Direct data-driven recursive controller unfalsification with analytic update

Abstract

Unfalsified Control is a data-driven, plant-model-free controller design method, which recursively falsifies controllers that fail to meet the specified performance requirement. In Ellipsoidal Unfalsified Control, the region of controllers that are unfalsified, the Unfalsified set, is described by an ellipsoid. Due to the combination of the performance requirement and controller structure, the update of the Unfalsified set can be computed analytically, resulting in a computationally cheap algorithm. Conditions for stability of Ellipsoidal Unfalsified Control are presented, and the effectiveness of the proposed algorithm is shown in a simulation.

Data-Driven Controller Unfalsification With Analytic Update Applied to a Motion System

“…The main contribution of this paper, therefore, is contained in the argued design of and application in an experiment, rather then in the development of the theory of EUC. For the latter, the reader is referred to [6].…”

“…In [6], sufficient conditions are provided to guarantee the stability of this plant-model-free control design method, based on the results in [12]. It only needs the fundamental feasibility assumption, i.e., the assumption that in the initial candidate controller pool there is at least some region with control parameter sets that fulfill the performance requirement at all times.…”

“…This last case is employed in ellipsoidal unfalsified control (EUC) [6]. Here, by construction, the separation between control parameter sets that are falsified by new measurement data and control parameter sets that are unfalsified, is defined by two parallel half-spaces.…”

“…The performance requirement (2) guarantees that destabilizing behavior of a candidate controller results in its falsification. This property is needed for the guarantee of a stable adaptive control system, see Section II-A and [4] and [6].…”

“…In [6], the EUC approach is introduced. This section shows the approach of this data-driven, plant-model-free controller design method.…”