nominal data-driven MPC scheme with terminal equality constraints in the case of no measurement noise. For bounded additive output measurement noise, we propose a robust modification of the scheme, including a slack variable with regularization in the cost. We prove that the application of this robust MPC scheme in a multistep fashion leads to practical exponential stability of the closed loop w.r.t. the noise level. The presented results provide the first (theoretical) analysis of closed-loop properties, resulting from a simple, purely data-driven MPC scheme.

Data Informativity: A New Perspective on Data-Driven Analysis and Control

Abstract: The use of persistently exciting data has recently been popularized in the context of data-driven analysis and control. Such data have been used to assess system-theoretic properties and to construct control laws, without using a system model. Persistency of excitation is a strong condition that also allows unique identification of the underlying dynamical system from the data within a given model class. In this article, we develop a new framework in order to work with data that are not necessarily persistently exciting. Within this framework, we investigate necessary and sufficient conditions on the informativity of data for several data-driven analysis and control problems. For certain analysis and design problems, our results reveal that persistency of excitation is not necessary. In fact, in these cases, data-driven analysis/control is possible while the combination of (unique) system identification and model-based control is not. For certain other control problems, our results justify the use of persistently exciting data, as data-driven control is possible only with data that are informative for system identification.

Distributionally Robust Chance Constrained Data-enabled Predictive Control

Abstract: We study the problem of finite-time constrained optimal control of unknown stochastic linear time-invariant systems, which is the key ingredient of a predictive control algorithm - albeit typically having access to a model. We propose a novel distributionally robust data-enabled predictive control (DeePC) algorithm which uses noise-corrupted input/output data to predict future trajectories and compute optimal control inputs while satisfying output chance constraints. The algorithm is based on (i) a non-parametric representation of the subspace spanning the system behaviour, where past trajectories are sorted in Page or Hankel matrices; and (ii) a distributionally robust optimization formulation which gives rise to strong probabilistic performance guarantees. We show that for certain objective functions, DeePC exhibits strong out-of-sample performance, and at the same time respects constraints with high probability. The algorithm provides an end-to-end approach to control design for unknown stochastic linear time-invariant systems. We illustrate the closed-loop performance of the DeePC in an aerial robotics case study.