The complete canonical piecewise-linear representation. I. The geometry of the domain space

General Dynamics of Pulsed Digital Oscillators

“…On the other hand, if , then (9) which means that (10) Therefore, the sequence generated through the detection of edges in belongs to , i.e., . And is an sequence generated by parameters and .…”

Identification of piecewise affine systems via mixed-integer programming

“…Then one algorithm which estimates the whole Wiener process is desirable. Here, we describe an algorithm based on mixed-integer programming, which identifies W-PWARX models of the form (28). Such PWA form is particularly useful when the identified system models an unknown part of a larger hybrid model.…”

“…On the other hand, in other fields there has been extensive research on identification of general nonlinear black-box models [13]. A few of these techniques lead to piecewise affine (PWA) models of nonlinear dynamical systems [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28], and thanks to the equivalence between PWA systems [1,29,30] and several classes of hybrid systems, they can be used to obtain hybrid models.…”

Identification of hybrid systems via mixed-integer programming

“…Otherwise, local search methods [16,17] are preferable, although they do not guarantee the best fit (i.e., a global minimum to the optimization problem). Figure 6 we compare the performance in terms of LP/QPs and total computation time of the linear criterion (14) versus the quadratic criterion (19). The reported numbers are computed on a Sun Ultra 60 (2 × 360 MHz) running Matlab 5.3 and the solver BARON [26], by averaging the result of ten estimation data sets generated by feeding random Gaussian inputs u(t) and zero output noise to system (15).…”

“…In parallel, the circuit and systems community developed piecewise linear techniques for the representation and the analysis of nonlinear electronic circuits, mostly based on Chua's canonical piecewise linear representation [18][19][20][21][22].…”