Feedback systems: Input-output properties

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L2 Gain And Passivity Techniques In Nonlinear Control

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-Driven Model Predictive Control With Stability and Robustness Guarantees

Introduction Part I: Preliminaries Linear Algebra and Preliminaries Disctrete-time Linear Systems Stochastic Processes Kalman Filter Part II: Realization Theory Realization of Deterministic Problems Stochastic Realization Theory I Stochastic Realization Theory II Part III: Subspace Identification Subspace Identification I: ORT Subspace Identification II: CCA Identification of Closed-loop System Appendices Least-squares Method Input Signals for System Identification Overlapping Parametrization Matlab(R) Programs Solutions to Problems

Subspace methods for system identification

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

Robust and optimal predictive control of the COVID-19 outbreak.

The vector space of all input-output trajectories of a discrete-time linear time-invariant (LTI) system is spanned by time-shifts of a single measured trajectory, given that the respective input signal is persistently exciting. This fact, which was proven in the behavioral control framework, shows that a single measured trajectory can capture the full behavior of an LTI system and might therefore be used directly for system analysis and controller design, without explicitly identifying a model. In this paper, we translate the result from the behavioral context to the classical state-space control framework and we extend it to certain classes of nonlinear systems, which are linear in suitable input-output coordinates. Moreover, we show how this extension can be applied to the data-driven simulation problem, where we introduce kernel-methods to obtain a rich set of basis functions.

A trajectory-based framework for data-driven system analysis and control.

We consider the problem of designing robust state-feedback controllers for discrete-time linear time-invariant systems, based directly on measured data. The proposed design procedures require no model knowledge, but only a single open-loop data trajectory, which may be affected by noise. First, a data-driven characterization of the uncertain class of closed-loop matrices under state-feedback is derived. By considering this parametrization in the robust control framework, we design data-driven state-feedback gains with guarantees on stability and performance, containing, e.g., the ℋ
 ∞
-control problem as a special case. Further, we show how the proposed framework can be extended to take partial model knowledge into account. The validity of the proposed approach is illustrated via a numerical example.

Robust data-driven state-feedback design

Due to their relevance in controller design and robustness analysis, we present a novel framework to find and verify dissipativity properties for discrete-time linear time-invariant systems from only one input–output trajectory. Introducing a new data-driven formulation for dissipativity, we obtain necessary and sufficient conditions for dissipativity based only on a definiteness condition on a single data-dependent matrix. Furthermore, we provide a promising relaxation in the case of measurement noise, which, as illustrated in numerous numerical examples, works remarkably well.

Julian Berberich

Papers

Data-Driven Model Predictive Control With Stability and Robustness Guarantees

Robust and optimal predictive control of the COVID-19 outbreak.

A trajectory-based framework for data-driven system analysis and control.

Robust data-driven state-feedback design

One-Shot Verification of Dissipativity Properties From Input–Output Data