2005 Volume 18 Issue 10 Pages 343-351
This paper proposes a new framework for designing a feedback control system, called the data space approach, in which a set of experimental input and output data of a dynamical system is directly and solely used to design a stabilizing controller, without employing any, mathematical model such as a transfer function, state equation, or kernel representation. In this approach, the notions of open-loop and closed-loop data spaces are introduced, which respectively contain all the open-loop and closed-loop behaviors of a dynamical system and serve as the data space representations of the system dynamics. By using the geometrical relationship between the open-loop and closed-loop data spaces, a data-based stabilizability condition is derived as a nonlinear matrix inequality (NMI), and the parameters of a stabilizing controller is obtained as an orthogonal vector to its solution. To compute the solution, the NMI is converted to a linear matrix inequality with a rank constraint and a computational algorithm using LMI relaxation and linear approximation methods is applied.