From Data to Reduced-Order Models Via Moment Matching

Burohman, Azka Muji; Besselink, Bart; Scherpen, Jacquelien M. A.; Camlibel, M. Kanat

doi:10.2139/ssrn.4305664

Cited by 2 publications

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“…The subset of R n n # consisting of all symmetric matrices is denoted by S n . For vectors x and y, we denote x y State feedback stabilization E-IS [68], [70], [71], and [72] Deadbeat controller E-IS [68] LQR E-IS [68] Suboptimal LQR E-IS [73] Suboptimal H2 E-IS [73] Synchronization E-IS [74] Robust MPC E-IS [75] Dynamic feedback stabilization E-ISO [68] Dynamic feedback stabilization E-IO [68] and [76] Dissipativity E-ISO [77] Tracking and regulation E-IS [78] Model reduction (moment matching) E-IO [79] Reachability (conic constraints) E-IO [80] Stability N-S [81] Stabilizability N-IS [81] State feedback stabilization N-IS [70], [72], and [82] Stabilization for switched system N-IS [83], [84], and [85] Control with input saturation N-IS [86] Control of positive systems N-IS [87] State feedback H2 control N-IS [72] and [82] Dynamic feedback H2 control N-IO [88] State feedback H3 control N-IS [72] and [82] Dynamic feedback H3 control N-IO [88] Stability N-IO [89] Dynamic feedback stabilization N-IO [88] and [89] Dissipativity N-ISO [77] Model reduction (balancing) N-ISO [90] Structural properties N-ISO [91] Absolute stabilization Luré systems N-ISO [72...…”

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confidence: 99%

The Informativity Approach: To Data-Driven Analysis and Control

Van Waarde,

Eising,

Camlibel

et al. 2023

IEEE Control Syst.

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Roughly speaking, systems and control theory deals with the problem of making a concrete physical system behave according to certain desired specifications. To achieve this desired behavior, the system can be interconnected with a physical device, called a controller. The problem of finding a mathematical description of such a controller is called the control design problem.To obtain a mathematical description of a controller for a to-be-controlled physical system, a possible first step is to obtain a mathematical model of the physical system. Such a mathematical model can take many forms. For example, the model could be in terms of ordinary or partial differential equations, difference equations, or transfer matrices.There are several ways to obtain a mathematical model for the physical system. The usual way is to apply the basic physical laws that are satisfied by the variables appearing in the system. This method is called first principles modeling. For example, for electromechanical systems, the set of basic physical laws that govern the behavior of the variables in the system (conservation laws, Newton's laws, and Kirchoff's laws) form a mathematical model.An alternative way to obtain a model is to do experiments on the physical system: certain external variables in the physical system are set to take particular values, while, at the same time, other variables are measured. In this way, one obtains data on the system that can be used to find mathematical descriptions of laws that are obeyed by the system variables, thus obtaining a model. This method is called system identification.The second step in a control system design problem is to decide which desired behavior we would like the physical system to have. Very often, this desired behavior can be formalized by requiring the mathematical model to have certain qualitative or quantitative mathematical properties. Together, these properties form the design objective.

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confidence: 99%

The Informativity Approach: To Data-Driven Analysis and Control

Van Waarde,

Eising,

Camlibel

et al. 2023

IEEE Control Syst.

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A tutorial on the informativity framework for data-driven control

Waarde

Eising

Camlibel

et al. 2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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The purpose of this paper is to provide a tutorial on the so-called informativity framework for direct data-driven control. This framework views data-driven analysis and design through the lens of robust control, and aims at assessing system properties and determining controllers for sets of systems unfalsified by the data. We will first introduce the informativity approach at an abstract level. Thereafter, we will study several case studies where we highlight the strength of the approach in the context of stabilizability analysis and stabilizing feedback design in different setups involving exact and noisy data, and for both input-state and input-output measurements. Finally, we provide an account of other applications of the data informativity framework.

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From Data to Reduced-Order Models Via Moment Matching

Cited by 2 publications

References 0 publications

The Informativity Approach: To Data-Driven Analysis and Control

The Informativity Approach: To Data-Driven Analysis and Control

A tutorial on the informativity framework for data-driven control

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