arXiv subjects

Tom R. V. Steentjes

Publications and source records attributed to Tom R. V. Steentjes.

7 recordsLinked to original sources

arXiv2023

On a Canonical Distributed Controller in the Behavioral Framework

Control in a classical transfer function or state-space setting typically views a controller as a signal processor: sensor outputs are mapped to actuator inputs. In behavioral system theory, control is simply viewed as interconnection; the interconnection of a plant with a controller. In this paper we consider the problem of control of interconnected systems in a behavioral setting. The behavioral setting is especially fit for modelling interconnected systems, because it allows for the interconnection of subsystems without imposing inputs and outputs. We introduce a so-called canonical distributed controller that implements a given interconnected behavior that is desired, provided that necessary and sufficient conditions hold true. The controller design can be performed in a decentralized manner, in the sense that a local controller only depends on the local system behavior. Regularity of interconnections is an important property in behavioral control that yields feedback interconnections. We provide conditions under which the interconnection of this distributed controller with the plant is regular. Furthermore, we show that the interconnections of subsystems of the canonical distributed controller are regular if and only if the interconnections of the plant and desired behavior are regular.

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arXiv2022

On data-driven control: informativity of noisy input-output data with cross-covariance bounds

In this paper we develop new data informativity based controller synthesis methods that extend existing frameworks in two relevant directions: a more general noise characterization in terms of cross-covariance bounds and informativity conditions for control based on input-output data. Previous works have derived necessary and sufficient informativity conditions for noisy input-state data with quadratic noise bounds via an S-procedure. Although these bounds do not capture cross-covariance bounds in general, we show that the S-procedure is still applicable for obtaining non-conservative conditions on the data. Informativity-conditions for stability, $\mathcal{H}_\infty$ and $\mathcal{H}_2$ control are developed, which are sufficient for input-output data and also necessary for input-state data. Simulation experiments illustrate that cross-covariance bounds can be less conservative for informativity, compared to norm bounds typically employed in the literature.

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arXiv2022

Informativity conditions for data-driven control based on input-state data and polyhedral cross-covariance noise bounds

Modeling and control of dynamical systems rely on measured data, which contains information about the system. Finite data measurements typically lead to a set of system models that are unfalsified, i.e., that explain the data. The problem of data-informativity for stabilization or control with quadratic performance is concerned with the existence of a controller that stabilizes all unfalsified systems or achieves a desired quadratic performance. Recent results in the literature provide informativity conditions for control based on input-state data and ellipsoidal noise bounds, such as energy or magnitude bounds. In this paper, we consider informativity of input-state data for control where noise bounds are defined through the cross-covariance of the noise with respect to an instrumental variable; bounds that were introduced originally as a noise characterization in parameter bounding identification. The considered cross-covariance bounds are defined by a finite number of hyperplanes, which induce a (possibly unbounded) polyhedral set of unfalsified systems. We provide informativity conditions for input-state data with polyhedral cross-covariance bounds for stabilization and $\mathcal{H}_2$/$\mathcal{H}_\infty$ control through vertex/half-space representations of the polyhedral set of unfalsified systems.

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arXiv2021

Guaranteed $\mathcal{H}_\infty$ performance analysis and controller synthesis for interconnected linear systems from noisy input-state data

The increase in available data and complexity of dynamical systems has sparked the research on data-based system performance analysis and controller design. Recent approaches can guarantee performance and robust controller synthesis based on noisy input-state data of a single dynamical system. In this paper, we extend a recent data-based approach for guaranteed performance analysis to distributed analysis of interconnected linear systems. We present a new set of sufficient LMI conditions based on noisy input-state data that guarantees $\mathcal{H}_\infty$ performance and have a structure that lends itself well to distributed controller synthesis from data. Sufficient LMI conditions based on noisy data are provided for the existence of a dynamic distributed controller that achieves $\mathcal{H}_\infty$ performance. The presented approach enables scalable analysis and control of large-scale interconnected systems from noisy input-state data sets.

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arXiv2021

Scalable distributed and decentralized $\mathscr{H}_2$ controller synthesis for interconnected linear discrete-time systems

The current limitation in the synthesis of distributed $\mathscr{H}_2$ controllers for linear interconnected systems is scalability due to non-convex or unstructured synthesis conditions. In this paper we develop convex and structured conditions for the existence of a distributed $\mathscr{H}_2$ controller for discrete-time interconnected systems with an interconnection structure that corresponds to an arbitrary graph. Neutral interconnections and a storage function with a block-diagonal structure are utilized to attain coupling conditions that are of a considerably lower computational complexity compared to the corresponding centralized $\mathscr{H}_2$ controller synthesis problem. Additionally, the developed conditions are adapted for the corresponding decentralized $\mathscr{H}_2$ controller synthesis problem with fixed supply functions for the interconnections. The effectiveness and scalability of the developed distributed $\mathscr{H}_2$ controller synthesis method is demonstrated for small- to large-scale oscillator networks on a cycle graph.

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arXiv2020

Data-driven distributed control: Virtual reference feedback tuning in dynamic networks

In this paper, the problem of synthesizing a distributed controller from data is considered, with the objective to optimize a model-reference control criterion. We establish an explicit ideal distributed controller that solves the model-reference control problem for a structured reference model. On the basis of input-output data collected from the interconnected system, a virtual experiment setup is constructed which leads to a network identification problem. We formulate a prediction-error identification criterion that has the same global optimum as the model-reference criterion, when the controller class contains the ideal distributed controller. The developed distributed controller synthesis method is illustrated on an academic example network of nine subsystems and the influence of the controller interconnection structure on the achieved closed-loop performance is analyzed.

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arXiv2018

A recursive estimation approach to distributed identification of large-scale multi-input-single-output FIR systems

The problem of identifying single modules in multiple-input-single-output (MISO) systems is considered. A novel approach to distributed identification of MISO finite impulse response systems is presented. The distributed identification is discerned by the local estimation of local parameters, which correspond to a module in the MISO system. The local estimators are derived from the standard recursive least squares estimator and require limited information exchange. By Lyapunov's second method, sufficient conditions are derived for asymptotic convergence of the estimators to the true parameters in the absence of disturbances, which lead to asymptotic unbiasedness in the presence of additive output disturbances.

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