Perturbations in polyhedral partitions and the related fragility of piecewise affine control.

Rajesh Koduri (1) , Sorin Olaru (2) , Pedro Rodriguez-Ayerbe (1)

1 L2S - Laboratoire des signaux et systèmes
2 DISCO - Dynamical Interconnected Systems in COmplex Environments

The control design techniques for linear or hybrid systems under constraints lead often to off-line state-space partitions with non-overlapping convex polyhedral regions. This corresponds to a piecewise affine (PWA) state feedback control laws associated to polyhedral partition of the state-space. The aim of this paper is to consider perturbation in the representation of the vertices of such polyhedral regions. Another idea behind this study is to perform a quantization operation on the representation of the state-space regions and the associated PWA control laws in order to reduce the hardware requirements in terms of processor speed and memory unit. The quantized state-space partitions lose some of the important properties of the explicit controllers: non-overlapping, convexity and invariant characterization. The major contribution of this work is to analyze to what extend the non-overlapping and the invariance characteristics of the PWA controller can be preserved when perturbation takes place on the vertex representation.

Keywords: explicit predictive control; PWA control; Robustness Margin; Explicit MPC; Predictive Control; robustness; piecewise affine control

Domains: Automatic

Rajesh Koduri, Sorin Olaru, Pedro Rodriguez-Ayerbe. Perturbations in polyhedral partitions and the related fragility of piecewise affine control.. Bulletin mathématique de la Société des Sciences mathématiques de Roumanie, 2018, 61, pp.439 - 452. ⟨hal-01968898⟩