Robust Verification of Piecewise Affine Systems

Abstract

Piecewise affine systems is an important class of hybrid systems. They consist of several affine dynamic subsystems, between which switchings occur at different occasions. In this paper, a verification method for piecewise affine systems is considered, and a method to determine how sensitive the verified properties are to changes in the dynamics and the locations of the switching surfaces is proposed. This information can then be used for robustness analysis or control design.

Identification of piecewise affine systems via mixed-integer programming

“…The relations (9) and (10) can be transformed into mixed-integer linear inequalities, by using a slight modification of standard techniques described in [6] (see also [31]). By assuming that the bounds over θ i are all finite, Eq.…”

“…By imposing the constraints expressed by (31) and (32), the degrees of freedom for the integer variables, and hence the complexity, are reduced considerably. In fact, instead of having to test 2 MN different cases in the worst case, only…”

“…The key idea is to transform the Boolean variables into 0-1 integers, and to express the relations as mixed-integer linear inequalities, similarly to what was done in (11) and (31). The MLD model has the form …”

Parameter estimation of switching piecewise linear system

“…Thus the time series is generated by the combination of s functions ϕ T k θ(ν). This is not the only way to describe switching system and the reader should refer to [4], [10], [11], [12], [13], [14] for other formulations using mixture of models, endogenous switching, structural break models, self exciting threshold autoregressions (SETAR), model smooth transition autoregressive model (STAR), neural network [15] and, at last, hybrid systems [16].…”