The Informativity Approach: To Data-Driven Analysis and Control

Abstract

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.

Data transformation technique in the data informativity approach via algebraic sequences

“…In addition, the notion of data informativity has been proposed in recent years for formulating control problems and investigating system properties in the data-driven framework to show that the system exhibited by a model consistent with the data has desirable properties [13]. Since its proposal, this framework has been applied to various aspects of system control theory [2,14,15,16,17,18].…”